Introduction to Time Series Analysis

setwd("C:/Users/maiam/Dropbox/PROFESSIONAL DEVELOPMENT/DATA SCIENCE/01_R/TIME SERIES ANALYSIS/Introduction to Time Series Analysis")

Exploratory time series data analysis

# Print the Nile dataset
print(Nile)

## Time Series:
## Start = 1871 
## End = 1970 
## Frequency = 1 
##   [1] 1120 1160  963 1210 1160 1160  813 1230 1370 1140  995  935 1110  994
##  [15] 1020  960 1180  799  958 1140 1100 1210 1150 1250 1260 1220 1030 1100
##  [29]  774  840  874  694  940  833  701  916  692 1020 1050  969  831  726
##  [43]  456  824  702 1120 1100  832  764  821  768  845  864  862  698  845
##  [57]  744  796 1040  759  781  865  845  944  984  897  822 1010  771  676
##  [71]  649  846  812  742  801 1040  860  874  848  890  744  749  838 1050
##  [85]  918  986  797  923  975  815 1020  906  901 1170  912  746  919  718
##  [99]  714  740

# List the number of observations in the Nile dataset
length(Nile)

## [1] 100

# Display the first 10 elements of the Nile dataset
head(Nile, n=10)

##  [1] 1120 1160  963 1210 1160 1160  813 1230 1370 1140

# Display the last 12 elements of the Nile dataset
tail(Nile,n=12)

##  [1]  975  815 1020  906  901 1170  912  746  919  718  714  740

Basic time series plots

# Plot the Nile data
plot(Nile)

# Plot the Nile data with xlab and ylab arguments
plot(Nile, xlab = "Year", ylab = "River Volume (1e9 m^{3})")

# Plot the Nile data with xlab, ylab, main, and type arguments
plot(Nile, xlab = "Year", ylab = "River Volume (1e9 m^{3})",main = "Annual River Nile Volume at Aswan, 1871-1970", type ="b")

**Ploting Air Passagers

# Plot AirPassengers
plot(AirPassengers)

# View the start and end dates of AirPassengers
start(AirPassengers)

## [1] 1949    1

end(AirPassengers)

## [1] 1960   12

# Use time(), deltat(), frequency(), and cycle() with AirPassengers 

time(AirPassengers)

##           Jan      Feb      Mar      Apr      May      Jun      Jul
## 1949 1949.000 1949.083 1949.167 1949.250 1949.333 1949.417 1949.500
## 1950 1950.000 1950.083 1950.167 1950.250 1950.333 1950.417 1950.500
## 1951 1951.000 1951.083 1951.167 1951.250 1951.333 1951.417 1951.500
## 1952 1952.000 1952.083 1952.167 1952.250 1952.333 1952.417 1952.500
## 1953 1953.000 1953.083 1953.167 1953.250 1953.333 1953.417 1953.500
## 1954 1954.000 1954.083 1954.167 1954.250 1954.333 1954.417 1954.500
## 1955 1955.000 1955.083 1955.167 1955.250 1955.333 1955.417 1955.500
## 1956 1956.000 1956.083 1956.167 1956.250 1956.333 1956.417 1956.500
## 1957 1957.000 1957.083 1957.167 1957.250 1957.333 1957.417 1957.500
## 1958 1958.000 1958.083 1958.167 1958.250 1958.333 1958.417 1958.500
## 1959 1959.000 1959.083 1959.167 1959.250 1959.333 1959.417 1959.500
## 1960 1960.000 1960.083 1960.167 1960.250 1960.333 1960.417 1960.500
##           Aug      Sep      Oct      Nov      Dec
## 1949 1949.583 1949.667 1949.750 1949.833 1949.917
## 1950 1950.583 1950.667 1950.750 1950.833 1950.917
## 1951 1951.583 1951.667 1951.750 1951.833 1951.917
## 1952 1952.583 1952.667 1952.750 1952.833 1952.917
## 1953 1953.583 1953.667 1953.750 1953.833 1953.917
## 1954 1954.583 1954.667 1954.750 1954.833 1954.917
## 1955 1955.583 1955.667 1955.750 1955.833 1955.917
## 1956 1956.583 1956.667 1956.750 1956.833 1956.917
## 1957 1957.583 1957.667 1957.750 1957.833 1957.917
## 1958 1958.583 1958.667 1958.750 1958.833 1958.917
## 1959 1959.583 1959.667 1959.750 1959.833 1959.917
## 1960 1960.583 1960.667 1960.750 1960.833 1960.917

deltat(AirPassengers)

## [1] 0.08333333

frequency(AirPassengers)

## [1] 12

cycle(AirPassengers)

##      Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1949   1   2   3   4   5   6   7   8   9  10  11  12
## 1950   1   2   3   4   5   6   7   8   9  10  11  12
## 1951   1   2   3   4   5   6   7   8   9  10  11  12
## 1952   1   2   3   4   5   6   7   8   9  10  11  12
## 1953   1   2   3   4   5   6   7   8   9  10  11  12
## 1954   1   2   3   4   5   6   7   8   9  10  11  12
## 1955   1   2   3   4   5   6   7   8   9  10  11  12
## 1956   1   2   3   4   5   6   7   8   9  10  11  12
## 1957   1   2   3   4   5   6   7   8   9  10  11  12
## 1958   1   2   3   4   5   6   7   8   9  10  11  12
## 1959   1   2   3   4   5   6   7   8   9  10  11  12
## 1960   1   2   3   4   5   6   7   8   9  10  11  12

# Plot the AirPassengers data
plot(AirPassengers)

# Compute the mean of AirPassengers

mean(AirPassengers)

## [1] 280.2986

# Impute mean values to NA in AirPassengers
AirPassengers[85:96] <- mean(AirPassengers, na.rm =TRUE )

# Generate another plot of AirPassengers
plot(AirPassengers)

# Add the complete AirPassengers data to your plot
rm(AirPassengers)
points(AirPassengers, type = "l", col = 2, lty = 3)

Creating a time series object with ts()

data_vector<-read.csv("C:/Users/maiam/Dropbox/PROFESSIONAL DEVELOPMENT/DATA SCIENCE/01_R/TIME SERIES ANALYSIS/Introduction to Time Series Analysis/data.csv")
# Use print() and plot() to view data_vector
head(data_vector)

##   X2.0521941073
## 1  4.2928852797
## 2  3.3294132944
## 3  3.5085950670
## 4  0.0009576938
## 5  1.9217186345
## 6  0.7978134128

plot(data_vector)

# Convert data_vector to a ts object with start = 2004 and frequency = 4
time_series <- ts(data_vector,start=2004,frequency=4)

# Use print() and plot() to view time_series
print(time_series)

##               Qtr1          Qtr2          Qtr3          Qtr4
## 2004  4.2928852797  3.3294132944  3.5085950670  0.0009576938
## 2005  1.9217186345  0.7978134128  0.2999543435  0.9435687536
## 2006  0.5748283388 -0.0034005903  0.3448649176  2.2229761136
## 2007  0.1763144576  2.7097622770  1.2501948965 -0.4007164754
## 2008  0.8852732121 -1.5852420266 -2.2829278891 -2.5609531290
## 2009 -3.1259963754 -2.8660295895 -1.7847009207 -1.8894912908
## 2010 -2.7255351194 -2.1033141800 -0.0174256893 -0.3613204151
## 2011 -2.9008403327 -3.2847440927 -2.8684594718 -1.9505074437
## 2012 -4.8801892525 -3.2634605353 -1.6396062522 -3.3012575840
## 2013 -2.6331245433 -1.7058354022 -2.2119825061 -0.5170595186
## 2014  0.0752508095 -0.8406994716 -1.4022683487 -0.1382114230
## 2015 -1.4065954703 -2.3046941055  1.5073891432  0.7118679477
## 2016 -1.1300519022

plot(time_series)

####Testing whether an object is a time series

# Check whether data_vector and time_series are ts objects
is.ts(time_series)

## [1] TRUE

is.ts(data_vector)

## [1] FALSE

# Check whether Nile is a ts object
is.ts(Nile)

## [1] TRUE

# Check whether AirPassengers is a ts object

is.ts(AirPassengers)

## [1] TRUE

Plotting a time series object

# Check whether eu_stocks is a ts object
eu_stocks<-EuStockMarkets
is.ts(eu_stocks)

## [1] TRUE

# View the start, end, and frequency of eu_stocks
start(eu_stocks)

## [1] 1991  130

end(eu_stocks)

## [1] 1998  169

frequency(eu_stocks)

## [1] 260

# Generate a simple plot of eu_stocks
plot(eu_stocks)

# Use ts.plot with eu_stocks
ts.plot(eu_stocks, col = 1:4, xlab = "Year", ylab = "Index Value", main = "Major European Stock Indices, 1991-1998")

# Add a legend to your ts.plot
legend("topleft", colnames(eu_stocks), lty = 1, col = 1:4, bty = "n")

## Trend Spotting! ### Removing trends in variability via the logarithmic transformation

rapid_growth<-read.csv("rapid_growth.csv")
rapid_growth<-ts(rapid_growth)
is.ts(rapid_growth)

## [1] TRUE

# Log rapid_growth
linear_growth <-log(rapid_growth)
  
# Plot linear_growth using ts.plot()
 ts.plot(linear_growth)

##Removing trends in level by differencing

z<-read.csv("z.csv")
z<-ts(z)
# Generate the first difference of z
dz <- diff(z)
  length(z)

## [1] 198

# Plot dz
ts.plot(dz)

# View the length of z and dz, respectively
length(z)

## [1] 198

length(dz)

## [1] 197

Removing seasonal trends with seasonal differencing

x<-read.csv("x.csv")
# # Generate a diff of x with lag = 4. Save this to dx
dx<-ts(x)
dx <- diff(dx,lag=4)
length(dx)

## [1] 95

# # Plot dx
ts.plot(dx)

# # View the length of x and dx, respectively 
length(x)

## [1] 1

length(dx)

## [1] 95

Simulate the white noise model

# Simulate a WN model with list(order = c(0, 0, 0))
white_noise <- arima.sim(model = list(order = c(0, 0, 0)), n = 100)

# Plot your white_noise data
ts.plot(white_noise)

# Simulate from the WN model with: mean = 100, sd = 10
white_noise_2 <- arima.sim(model = list(order = c(0, 0, 0)), n = 100, mean =100, sd = 10)

# Plot your white_noise_2 data
ts.plot(white_noise_2)

Estimate the white noise model

y<-read.csv("y.csv")
y<-ts(y)

# # Fit the WN model to y using the arima command
arima(y,order=c(0,0,0))

## 
## Call:
## arima(x = y, order = c(0, 0, 0))
## 
## Coefficients:
##       intercept
##         97.4194
## s.e.     0.9716
## 
## sigma^2 estimated as 93.46:  log likelihood = -365.08,  aic = 734.16

# # Calculate the sample mean and sample variance of y
mean(y)

## [1] 97.41942

var(y)

##            X109.76134
## X109.76134   94.41217

3. Correlation analysis and the autocorrelation function

# Plot eu_stocks
plot(eu_stocks)

# Use this code to convert prices to returns
returns <- eu_stocks[-1,] / eu_stocks[-1860,] - 1

# Convert returns to ts
returns <- ts(returns, start = c(1991, 130), frequency =260)

# Plot returns

plot(returns)

# Use this code to convert prices to log returns
logreturns <- diff(log(eu_stocks))

# Plot logreturns
plot(logreturns)

Characteristics of financial time series

# Generate means from eu_percentreturns
eu_percentreturns<-returns*100
colMeans(eu_percentreturns) 

##        DAX        SMI        CAC       FTSE 
## 0.07052174 0.08609470 0.04979471 0.04637479

# Use apply to calculate sample variance from eu_percentreturns
apply(eu_percentreturns, MARGIN = 2, FUN = var)

##       DAX       SMI       CAC      FTSE 
## 1.0569648 0.8523711 1.2159091 0.6344767

# Use apply to calculate standard deviation from eu_percentreturns
apply(eu_percentreturns, MARGIN = 2, FUN = sd)

##       DAX       SMI       CAC      FTSE 
## 1.0280879 0.9232394 1.1026827 0.7965405

# Display a histogram of percent returns for each index
par(mfrow = c(2,2))
apply(eu_percentreturns, MARGIN = 2, FUN = hist, main = "", xlab = "Percentage Return")

## $DAX
## $breaks
##  [1] -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6
## 
## $counts
##  [1]   1   0   0   0   1   1   8  40 157 683 700 218  34  13   2   1
## 
## $density
##  [1] 0.0005379236 0.0000000000 0.0000000000 0.0000000000 0.0005379236
##  [6] 0.0005379236 0.0043033889 0.0215169446 0.0844540075 0.3674018289
## [11] 0.3765465304 0.1172673480 0.0182894029 0.0069930070 0.0010758472
## [16] 0.0005379236
## 
## $mids
##  [1] -9.5 -8.5 -7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5  0.5  1.5  2.5  3.5
## [15]  4.5  5.5
## 
## $xname
## [1] "newX[, i]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## $SMI
## $breaks
##  [1] -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6
## 
## $counts
##  [1]   1   0   0   0   2   6  35 127 676 782 194  27   8   0   1
## 
## $density
##  [1] 0.0005379236 0.0000000000 0.0000000000 0.0000000000 0.0010758472
##  [6] 0.0032275417 0.0188273265 0.0683162991 0.3636363636 0.4206562668
## [11] 0.1043571813 0.0145239376 0.0043033889 0.0000000000 0.0005379236
## 
## $mids
##  [1] -8.5 -7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5  0.5  1.5  2.5  3.5  4.5
## [15]  5.5
## 
## $xname
## [1] "newX[, i]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## $CAC
## $breaks
##  [1] -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7
## 
## $counts
##  [1]   1   0   0   2   9  50 206 677 579 264  60   7   3   0   1
## 
## $density
##  [1] 0.0005379236 0.0000000000 0.0000000000 0.0010758472 0.0048413125
##  [6] 0.0268961807 0.1108122647 0.3641742873 0.3114577730 0.1420118343
## [11] 0.0322754169 0.0037654653 0.0016137708 0.0000000000 0.0005379236
## 
## $mids
##  [1] -7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5  0.5  1.5  2.5  3.5  4.5  5.5
## [15]  6.5
## 
## $xname
## [1] "newX[, i]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## $FTSE
## $breaks
##  [1] -5 -4 -3 -2 -1  0  1  2  3  4  5  6
## 
## $counts
##  [1]   1   2  18 128 771 763 158  13   3   1   1
## 
## $density
##  [1] 0.0005379236 0.0010758472 0.0096826251 0.0688542227 0.4147391070
##  [6] 0.4104357181 0.0849919311 0.0069930070 0.0016137708 0.0005379236
## [11] 0.0005379236
## 
## $mids
##  [1] -4.5 -3.5 -2.5 -1.5 -0.5  0.5  1.5  2.5  3.5  4.5  5.5
## 
## $xname
## [1] "newX[, i]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"

# Display normal quantile plots of percent returns for each index
par(mfrow = c(2,2))
apply(eu_percentreturns, MARGIN = 2, FUN = qqnorm, main = "")

## $DAX
## $DAX$x
##    [1] -1.142221353 -0.641422863  0.955292497 -0.359523002 -0.673220713
##    [6]  1.276662700  0.611885927 -0.459261681  0.673220713  0.082343808
##   [11] -0.800629988 -0.738970862 -0.746076339  0.180306035  0.152960705
##   [16]  0.266038199 -0.897309997 -0.691943891 -0.749643230  0.004045135
##   [21]  0.716130610  0.128447917  0.035064922 -0.214680871  0.198151791
##   [26] -0.787692121  1.171176839 -0.257665760  0.170720874 -0.616771139
##   [31]  1.462421997 -0.178935732  0.243751421 -0.187162683 -3.461124681
##   [36]  1.486410698  3.461124681  1.223643862  0.919719798  0.987715314
##   [41] -0.573311845  0.278632114  0.031017587 -0.270231385  0.217441306
##   [46]  0.239586428 -0.695374126 -0.181676676 -0.345175621 -0.685107711
##   [51] -1.016679169  0.147505990  0.216060883  0.047210641 -0.332323535
##   [56]  0.291270379 -1.109190438  0.203655249 -0.753219684  0.089110513
##   [61]  0.629871114 -0.302543521 -0.903376738 -0.303955341 -0.661428091
##   [66]  0.236812077 -0.287052552 -0.150232789 -0.343744832 -1.203927669
##   [71] -0.628227740 -1.121749883 -0.039112832  0.055311546  0.098590829
##   [76]  0.915611117 -1.181953091 -0.744296449  0.200902759  0.350905885
##   [81]  0.451782750  0.881291064 -1.307735956 -0.199527087  0.483370478
##   [86]  0.638113687 -0.355211147 -0.586072510 -0.663107092 -0.457763852
##   [91]  0.683403669 -0.441354429  0.551201681  1.719464344 -0.489441280
##   [96]  1.206715600 -0.755011527  0.767623099 -0.158419976 -1.454609861
##  [101] -1.209512942 -0.148869251  0.901350805 -0.392810584 -0.780357962
##  [106]  0.838359300 -1.065359478 -0.296902233 -1.258595595 -1.490492928
##  [111] -0.185790660  0.362401286  0.163883972 -0.322365390  0.296902233
##  [116] -0.959557224 -0.462260438  0.433934970  0.468270477 -0.515448120
##  [121]  0.747858595  0.509298081 -0.934224165 -1.070128233 -0.378286384
##  [126] -0.147505990 -0.146143003 -0.144780288  1.384457552  0.867457786
##  [131] -0.143417841 -0.142055660  1.327002669  0.391354480 -0.010787206
##  [136] -0.921779971 -0.974623251  1.163183043  0.965987242  0.441354429
##  [141]  0.595705916  2.018186777 -0.029668592  0.326629195  0.998756101
##  [146]  0.076933172 -0.600543374 -0.712649943 -0.319526110  1.091895656
##  [151] -0.235425586 -1.074921450  0.756805798  0.125729300 -0.151596606
##  [156] -0.598929332  0.448798263 -0.311023602  0.140693743 -0.353775332
##  [161] -0.444329005  0.372499146 -0.420639577 -0.451782750  0.771248856
##  [166]  0.513908791 -0.557490953  1.273622589 -0.155689761  1.147414556
##  [171] -0.996538226  1.528404858  0.064767230  0.049910572  0.106723840
##  [176]  0.871393127 -0.253486340 -0.051260673 -1.101738030  0.416224367
##  [181] -0.170720874 -0.989913817 -1.134488812  0.639767399 -0.875342009
##  [186]  0.602158982 -0.356647694 -0.411817256  0.316689404 -1.179246182
##  [191]  0.080990929  0.136609547 -0.211922070 -1.330262031  0.981148261
##  [196]  0.195402322 -0.907439769  1.023485109 -0.607015276  1.323757343
##  [201] -0.247920647 -1.443055487  0.586072510  0.587674282 -0.394267521
##  [206]  0.260454538  0.607015276  0.108080014 -0.140693743 -0.139332087
##  [211] -0.017529767  0.342314746 -0.659750952 -0.018878365 -0.342314746
##  [216] -0.867457786 -0.184418986 -0.360961770 -0.137970689  0.165250729
##  [221]  0.110792961  0.728382008  0.422113133 -0.423587607  0.112149739
##  [226] -0.338028671 -0.294085140 -0.821236508 -1.111688306  2.253834800
##  [231]  0.155689761  1.124283082 -0.271630167  1.217962298  0.465263357
##  [236] -0.936312283 -0.560643862 -0.136609547  0.813703281 -0.658075667
##  [241]  0.102656486 -1.025764317  0.301132303 -0.313855244 -0.135248658
##  [246] -0.414754435  0.264641513 -0.767623099  0.438383752 -1.003206657
##  [251]  0.507763585 -0.643080086 -0.133888019  0.109436387 -0.498581510
##  [256]  0.053961158 -0.778530978  0.062065052 -0.877321577  0.154325089
##  [261] -0.221585076  0.289863864 -0.154325089  0.994325241 -0.552771947
##  [266] -0.352340246 -1.051196457  0.480341759 -0.785854621 -1.273622589
##  [271]  0.231268816 -0.261849685 -0.358084978 -1.775306882 -2.328168205
##  [276]  0.041811790 -1.243847553 -1.067740821 -0.811827184  0.271630167
##  [281] -0.195402322  1.285854591 -1.152638890 -1.060614828 -0.384086320
##  [286]  0.281436703  1.000978901 -0.615141105 -0.565383709 -1.932851955
##  [291] -1.323757343 -1.084582727  0.002696752  0.785854621 -0.523163215
##  [296] -1.577947245 -0.563802354 -1.327002669  1.380950295 -2.501345446
##  [301] -1.524083329  0.817464095  2.348932362  0.232653959  0.712649943
##  [306] -1.104215353 -0.222967175  1.830063448 -0.815582246  0.254878985
##  [311] -0.309608718 -1.053542290  0.210543276  0.187162683  3.153406194
##  [316] -1.470324418  0.976793633 -1.195619501  1.336823495 -2.039299773
##  [321] -0.796919854 -1.131926322 -0.610260769 -1.701989181 -1.882932462
##  [326]  0.169352865 -1.139636266  1.058251433 -0.849912281 -3.001150261
##  [331]  1.356861648  0.972457450  0.857677680 -0.823127102  0.268833132
##  [336]  1.988111548 -1.387981923 -0.163883972  0.309608718  1.466361761
##  [341]  1.657768635 -0.776706588  1.014420963  1.229365201  0.359523002
##  [346]  0.137970689 -1.815858073 -1.184668689 -0.428016575 -0.705714361
##  [351]  0.012135669 -1.077327344  1.016679169  0.174826828  1.402254840
##  [356]  0.469775625 -0.540247501  2.061362980 -0.188535059 -0.001348375
##  [361]  0.538687927 -0.132527628 -0.646399844  0.305367768 -1.641991740
##  [366]  0.181676676 -1.087013912  0.668155360  0.463761374  1.070128233
##  [371]  0.070173025 -1.395082856  0.135248658 -0.463761374 -0.644739077
##  [376] -1.058251433 -0.335174740 -1.647205232 -0.433934970  0.051260673
##  [381]  0.066118496 -0.320945426 -0.513908791  1.532755121  1.450736862
##  [386]  0.224349699  0.435416939 -0.131167483 -0.129807580  1.340125919
##  [391] -0.280034133 -0.690231824 -0.128447917 -0.127088491 -0.180306035
##  [396]  1.096803562 -0.363841553 -1.044193418 -0.825020643 -0.649726742
##  [401]  0.819348844 -1.611610156  1.168503942  1.837306881  1.631696630
##  [406] -0.791375125 -0.048560562  0.540247501  0.847978932 -1.498732738
##  [411]  0.274429329 -1.094346314  0.735432089  0.045860805  1.094346314
##  [416] -0.579680379  1.370529139  0.658075667  1.668520329  0.162517520
##  [421] -0.680001523  0.221585076  1.048856395 -0.795068896  1.502891083
##  [426] -1.507075579  0.299721685  0.927984105  0.780357962 -0.405953507
##  [431] -1.424215576 -0.490961795  0.578086050  1.150022800  0.709177888
##  [436]  0.626586061 -0.869423773 -0.471281838 -0.006741924  1.005439403
##  [441]  0.600543374  0.116221323 -0.516988672 -1.367088290  1.012167918
##  [446] -0.453276503 -0.844121708  0.428016575 -0.802489192 -1.749812815
##  [451] -0.381184749  0.859627120 -0.382635132  0.238199023  0.510833777
##  [456]  0.723118123 -0.806215951 -0.595705916 -1.007677172  0.039112832
##  [461]  0.597316848 -1.012167918  0.209164881 -0.125729300 -0.124370342
##  [466]  0.851848813  0.189907790 -0.172089202  0.234039548  0.541808390
##  [471] -0.611885927 -1.034934930  0.855731495 -1.541543733 -0.981148261
##  [476] -0.613512703 -0.527807233 -0.976793633  0.544934137  0.333748798
##  [481] -0.965987242  0.590882359 -0.917663521 -0.840277002  0.574901790
##  [486] -0.365282575  1.258595595  0.166617795 -0.397183912 -0.295493393
##  [491] -0.911517835 -1.009919999 -0.123011613  0.484886501 -0.510833777
##  [496]  0.946814739 -0.543370600  1.046522062 -0.549632774 -0.121653111
##  [501] -0.266038199  0.158419976  0.093172475  0.524709963  1.360254733
##  [506]  0.044511053  1.106699472 -0.120294834  0.392810584 -0.016181201
##  [511] -0.284243507  0.335174740 -0.726625143  0.358084978  0.631516191
##  [516]  0.016181201 -0.629871114  0.029668592  0.460760541  0.806215951
##  [521] -0.764007406 -0.306780804 -0.330898947 -0.220203400 -0.329475030
##  [526]  0.676607229  1.907298228  2.649174982 -0.165250729  0.610260769
##  [531] -0.299721685  0.537129662 -0.678303399  1.270594204  0.330898947
##  [536] -0.683403669 -0.454771268  0.430973886  0.074228709  1.550453053
##  [541] -0.957422684 -0.972457450 -0.697092314 -0.176196131 -0.445817767
##  [546]  2.084477779  0.194028142  0.548065218  0.462260438 -0.671530349
##  [551] -0.484886501  1.587382521  0.787692121  0.506230285 -0.970296201
##  [556]  0.849912281  0.633162979  0.420639577 -1.564052364 -1.055893934
##  [561]  0.798773547  0.444329005 -1.450736862  1.065359478  1.111688306
##  [566]  0.083696837 -0.618402813  0.259059897 -0.620036135 -0.702259280
##  [571] -1.713581019 -0.656402227 -0.045860805 -0.288457923  0.346607117
##  [576] -0.447307518 -1.099267451  0.560643862  1.235127068  1.932851955
##  [581] -0.192654329 -1.370529139  0.104012078 -0.846048746  1.304571699
##  [586]  0.017529767 -0.526257967  0.020226997  0.566966480  0.815582246
##  [591]  1.915677702  1.101738030 -0.277230642  1.240930235 -0.500108919
##  [596] -0.426539323 -0.398643373 -0.388444757  1.391523619  0.475806917
##  [601]  0.228499859 -0.524709963  0.942601281  1.685018832 -1.270594204
##  [606] -0.826917147 -0.571723349  0.651392890  0.582873468  0.139332087
##  [611]  0.911517835 -0.161151372 -1.511286632 -1.978474507 -0.483370478
##  [616]  1.606688823 -1.223643862  0.043161383  0.013484154  1.243847553
##  [621]  1.181953091 -0.118936778  0.282839826 -0.366724356 -2.220892296
##  [626]  0.410349998  0.445817767  1.109190438 -0.828816630  0.355211147
##  [631] -0.009438762  1.737480953  0.512370678  1.353484113 -0.703985770
##  [636]  0.474297479  1.756079872 -0.021575667 -0.213301268 -0.243751421
##  [641] -1.685018832  0.021575667  0.717874200  0.535572701  1.519790077
##  [646] -0.379735168  1.203927669  0.873365866 -0.117578942  1.701989181
##  [651] -1.462421997 -0.506230285  1.198379702 -0.116221323  0.903376738
##  [656] -1.295156428 -0.953166636 -0.808083534  0.177565765 -0.049910572
##  [661]  0.105367863 -1.959733938 -1.795213515  0.436899865 -1.679468436
##  [666]  0.737200322  0.060714135 -1.663120450 -1.363663552  1.577947245
##  [671] -1.014420963  1.749812815 -0.422113133  1.537134586  1.626613277
##  [676] -0.709177888  0.056662036 -2.028630245  0.338028671 -2.096465896
##  [681]  0.206409282  0.846048746  0.121653111 -0.742518914 -0.503167245
##  [686]  1.367088290  0.207786884  1.288942818 -1.466361761 -1.391523619
##  [691]  0.263245342  1.279714656 -2.289421602 -0.546499008  1.343443023
##  [696] -2.061362980 -1.830063448  1.295156428  1.554954248  2.308361815
##  [701] -0.492483445 -0.530909576  0.323786003 -1.264572142  2.471677151
##  [706]  0.466766389 -0.719619975 -0.538687927 -1.144814095 -0.666470718
##  [711]  0.554343576  1.053542290 -1.072521761 -0.173457852  1.165839367
##  [716] -0.401564849 -0.735432089 -0.605394926 -0.114863917 -0.113506724
##  [721]  1.568650389  0.384086320  0.853788545 -0.026970760  1.037241217
##  [726] -0.836444677  0.159785525 -0.998756101  0.653060847  0.311023602
##  [731] -1.304571699 -0.044511053 -0.035064922  1.142221353 -0.621671114
##  [736]  1.470324418  0.733666152 -1.062984162  0.693657988  0.663107092
##  [741] -0.395725296 -1.096803562  0.378286384 -0.951045074 -0.895295078
##  [746]  1.079739490  0.315272007 -0.112149739  0.442841227  0.730141123
##  [751] -0.389899206 -0.832624598 -0.562222407 -0.478829051 -0.110792961
##  [756] -2.108763102 -2.121387721  0.429494761 -1.626613277  0.844121708
##  [761]  0.381184749 -1.320525901  0.328051780  1.775306882  0.213301268
##  [766] -1.573281819  0.603776164 -0.817464095  0.615141105 -2.370761549
##  [771]  0.173457852 -0.961696145 -1.409499686 -0.985521574 -2.072781954
##  [776] -1.582647271  2.175591776  1.373986290 -1.486410698 -0.403026872
##  [781]  1.152638890  1.055893934 -1.252663668  1.030338792  1.089451538
##  [786] -1.458504802 -0.346607117  0.923844064 -0.227116039  1.126823516
##  [791] -1.220798154  0.099945863  0.996538226  1.559487170  0.674913004
##  [796]  0.641422863 -0.608637221  0.267435404  1.072521761 -0.369610210
##  [801]  0.938404491 -1.416819278 -0.250702523  0.885274487  0.459261681
##  [806]  1.478319741 -0.312439110 -0.873365866  0.594096529 -0.468270477
##  [811] -1.212319781  0.275829715 -0.681701610 -1.246775496 -0.024273125
##  [816]  0.905406385  0.685107711 -0.932140112 -0.537129662 -1.532755121
##  [821]  0.401564849  0.589277562  1.007677172  1.663120450  1.195619501
##  [826] -0.648062397  0.006741924 -1.173858130  0.562222407 -1.285854591
##  [831] -0.942601281  0.477317439  0.515448120 -1.238023440 -0.040462274
##  [836]  0.014832664 -1.768825039  0.555916576 -1.601806100  0.114863917
##  [841] -1.890930113  0.425063002  0.270231385  1.232241021 -1.837306881
##  [846] -0.207786884  0.691943891 -2.271268723 -0.915611117 -0.109436387
##  [851] -0.909476911 -1.997936847  1.021211206  0.654730623  2.697177092
##  [856]  1.859635855 -0.948927784  1.652463885  0.529357768 -1.288942818
##  [861] -1.405868039 -0.889272006 -0.568550673 -1.616570833  0.318107437
##  [866] -1.474310299  0.719619975  0.877321577  1.844648016 -0.336601363
##  [871]  0.218822145 -1.427943123  1.121749883  0.423587607 -1.413150018
##  [876]  0.678303399  1.636822499  0.369610210 -1.360254733  0.875342009
##  [881]  1.074921450 -0.108080014 -1.168503942 -0.289863864  0.395725296
##  [886] -1.340125919 -1.668520329  0.970296201 -0.298311662 -0.430973886
##  [891] -0.938404491  1.084582727 -0.789532284 -0.333748798  1.261578236
##  [896] -1.201149064 -0.323786003 -0.275829715 -1.082157935 -1.229365201
##  [901]  0.832624598  1.139636266  0.688521779  0.821236508 -0.340885359
##  [906]  0.695374126  0.776706588  0.340885359 -0.224349699 -0.106723840
##  [911]  0.498581510 -0.859627120 -1.282778578  1.157894875 -1.091895656
##  [916] -0.714389194  0.172089202 -1.240930235  0.349472246 -0.407418129
##  [921]  0.450290005 -0.167985173 -0.268833132  0.211922070  1.215136204
##  [926] -0.509298081  0.188535059 -0.466766389 -1.494600149 -1.808890648
##  [931]  0.762203300 -0.194028142  0.721367945 -0.728382008 -0.372499146
##  [936] -0.256272124  1.176547886 -0.634811485  1.890930113  0.368166900
##  [941]  0.413285400 -0.419166933  1.427943123  0.492483445 -0.594096529
##  [946]  0.472789121  0.356647694 -1.301420449  0.365282575 -1.041870422
##  [951] -0.159785525 -0.429494761  1.431690617 -0.603776164 -0.773065541
##  [956] -0.581276182  1.395082856 -0.721367945 -1.261578236 -1.356861648
##  [961] -1.502891083 -0.809953940 -1.907298228  1.044193418 -1.725407795
##  [966]  2.190197016 -1.482353090  1.114193130 -1.781864184  0.277230642
##  [971] -0.202278813 -0.486403639 -2.050206632 -0.008090336 -0.548065218
##  [976] -1.106699472  0.404489757  1.582647271 -1.756079872  1.129371243
##  [981]  1.564052364  0.373944779  0.178935732  0.071524788  0.068821391
##  [986] -0.246530430  0.628227740 -0.597316848 -0.105367863 -0.104012078
##  [991] -1.545983054 -0.774884781  0.620036135  1.601806100 -0.636461719
##  [996]  1.435458325  1.099267451 -0.385538318 -0.487921897 -0.102656486
## [1001]  0.963839475  0.036414159 -0.371054291 -0.857677680  0.501637496
## [1006]  1.039553035  0.707445064  1.131926322  0.825020643 -0.716130610
## [1011]  0.865495146 -1.176547886 -0.417695198 -1.147414556  1.545983054
## [1016] -0.855731495  1.134488812 -0.101301081 -1.859635855  0.142055660
## [1021]  0.621671114  0.934224165  0.968139475  0.671530349 -0.099945863
## [1026]  1.067740821 -1.039553035 -0.031017587 -1.519790077  1.028048865
## [1031] -0.350905885 -0.025621919  0.280034133 -0.438383752  1.363663552
## [1036] -0.861579831  0.202278813 -0.098590829 -0.097235975 -0.529357768
## [1041] -0.582873468 -1.737480953  0.127088491 -0.439868605  0.546499008
## [1046]  0.534017037  0.379735168 -0.469775625  2.205284963  1.018942572
## [1051]  0.478829051  0.284243507 -0.474297479 -0.285647748  0.494006236
## [1056] -1.028048865  0.563802354 -0.762203300  0.624946069  1.592153635
## [1061] -0.043161383  0.245140689  0.033715750 -1.165839367  0.192654329
## [1066] -0.731902501  1.679468436 -0.885274487  0.040462274  0.376838394
## [1071] -0.521617717 -0.879304589  0.686813744 -0.555916576 -1.119223863
## [1076]  1.310913362  0.702259280  0.059363328  0.559066713  0.133888019
## [1081] -0.676607229  0.132527628 -0.578086050  0.120294834 -0.978968627
## [1086] -0.651392890  0.989913817 -0.987715314  0.414754435  0.957422684
## [1091]  0.123011613 -0.162517520 -0.318107437  0.124370342  0.018878365
## [1096] -0.264641513  1.498732738 -0.177565765  0.227116039 -0.930060100
## [1101]  0.800629988 -0.765814001 -1.032634134 -2.606596640  0.419166933
## [1106]  0.907439769 -1.802009946 -0.480341759  0.836444677 -0.375391193
## [1111] -0.095881300  0.700534881 -1.126823516 -0.925912101 -1.089451538
## [1116] -1.157894875  0.834533115  0.298311662  2.050206632 -0.782187555
## [1121] -0.570136293  0.584472241 -1.190126255 -1.431690617 -1.559487170
## [1126] -0.259059897  1.264572142  0.052610867 -1.550453053  1.731412828
## [1131]  0.791375125  0.809953940 -0.240974293 -0.717874200 -0.216060883
## [1136]  0.261849685  0.481855566 -0.238199023 -0.534017037  0.978968627
## [1141]  0.058012629 -0.189907790  0.086403358 -0.301132303  0.360961770
## [1146] -0.260454538 -0.512370678  0.091818320  0.649726742  1.641991740
## [1151] -0.400103684  0.322365390  0.229884118  0.549632774 -0.413285400
## [1156]  0.389899206  0.246530430 -0.847978932  0.811827184 -0.094526801
## [1161] -0.005393524  0.184418986  0.097235975 -0.273029480 -1.867289179
## [1166]  0.005393524  1.238023440 -0.037763461  0.581276182 -0.093172475
## [1171] -0.091818320 -0.169352865 -0.460760541 -0.804351175 -0.090464333
## [1176]  1.978474507  0.842197799  0.294085140 -0.963839475  0.961696145
## [1181]  0.661428091 -0.688521779 -0.587674282  1.032634134  0.336601363
## [1186]  0.823127102 -0.339456669  0.618402813  0.489441280 -0.554343576
## [1191]  0.008090336  1.762416670 -0.036414159  0.552771947 -0.710912844
## [1196]  0.808083534  0.287052552  0.417695198 -0.740743723 -1.731412828
## [1201]  0.921779971  0.161151372 -1.420507713  1.025764317 -0.432453954
## [1206]  0.325207270 -0.520073465 -0.217441306 -0.292677470 -1.592153635
## [1211] -0.830719108  1.249714166  0.887271474  1.192868378 -0.639767399
## [1216]  0.453276503  1.515524656 -0.236812077  0.113506724 -0.249311344
## [1221] -0.798773547 -0.209164881  0.345175621 -1.398659855 -1.373986290
## [1226] -0.362401286  0.028319650  0.680001523  1.119223863  0.623307755
## [1231]  0.527807233  0.285647748  0.576493189 -1.232241021  1.405868039
## [1236] -0.541808390  0.753219684 -1.046522062 -0.771248856  0.486403639
## [1241]  0.312439110 -0.968139475  0.398643373 -0.089110513 -0.087756855
## [1246]  0.516988672  0.616771139 -0.923844064  0.782187555  0.592488679
## [1251]  0.257665760 -1.276662700  0.146143003  0.495530174  0.557490953
## [1256] -0.157054722 -1.163183043  0.579680379  0.000000000 -1.478319741
## [1261] -0.758602509 -0.086403358 -1.292043388  0.288457923 -0.002696752
## [1266]  0.101301081 -0.623307755  0.150232789  1.201149064 -0.278632114
## [1271]  1.298282071  0.242362624 -0.085050020  0.742518914 -0.592488679
## [1276]  0.917663521 -0.819348844 -0.252094188  0.079638199 -0.083696837
## [1281]  0.408883624 -0.602158982 -0.724870519 -0.686813744  0.840277002
## [1286]  0.252094188 -0.028319650  0.329475030 -1.116704964  0.703985770
## [1291]  0.746076339 -0.210543276 -0.326629195 -1.048856395  0.167985173
## [1296]  0.144780288 -0.497055264 -0.769434713  0.646399844  0.598929332
## [1301]  0.664787965 -0.416224367 -1.018942572  0.765814001  0.078285614
## [1306] -0.495530174 -0.013484154  0.521617717 -0.576493189 -0.456267049
## [1311] -0.022924375  0.447307518 -0.624946069 -0.733666152 -0.992117116
## [1316] -1.988111548  0.925912101  0.332323535 -0.465263357 -1.384457552
## [1321]  0.869423773 -1.380950295  0.214680871  0.185790660  0.072876682
## [1326] -0.391354480  1.060614828  0.543370600  0.681701610 -0.041811790
## [1331]  0.295493393  0.571723349 -0.435416939 -0.231268816 -0.328051780
## [1336]  0.690231824 -0.196776871 -0.239586428  1.051196457 -0.664787965
## [1341]  0.225732653 -1.279714656  1.041870422  0.067469881 -0.475806917
## [1346]  0.386991129 -0.442841227 -0.481855566 -0.793220658  0.118936778
## [1351] -0.566966480 -0.267435404  0.250702523  0.432453954  0.273029480
## [1356]  0.795068896 -0.152960705  0.802489192  1.082157935  0.634811485
## [1361] -0.325207270 -0.376838394  0.131167483  0.643080086 -0.887271474
## [1366]  0.769434713  0.784019770  0.026970760 -0.373944779 -0.349472246
## [1371] -0.203655249  1.212319781 -0.082343808  0.744296449 -0.014832664
## [1376] -0.263245342 -0.863535834 -0.229884118  0.363841553  0.320945426
## [1381]  0.698812562 -0.730141123  0.490961795  0.397183912  0.220203400
## [1386] -0.631516191 -1.652463885  0.075580872  0.352340246  0.500108919
## [1391] -1.235127068 -0.589277562  0.247920647 -0.206409282  0.339456669
## [1396]  1.387981923  0.740743723 -0.590882359  0.313855244 -0.232653959
## [1401]  1.267577427  0.235425586  0.532462664  0.613512703 -1.336823495
## [1406]  0.497055264 -0.784019770 -0.183047659  0.117578942  1.179246182
## [1411]  0.302543521 -0.751430255  1.307735956  0.714389194  0.129807580
## [1416]  1.616570833 -0.919719798  0.503167245 -2.007958893  1.333535586
## [1421]  0.751430255 -1.844648016  0.403026872 -1.298282071  0.951045074
## [1426] -1.353484113  0.191280879  0.405953507  0.411817256  0.319526110
## [1431] -0.080990929 -0.079638199 -0.078285614  0.565383709  0.764007406
## [1436] -0.076933172 -0.075580872 -1.950615992  1.490492928  0.985521574
## [1441] -0.693657988  1.009919999  1.184668689 -0.940500815  1.398659855
## [1446]  0.789532284 -0.242362624  0.697092314  0.385538318 -0.425063002
## [1451]  0.001348375  0.913562563  0.375391193 -1.762416670  0.353775332
## [1456]  1.246775496 -1.217962298  0.726625143  0.666470718  0.936312283
## [1461]  0.048560562  1.507075579  0.343744832  1.220798154  0.828816630
## [1466]  0.157054722  0.644739077  1.420507713 -0.408883624  0.366724356
## [1471] -1.124283082 -0.901350805 -0.559066713  0.196776871 -0.955292497
## [1476]  1.611610156  0.388444757  0.891276104 -0.535572701 -0.234039548
## [1481]  2.289421602  0.959557224  0.656402227  0.710912844  0.205032071
## [1486]  0.087756855 -1.528404858 -0.626586061  1.144814095 -1.899050574
## [1491] -1.537134586  0.526257967 -1.743613740  1.301420449  0.456267049
## [1496]  2.134359789  1.852089931 -1.129371243 -0.074228709 -0.072876682
## [1501] -2.897169268 -2.018186777  0.009438762  0.738970862  2.606596640
## [1506] -0.633162979  1.160534902 -0.544934137 -1.206715600 -0.883281024
## [1511]  2.121387721 -0.865495146  0.454771268 -0.174826828 -1.187393051
## [1516]  0.648062397  0.568550673  0.930060100 -1.350121948  0.487921897
## [1521]  1.541543733  0.382635132 -0.071524788  1.511286632  2.039299773
## [1526] -0.698812562 -0.494006236 -0.070173025 -0.291270379  1.647205232
## [1531] -1.155262893  0.863535834 -0.893283788  0.090464333 -0.068821391
## [1536] -1.596961269  2.161436385 -0.927984105  1.314104058  1.320525901
## [1541] -0.274429329 -1.255624109  0.240974293 -1.915677702  0.992117116
## [1546]  1.596961269 -0.281436703  0.953166636  0.457763852 -1.079739490
## [1551]  0.025621919 -0.032366639  1.725407795  0.439868605 -0.228499859
## [1556] -1.005439403  0.249311344  1.282778578  0.308194453 -1.249714166
## [1561]  0.348039324  1.524083329 -0.033715750 -0.436899865 -1.333535586
## [1566]  1.743613740  0.899328566  1.815858073  0.151596606  1.424215576
## [1571]  0.705714361 -0.245140689 -0.881291064  1.788499010  1.621571613
## [1576] -0.225732653  1.959733938 -0.674913004 -1.719464344  0.176196131
## [1581]  2.752336985  1.950615992 -1.568650389  1.173858130  0.760401672
## [1586] -0.737200322  1.808890648 -1.377459942 -1.636822499 -1.021211206
## [1591]  0.573311845  0.932140112  1.454609861 -1.875053466 -0.386991129
## [1596]  1.087013912 -2.697177092 -1.198379702 -2.444036983  0.032366639
## [1601]  2.328168205  1.458504802 -1.314104058 -2.308361815 -0.507763585
## [1606] -1.924193887 -0.200902759 -2.134359789  0.608637221  2.007958893
## [1611]  2.444036983 -1.657768635  0.826917147 -0.700534881  1.413150018
## [1616] -0.871393127 -1.822914780 -2.752336985 -2.147701284  1.875053466
## [1621]  2.533393817 -0.853788545  0.883281024 -0.747858595  2.370761549
## [1626] -0.305367768  1.439246522 -1.317308188  0.773065541 -0.654730623
## [1631]  0.974623251  2.271268723  0.037763461 -0.067469881  1.409499686
## [1636] -0.532462664 -1.226499513 -1.941657387 -0.551201681  1.446885503
## [1641] -0.410349998 -1.310913362 -0.653060847 -2.161436385  0.530909576
## [1646]  2.237060137 -1.343443023 -2.817407051  0.094526801 -2.393782545
## [1651] -3.153406194  3.001150261 -1.606688823  0.095881300  2.220892296
## [1656] -1.673969302  1.482353090 -0.946814739 -2.237060137  0.371054291
## [1661]  0.143417841 -1.215136204  0.085050020 -0.913562563  2.817407051
## [1666]  0.749643230  0.895295078  1.416819278  0.256272124 -2.418146732
## [1671]  0.504698173  1.924193887  0.940500815  0.253486340  2.897169268
## [1676] -0.944705914 -0.760401672  1.997936847  0.830719108  0.426539323
## [1681] -0.723118123 -1.707756416 -2.175591776  1.187393051 -1.037241217
## [1686]  2.393782545  0.063416084  0.183047659 -2.253834800  1.673969302
## [1691]  0.148869251 -0.066118496 -0.064767230 -0.063416084  2.501345446
## [1696] -1.192868378 -0.062065052 -0.060714135  2.568276871  1.252663668
## [1701] -1.435458325 -0.669841901 -1.267577427 -1.439246522 -2.190197016
## [1706]  0.400103684 -0.282839826 -0.308194453  1.781864184  1.696278006
## [1711]  0.523163215 -1.515524656 -0.448798263 -0.584472241  1.104215353
## [1716]  1.209512942  1.573281819  1.346774976 -0.205032071  1.899050574
## [1721] -0.166617795 -0.638113687 -0.501637496  0.983332566 -0.574901790
## [1726]  0.909476911 -0.316689404 -1.160534902  0.303955341  0.306780804
## [1731]  1.941657387 -0.518530452 -0.899328566 -0.004045135  0.636461719
## [1736] -0.315272007  2.108763102 -0.368166900 -0.198151791  1.822914780
## [1741] -0.668155360 -1.554954248 -0.477317439  1.802009946  1.377459942
## [1746]  0.520073465  0.199527087 -0.707445064  0.731902501  0.724870519
## [1751]  0.861579831 -0.983332566  0.879304589  1.882932462 -0.838359300
## [1756]  1.062984162  1.034934930 -1.690621630  0.804351175  0.010787206
## [1761]  0.570136293  0.793220658  0.893283788  1.443055487  1.690621630
## [1766] -0.905406385 -1.023485109  0.897309997 -0.059363328 -0.058012629
## [1771]  1.116704964 -0.348039324 -1.402254840  0.669841901  1.494600149
## [1776] -0.851848813 -1.346774976 -1.150022800 -2.084477779 -2.348932362
## [1781]  2.096465896 -0.756805798  2.418146732 -0.056662036  1.795213515
## [1786] -1.969017784  0.774884781 -1.852089931  1.969017784  1.474310299
## [1791] -1.000978901  1.255624109 -0.012135669  0.796919854 -1.446885503
## [1796]  1.768825039  1.350121948 -0.055311546  0.292677470  1.190126255
## [1801]  0.889272006 -2.533393817  0.778530978  0.948927784 -0.053961158
## [1806]  0.518530452  1.077327344 -0.842197799  2.028630245  1.155262893
## [1811] -0.404489757  0.471281838 -0.052610867 -2.471677151 -1.114193130
## [1816]  0.758602509  2.072781954 -1.137058773 -1.030338792  0.024273125
## [1821]  1.713581019  0.659750952  1.707756416 -0.450290005  1.137058773
## [1826] -1.631696630  1.226499513 -0.254878985  1.003206657 -0.504698173
## [1831]  0.605394926  0.755011527 -0.472789121 -0.047210641  0.394267521
## [1836]  1.317308188  0.022924375 -0.020226997  0.944705914  0.407418129
## [1841] -0.191280879 -1.696278006 -0.834533115 -0.218822145 -2.568276871
## [1846]  0.222967175 -0.891276104  1.330262031 -0.994325241 -1.587382521
## [1851] -1.171176839 -1.788499010 -1.621571613  1.292043388 -2.205284963
## [1856] -2.649174982  1.867289179 -0.813703281  2.147701284
## 
## $DAX$y
##    [1] -0.928319263 -0.441241177  0.904445039 -0.177663722 -0.466579325
##    [6]  1.250457901  0.577648321 -0.286555662  0.637125719  0.118476933
##   [11] -0.575905428 -0.513931700 -0.517813648  0.200432935  0.177874614
##   [16]  0.267874148 -0.662381510 -0.478663689 -0.524971799  0.049845790
##   [21]  0.680056049  0.162061522  0.074106553 -0.050601978  0.209919305
##   [26] -0.560049782  1.108440005 -0.091919087  0.190140888 -0.423638022
##   [31]  1.468138084 -0.022418400  0.245445620 -0.030832290 -9.178761490
##   [36]  1.495518771  5.207048574  1.174819942  0.874581662  0.942151184
##   [41] -0.380727559  0.276459616  0.072105480 -0.101117132  0.220622106
##   [46]  0.241303401 -0.480238430 -0.027886393 -0.162513871 -0.471328527
##   [51] -0.784182101  0.174683233  0.219815306  0.087610739 -0.151807303
##   [56]  0.283845338 -0.888250397  0.211562540 -0.527481997  0.123133659
##   [61]  0.598225101 -0.123479543 -0.675979062 -0.123854347 -0.454489087
##   [66]  0.239805166 -0.114334004  0.000000000 -0.161121756 -0.982621862
##   [71] -0.431056182 -0.902500837  0.010841906  0.098841955  0.129323251
##   [76]  0.869736725 -0.971357567 -0.517194158  0.210642235  0.329674542
##   [81]  0.424111976  0.842739379 -1.104829937 -0.041329671  0.452906041
##   [86]  0.604107169 -0.171205932 -0.393440142 -0.455129544 -0.285518066
##   [91]  0.645371120 -0.270559685  0.515902766  1.777429427 -0.311766386
##   [96]  1.163746916 -0.528377180  0.731770737 -0.006760577 -1.307338181
##  [101] -0.996450146  0.000000000  0.852991130 -0.218928932 -0.555711830
##  [106]  0.794538803 -0.850639227 -0.122023323 -1.061766336 -1.352589971
##  [111] -0.029035817  0.341431301  0.184607468 -0.141892239  0.286116594
##  [116] -0.725752680 -0.287386014  0.402852350  0.439940395 -0.337180401
##  [121]  0.715952004  0.472841979 -0.701785669 -0.858740685 -0.200534327
##  [126]  0.000000000  0.000000000  0.000000000  1.393597231  0.830419301
##  [131]  0.000000000  0.000000000  1.326984771  0.366664790  0.039899006
##  [136] -0.687983349 -0.751105952  1.103889535  0.917993421  0.410826486
##  [141]  0.559103953  2.098176753  0.023441726  0.312483099  0.949505478
##  [146]  0.114530543 -0.411364081 -0.493414200 -0.138769260  1.029637261
##  [151] -0.071144417 -0.860273745  0.721120759  0.156857153 -0.002372901
##  [156] -0.408741976  0.421737343 -0.126938933  0.171050834 -0.169572925
##  [161] -0.272609029  0.350774801 -0.250440645 -0.276057377  0.733219184
##  [166]  0.479134833 -0.371931272  1.248935062 -0.003506004  1.085146293
##  [171] -0.764801776  1.557120638  0.103822504  0.091108603  0.144839589
##  [176]  0.832909352 -0.090143209  0.001134900 -0.880672307  0.385282550
##  [181] -0.016538352 -0.760319642 -0.917304642  0.609076987 -0.650938066
##  [186]  0.568152142 -0.174849387 -0.239899647  0.299002167 -0.966549194
##  [191]  0.118424660  0.166647244 -0.049445627 -1.127336007  0.937110028
##  [196]  0.209358744 -0.678557919  0.977330388 -0.417205823  1.316878183
##  [201] -0.078790876 -1.303089081  0.552260653  0.552707280 -0.219752332
##  [206]  0.260121621  0.570206289  0.145039700  0.000000000  0.000000000
##  [211]  0.033774501  0.322180066 -0.452341566  0.031515554 -0.160392274
##  [216] -0.644894774 -0.028873695 -0.178490971  0.000000000  0.185175541
##  [221]  0.146133808  0.689806324  0.388937896 -0.253342235  0.147014238
##  [226] -0.159364825 -0.121287709 -0.598582877 -0.888586675  2.539071585
##  [231]  0.179746993  1.055038602 -0.103058138  1.169570970  0.438368007
##  [236] -0.707376692 -0.372879284  0.000000000  0.756358768 -0.450076397
##  [241]  0.132908471 -0.801390632  0.288883042 -0.128394786  0.000000000
##  [246] -0.242586848  0.265589367 -0.542624829  0.406239114 -0.767780097
##  [251]  0.472014662 -0.441732805  0.000000000  0.146018323 -0.316380873
##  [256]  0.094311918 -0.555182550  0.102124762 -0.652931675  0.179709384
##  [261] -0.058656705  0.282059318 -0.003409285  0.946676971 -0.367013791
##  [266] -0.169493441 -0.831361985  0.449697253 -0.559605038 -1.078659902
##  [271]  0.235064455 -0.096225317 -0.176486873 -1.809588740 -2.750873807
##  [276]  0.083499222 -1.044683179 -0.855322243 -0.582323254  0.273962414
##  [281] -0.037087861  1.263928567 -0.941610386 -0.845148564 -0.210134971
##  [286]  0.280354617  0.952404620 -0.422784841 -0.377610363 -2.047817564
##  [291] -1.112131480 -0.865895132  0.049099731  0.744529035 -0.346118347
##  [296] -1.472252952 -0.374052628 -1.121129123  1.391622433 -2.945040293
##  [301] -1.410129498  0.756815093  2.780131651  0.235469488  0.676453750
##  [306] -0.884331065 -0.060008968  1.871292551 -0.593954232  0.256724354
##  [311] -0.126733651 -0.838154239  0.214590866  0.202999149  4.659521631
##  [316] -1.324383391  0.936536965 -0.979255089  1.337157401 -2.161078102
##  [321] -0.574074074 -0.916500215 -0.417439102 -1.668944868 -1.961394357
##  [326]  0.189057615 -0.925982087  0.999258549 -0.631069923 -4.952521672
##  [331]  1.365574682  0.922975188  0.816249712 -0.599452403  0.272667200
##  [336]  2.085920212 -1.202060286 -0.011004505  0.290963619  1.479403575
##  [341]  1.709933157 -0.554857830  0.966228768  1.181998676  0.337506377
##  [346]  0.168185552 -1.848887153 -0.971363025 -0.258446376 -0.486010418
##  [351]  0.060710720 -0.860895007  0.970372033  0.193286819  1.406188034
##  [356]  0.440134427 -0.358351977  2.148572034 -0.031771144  0.044753177
##  [361]  0.505030859  0.000000000 -0.445083760  0.289625948 -1.564761216
##  [366]  0.200837479 -0.868551366  0.634324907  0.437945661  1.008701109
##  [371]  0.110023817 -1.208931873  0.165562914 -0.287459576 -0.443570844
##  [376] -0.844367810 -0.155975177 -1.572159809 -0.266774727  0.092774429
##  [381]  0.104866481 -0.139900785 -0.335690840  1.562553053  1.460952126
##  [386]  0.229332103  0.403042875  0.000000000  0.000000000  1.339174623
##  [391] -0.109207695 -0.478063423  0.000000000  0.000000000 -0.025350520
##  [396]  1.039634860 -0.184037631 -0.825183571 -0.602585854 -0.447321954
##  [401]  0.757426458 -1.539324158  1.107814962  1.873718818  1.669538161
##  [406] -0.561495805  0.005087085  0.505503310  0.804104666 -1.385131955
##  [411]  0.274298661 -0.876497058  0.697921602  0.086476588  1.034916521
##  [416] -0.389227393  1.374247226  0.627058802  1.723412418  0.183717294
##  [421] -0.469380939  0.224510713  0.990382274 -0.568390725  1.533061759
##  [426] -1.392894031  0.287599903  0.878437528  0.742115028 -0.231093685
##  [431] -1.269493453 -0.311804546  0.546910921  1.086668753  0.675587195
##  [436]  0.596557820 -0.645328130 -0.296957077  0.040938379  0.956024079
##  [441]  0.566302643  0.150124715 -0.340044795 -1.165247418  0.965808828
##  [446] -0.279757192 -0.621662314  0.394742293 -0.578290242 -1.777572232
##  [451] -0.204637237  0.817807888 -0.206993376  0.239888894  0.475030889
##  [456]  0.684105589 -0.581036854 -0.405524677 -0.777226893  0.078452198
##  [461]  0.559588992 -0.781943345  0.213344615  0.000000000  0.000000000
##  [466]  0.808742378  0.204003494 -0.016716917  0.237658763  0.505763560
##  [471] -0.419645080 -0.807709248  0.811285996 -1.427372456 -0.754817244
##  [476] -0.422261839 -0.348896180 -0.752967723  0.508464105  0.317795959
##  [481] -0.740196078  0.553113734 -0.683905506 -0.620618888  0.544255769
##  [486] -0.184973244  1.210442155  0.185549207 -0.224324886 -0.121297516
##  [491] -0.681440409 -0.779368353  0.000000000  0.456854056 -0.334576637
##  [496]  0.899551157 -0.361664767  0.989376569 -0.365544521  0.000000000
##  [501] -0.099556910  0.180857412  0.124652294  0.485109410  1.367739415
##  [506]  0.084292664  1.047356643  0.000000000  0.366734338  0.034997182
##  [511] -0.110884467  0.318182088 -0.500612451  0.337204946  0.599831668
##  [516]  0.063042787 -0.433955709  0.070965605  0.434947050  0.753742233
##  [521] -0.541951610 -0.124482546 -0.151093813 -0.057113922 -0.150819788
##  [526]  0.639002142  1.982810173  3.400441511 -0.015011425  0.577192553
##  [531] -0.122737375  0.504284481 -0.468707831  1.230687503  0.313224297
##  [536] -0.470821595 -0.283062772  0.398071686  0.113752577  1.577616204
##  [541] -0.724392172 -0.748637610 -0.480296911 -0.018098059 -0.272617069
##  [546]  2.159397173  0.207821855  0.514716154  0.435107975 -0.463027026
##  [551] -0.306377791  1.611683499  0.745819610  0.471527592 -0.743081520
##  [556]  0.804333207  0.601433225  0.387506540 -1.457345299 -0.840520966
##  [561]  0.748357522  0.416218908 -1.305602973  1.002866845  1.048420038
##  [566]  0.120234665 -0.424974636  0.257840482 -0.425172273 -0.483225111
##  [571] -1.694267849 -0.449762345  0.007485350 -0.116548870  0.326503522
##  [576] -0.273690500 -0.879497125  0.529466054  1.183816345  2.017329294
##  [581] -0.033286697 -1.171145392  0.136875243 -0.628765496  1.281359447
##  [586]  0.063205182 -0.346625879  0.066004180  0.535537605  0.756589567
##  [591]  1.987607171  1.045884112 -0.107317122  1.192801024 -0.318994300
##  [596] -0.257306100 -0.225037548 -0.212542509  1.398752099  0.444332414
##  [601]  0.230286628 -0.346600030  0.895623858  1.736774005 -1.076971809
##  [606] -0.603052620 -0.379743746  0.621763181  0.551211009  0.170945966
##  [611]  0.864873750 -0.008627301 -1.395825944 -2.112196782 -0.305415539
##  [616]  1.655790785 -1.010907808  0.084153833  0.061825790  1.193241921
##  [621]  1.122020320  0.000000000  0.281136332 -0.185935385 -2.498395371
##  [626]  0.377655467  0.417161820  1.048393037 -0.609874623  0.334433443
##  [631]  0.040446569  1.795004189  0.478043038  1.359202957 -0.483484471
##  [636]  0.442868542  1.812549650  0.029086544 -0.049848148 -0.077118448
##  [641] -1.652625206  0.068136856  0.681374206  0.500459415  1.550984796
##  [646] -0.201080350  1.162662906  0.835607943  0.000000000  1.753881928
##  [651] -1.314245379 -0.325895990  1.151317265  0.000000000  0.857095983
##  [656] -1.088973103 -0.721825900 -0.581122040  0.194539387  0.002247242
##  [661]  0.139325843 -2.066334545 -1.818923403  0.405158773 -1.649891913
##  [666]  0.699105674  0.101861197 -1.601860709 -1.163765989  1.608050378
##  [671] -0.783470714  1.811764031 -0.251331824  1.568306088  1.668822828
##  [676] -0.488917267  0.099455515 -2.150591790  0.319127033 -2.275759131
##  [681]  0.212876651  0.803021571  0.154032971 -0.515169671 -0.324359698
##  [686]  1.369217814  0.213074515  1.266362253 -1.315272235 -1.208613539
##  [691]  0.264698348  1.258965576 -2.679593505 -0.363435595  1.344846362
##  [696] -2.189003632 -1.871961890  1.276075078  1.580376140  2.665690788
##  [701] -0.311896141 -0.350981195  0.306891847 -1.064716099  3.211871221
##  [706]  0.438370056 -0.495660674 -0.353303107 -0.928510264 -0.459729302
##  [711]  0.523339044  0.992669375 -0.859932685 -0.016788226  1.106343284
##  [716] -0.226043954 -0.507670541 -0.416387836  0.000000000  0.000000000
##  [721]  1.596449638  0.358276415  0.809194056  0.027694920  0.983578282
##  [726] -0.613973976  0.180898068 -0.765171385  0.622316035  0.291601866
##  [731] -1.103512940  0.009116227  0.014584634  1.080928359 -0.426034543
##  [736]  1.479616785  0.696898312 -0.848922011  0.656442431  0.630851805
##  [741] -0.221024211 -0.878096661  0.353725718 -0.721403871 -0.661726847
##  [746]  1.017230267  0.298035996  0.000000000  0.414142223  0.692410946
##  [751] -0.213378150 -0.612845056 -0.373523319 -0.303679329  0.000000000
##  [756] -2.276046575 -2.305748146  0.394842718 -1.547064306  0.802726240
##  [761]  0.355908647 -1.109790674  0.312733604  1.822915438  0.218168680
##  [766] -1.469317200  0.569002721 -0.596567985  0.583725142 -2.759869004
##  [771]  0.192859405 -0.729252456 -1.250235143 -0.756609958 -2.233487548
##  [776] -1.477029027  2.444969036  1.376107894 -1.350540216 -0.228919689
##  [781]  1.088238823  0.998887378 -1.057553428  0.981765099  1.029553729
##  [786] -1.312509094 -0.162682342  0.874796316 -0.061978430  1.056240020
##  [791] -1.009442077  0.130822964  0.948689823  1.585446538  0.637972180
##  [796]  0.609364372 -0.417398327  0.272516820  1.009991771 -0.187130801
##  [801]  0.891237332 -1.266109498 -0.084740605  0.846719022  0.432582625
##  [806]  1.486467731 -0.127642310 -0.646786834  0.558194665 -0.296508148
##  [811] -0.997103999  0.275391565 -0.470803273 -1.046695512  0.028119640
##  [816]  0.857876440  0.646180289 -0.697880511 -0.353251776 -1.421281439
##  [821]  0.372864193  0.552975840  0.961096682  1.722792875  1.147641264
##  [826] -0.446807358  0.057574961 -0.965524741  0.530702998 -1.082197890
##  [831] -0.714482886  0.445305296  0.480698258 -1.033928653  0.010669982
##  [836]  0.062157611 -1.807013884  0.528286209 -1.498572341  0.147798517
##  [841] -1.970912380  0.389481097  0.272836777  1.182935242 -1.883346922
##  [846] -0.045679186  0.654872161 -2.621766263 -0.683504623  0.000000000
##  [851] -0.680717175 -2.121015553  0.972006021  0.623788421  3.584521179
##  [856]  1.911098528 -0.719927576  1.707933690  0.495237372 -1.082831411
##  [861] -1.240706630 -0.659070923 -0.378902108 -1.540414520  0.299514034
##  [866] -1.324506585  0.681413934  0.842021449  1.899455677 -0.158848542
##  [871]  0.223129832 -1.271428433  1.052007196  0.389061643 -1.260758001
##  [876]  0.639162140  1.673831430  0.347238830 -1.161560313  0.837645334
##  [881]  1.012414875  0.000000000 -0.959658367 -0.117594195  0.369469916
##  [886] -1.140091551 -1.603248943  0.918604936 -0.122401993 -0.265043015
##  [891] -0.710935138  1.023454995 -0.560989364 -0.154482435  1.218186625
##  [896] -0.980524946 -0.144114041 -0.107140760 -0.864901927 -1.015220903
##  [901]  0.773092971  1.080168191  0.651170539  0.762816238 -0.159911107
##  [906]  0.656637262  0.737443274  0.322118826 -0.060411464  0.000000000
##  [911]  0.465973022 -0.636260701 -1.080416146  1.100410666 -0.873416575
##  [916] -0.493942353  0.192370899 -1.034299773  0.328546499 -0.232727626
##  [921]  0.422224495 -0.015518312 -0.100884681  0.216538491  1.168040927
##  [926] -0.328504729  0.203229573 -0.288643185 -1.381996538 -1.844592025
##  [931]  0.727261889 -0.034522383  0.681805848 -0.501276466 -0.191080293
##  [936] -0.091775712  1.117136338 -0.438596491  1.936756179  0.343609536
##  [941]  0.380321139 -0.249879360  1.437890966  0.460855605 -0.404218917
##  [946]  0.442198059  0.336413996 -1.097172078  0.342319820 -0.816782979
##  [951] -0.007611871 -0.264532643  1.439706907 -0.416188559 -0.544959128
##  [956] -0.389354479  1.399528088 -0.496894994 -1.062060624 -1.156072124
##  [961] -1.386023817 -0.581993475 -1.979915048  0.987834305 -1.727854245
##  [966]  2.449674289 -1.348825711  1.049007127 -1.816829105  0.276329615
##  [971] -0.042317594 -0.306428445 -2.173330570  0.040825186 -0.364177347
##  [976] -0.887589303  0.374012659  1.610860672 -1.798682915  1.058657015
##  [981]  1.587629718  0.351532294  0.199230453  0.110800801  0.106129751
##  [986] -0.078250817  0.597192890 -0.406312152  0.000000000  0.000000000
##  [991] -1.430667830 -0.549467416  0.589028129  1.655475035 -0.439201087
##  [996]  1.445196238  1.043550163 -0.210498294 -0.311226380  0.000000000
## [1001]  0.917763076  0.074638959 -0.188420944 -0.635646339  0.466549906
## [1006]  0.985398764  0.670515834  1.065679783  0.766388198 -0.494672755
## [1011]  0.829827916 -0.965695756 -0.248445421 -0.930031673  1.571870065
## [1016] -0.635232513  1.071728540  0.000000000 -1.907516098  0.171853745
## [1021]  0.589582749  0.888318776  0.918593300  0.636077084  0.000000000
## [1026]  1.005757905 -0.810056774  0.022932345 -1.406038714  0.979042882
## [1031] -0.166369802  0.027774509  0.279550460 -0.268446297  1.367961375
## [1036] -0.639237186  0.211179428  0.000000000  0.000000000 -0.350602365
## [1041] -0.391604596 -1.770323017  0.161621958 -0.269253538  0.509324857
## [1046]  0.497694887  0.355428339 -0.296557944  2.463826462  0.971632222
## [1051]  0.446806660  0.281202288 -0.299956370 -0.112594132  0.461380491
## [1056] -0.801777083  0.531206067 -0.537053992  0.596284898  1.615267648
## [1061]  0.009408518  0.246390381  0.072841674 -0.957862961  0.207402464
## [1066] -0.506184449  1.733853097 -0.655227596  0.081436869  0.352307885
## [1071] -0.341715080 -0.653138956  0.649783106 -0.370184914 -0.898835060
## [1076]  1.282370574  0.666598114  0.101703647  0.529297716  0.165058741
## [1081] -0.468364470  0.163348783 -0.386712984  0.152179989 -0.754427778
## [1086] -0.448152265  0.942935160 -0.758228579  0.381787014  0.906026503
## [1091]  0.154214610 -0.008823906 -0.136782608  0.154643503  0.065732297
## [1096] -0.096549778  1.529078978 -0.018689801  0.229971004 -0.697872119
## [1101]  0.749948679 -0.542342608 -0.803347645 -3.132195525  0.386946345
## [1106]  0.860834083 -1.842277399 -0.303984664  0.779676226 -0.193524647
## [1111]  0.000000000  0.664084369 -0.907035630 -0.693119907 -0.870264434
## [1116] -0.945578263  0.774446540  0.286502350  2.147490659 -0.555729315
## [1121] -0.379697792  0.551356199 -0.977443267 -1.285332868 -1.455225965
## [1126] -0.093534764  1.222764412  0.093425638 -1.434145067  1.785029427
## [1131]  0.746612334  0.754931294 -0.074240070 -0.495301515 -0.051620278
## [1136]  0.262846023  0.449806142 -0.072342666 -0.352353068  0.936646465
## [1141]  0.099765392 -0.031856699  0.120638794 -0.122766893  0.337796312
## [1146] -0.095734593 -0.334710931  0.124400213  0.621683369  1.675772981
## [1151] -0.225091972  0.304960966  0.231136793  0.514867292 -0.241776084
## [1156]  0.365312152  0.246767783 -0.629467151  0.755544939  0.000000000
## [1161]  0.041269702  0.202752519  0.129201230 -0.103665018 -1.909065434
## [1166]  0.053119309  1.188526967  0.012345298  0.549297948  0.000000000
## [1171]  0.000000000 -0.016222307 -0.286786760 -0.580940235  0.000000000
## [1176]  2.079453618  0.800797331  0.285016637 -0.735164887  0.911187307
## [1181]  0.629504100 -0.474596742 -0.398665134  0.982848416  0.318196687
## [1186]  0.764383538 -0.159702114  0.588896419  0.458650329 -0.368244341
## [1191]  0.057698579  1.820217958  0.013953412  0.520717926 -0.490262113
## [1196]  0.754399639  0.281341482  0.386926512 -0.514452807 -1.746882889
## [1201]  0.874695884  0.182528159 -1.266771207  0.977818693 -0.266111446
## [1206]  0.308821168 -0.341530896 -0.051899480 -0.119925325 -1.485393629
## [1211] -0.611073882  1.204377563  0.846938903  1.139174130 -0.440494464
## [1216]  0.424811275  1.545880307 -0.071171515  0.147675420 -0.081161982
## [1221] -0.575431372 -0.046106806  0.323705784 -1.233372859 -1.187520418
## [1226] -0.183079034  0.070798952  0.639635912  1.049965878  0.591944670
## [1231]  0.493013286  0.281317160  0.545404197 -1.017035748  1.409768372
## [1236] -0.358676634  0.719536432 -0.826924372 -0.542961477  0.457950871
## [1241]  0.294311706 -0.741195562  0.370754202  0.000000000  0.000000000
## [1246]  0.482641321  0.588654657 -0.691719559  0.742388721  0.556052463
## [1251]  0.257006679 -1.079565975  0.173028232  0.462724528  0.528814682
## [1256] -0.005884037 -0.952485564  0.548153546  0.047268659 -1.335102446
## [1261] -0.532328799  0.000000000 -1.088809811  0.281485628  0.044086182
## [1266]  0.132200265 -0.427165807  0.176789487  1.151556119 -0.107642196
## [1271]  1.276674158  0.245233763  0.000000000  0.705886995 -0.403950962
## [1276]  0.870974595 -0.597865935 -0.087884839  0.117021068  0.000000000
## [1281]  0.377324448 -0.414981537 -0.500288402 -0.472044105  0.799584755
## [1286]  0.252752566  0.023917629  0.313206822 -0.898390790  0.667578854
## [1291]  0.710547756 -0.046672630 -0.146698315 -0.827315841  0.189005462
## [1296]  0.172960847 -0.316351620 -0.542803727  0.614480574  0.565590436
## [1301]  0.631100738 -0.244341364 -0.787695466  0.730464770  0.116711536
## [1306] -0.315530962  0.038981492  0.483961470 -0.385847352 -0.283401913
## [1311]  0.028498815  0.419945048 -0.429459775 -0.506645329 -0.763837942
## [1316] -2.115833169  0.876824530  0.315091144 -0.287760022 -1.201993316
## [1321]  0.830524405 -1.192934804  0.218776559  0.202880086  0.110953185
## [1326] -0.218829002  0.999659483  0.508127634  0.642930164  0.010316396
## [1331]  0.286052084  0.541197042 -0.266781039 -0.065887329 -0.150811699
## [1336]  0.652791067 -0.040854006 -0.073095681  0.991446269 -0.456003988
## [1341]  0.229633252 -1.080355331  0.985622070  0.105492651 -0.300532372
## [1346]  0.358985601 -0.271104194 -0.305087928 -0.563001208  0.151904328
## [1351] -0.378593884 -0.100841134  0.252159387  0.402361256  0.274113751
## [1356]  0.747535994 -0.002725040  0.752910032  1.022395326  0.602027156
## [1361] -0.144853702 -0.199129617  0.162520983  0.610940559 -0.655688056
## [1366]  0.733181413  0.744490092  0.069843416 -0.191372478 -0.164294361
## [1371] -0.043306508  1.166014904  0.000000000  0.706068991  0.035499676
## [1376] -0.096480495 -0.642714423 -0.063681696  0.341715359  0.302299931
## [1381]  0.662759226 -0.502808297  0.459878894  0.370193192  0.224009738
## [1386] -0.436409662 -1.574360519  0.113853126  0.329985011  0.466034139
## [1391] -1.029471060 -0.402915343  0.250682999 -0.045294602  0.319827428
## [1396]  1.397303946  0.703934967 -0.403249393  0.295127099 -0.067708772
## [1401]  1.229105932  0.239146165  0.497363397  0.582174193 -1.139755767
## [1406]  0.464481269 -0.555807215 -0.028560273  0.151159553  1.121153145
## [1411]  0.289232000 -0.525524991  1.282097170  0.677108366  0.162171270
## [1416]  1.657636694 -0.684992898  0.469993648 -2.138590327  1.333436892
## [1421]  0.719436993 -1.888306612  0.373013299 -1.094859744  0.901707171
## [1426] -1.149530473  0.204023500  0.376657203  0.379137860  0.301529867
## [1431]  0.000000000  0.000000000  0.000000000  0.531980352  0.729219857
## [1436]  0.000000000  0.000000000 -2.057588878  1.504886894  0.940885564
## [1441] -0.479551588  0.964420062  1.122902950 -0.711004566  1.405098412
## [1446]  0.746081886 -0.076539861  0.657134410  0.358797378 -0.255415099
## [1451]  0.049013234  0.865476262  0.351876510 -1.799307275  0.332592377
## [1456]  1.193630850 -1.001231726  0.688136894  0.633410412  0.888830365
## [1461]  0.090710347  1.540352341  0.322660391  1.170642413  0.770554445
## [1466]  0.179865148  0.612887559  1.427899633 -0.236116996  0.342549020
## [1471] -0.903904549 -0.674439695 -0.372385511  0.209565574 -0.722893823
## [1476]  1.657218853  0.361236369  0.849301391 -0.352626979 -0.070529647
## [1481]  2.649797161  0.907598899  0.625101838  0.675980039  0.212311121
## [1486]  0.121980757 -1.415059969 -0.431054872  1.082896354 -1.973392396
## [1491] -1.423986623  0.490334662 -1.775407476  1.277783082  0.427243867
## [1496]  2.191020932  1.904928399 -0.912706951  0.000000000  0.000000000
## [1501] -3.708224882 -2.149043414  0.058549833  0.701253105  3.320197197
## [1506] -0.437960135  1.100618065 -0.361987185 -0.994458000 -0.654366662
## [1511]  2.175574371 -0.644651941  0.425984454 -0.017847582 -0.975544448
## [1516]  0.615609255  0.536594106  0.879748847 -1.145888844  0.458367212
## [1521]  1.568355391  0.356990653  0.000000000  1.541262736  2.137160993
## [1526] -0.481533728 -0.311961043  0.000000000 -0.119860351  1.696191282
## [1531] -0.942072950  0.822635975 -0.660987524  0.123707870  0.000000000
## [1536] -1.486582653  2.394630567 -0.693256305  1.294386145  1.314016545
## [1541] -0.105741951 -1.059357292  0.242100039 -1.998415571  0.945061793
## [1546]  1.645812479 -0.109421461  0.903989769  0.432340010 -0.862579144
## [1551]  0.069508615  0.019339936  1.778113060  0.406993546 -0.062627086
## [1556] -0.769062565  0.252070580  1.259864471  0.290663815 -1.049216849
## [1561]  0.327572363  1.554079025  0.016756032 -0.268051600 -1.129420040
## [1566]  1.803875345  0.852447560  1.866824562  0.177677150  1.434605357
## [1571]  0.668190391 -0.077665567 -0.653593148  1.840950845  1.666298505
## [1576] -0.060595965  2.029383914 -0.468310885 -1.711977659  0.194097688
## [1581]  3.808732452  2.028555207 -1.466422795  1.111440290  0.727016349
## [1586] -0.513601345  1.849372958 -1.191837906 -1.555775482 -0.795023265
## [1591]  0.542940151  0.887453593  1.462565160 -1.936956875 -0.210947629
## [1596]  1.023735620 -3.208444984 -0.980160772 -2.811087038  0.072591899
## [1601]  2.693264388  1.467145533 -1.108202628 -2.727114899 -0.327372657
## [1606] -2.037161955 -0.041815860 -2.369721670  0.573711394  2.092459035
## [1611]  3.135331263 -1.578521448  0.770531716 -0.481747581  1.412717155
## [1616] -0.646049873 -1.865481646 -3.420059583 -2.406792383  1.920660800
## [1621]  3.260344280 -0.631930906  0.846253816 -0.523970790  2.856848754
## [1626] -0.123997706  1.446317853 -1.108661873  0.734726293 -0.449083333
## [1631]  0.932097986  2.601512916  0.074830283  0.000000000  1.410632956
## [1636] -0.351797705 -1.014351226 -2.049960163 -0.366035714  1.456315342
## [1641] -0.237617951 -1.105752237 -0.448589701 -2.427998612  0.496152288
## [1646]  2.536585366 -1.141050745 -3.599637321  0.127251420 -2.764075309
## [1651] -5.829947383  4.415350729 -1.517866056  0.127504748  2.506087392
## [1656] -1.635509768  1.495191291 -0.716147020 -2.582671715  0.349627764
## [1661]  0.172193210 -0.998985217  0.120622694 -0.683155319  3.809446099
## [1666]  0.718681797  0.852206215  1.416337796  0.256879147 -2.785705407
## [1671]  0.470760158  1.994472928  0.892300092  0.255176087  3.873033776
## [1676] -0.715476791 -0.533395176  2.090292180  0.771446155  0.389569184
## [1681] -0.499270462 -1.682059071 -2.429130129  1.125550825 -0.808240458
## [1686]  3.008875475  0.102642935  0.200983495 -2.584003536  1.730800054
## [1691]  0.175734571  0.000000000  0.000000000  0.000000000  3.223730216
## [1696] -0.977960722  0.000000000  0.000000000  3.314632010  1.205915240
## [1701] -1.288219246 -0.460315822 -1.067746856 -1.301692736 -2.433130789
## [1706]  0.371737322 -0.110843106 -0.125198714  1.836134312  1.750611920
## [1711]  0.484376639 -1.400194394 -0.275263677 -0.391858959  1.046383841
## [1716]  1.165167333  1.604244622  1.350879873 -0.044999134  1.966221950
## [1721] -0.015452948 -0.440035503 -0.322226534  0.938656913 -0.382418871
## [1726]  0.864243422 -0.135128613 -0.946521221  0.289397410  0.290552403
## [1731]  2.025328736 -0.340578551 -0.663101790  0.042566382  0.602876263
## [1736] -0.132518989  2.172416414 -0.187051767 -0.040887776  1.869676556
## [1741] -0.460095114 -1.451796572 -0.300606329  1.845214929  1.389545028
## [1746]  0.483133805  0.210006966 -0.488235258  0.693785689  0.684490091
## [1751]  0.821919484 -0.755371610  0.842611362  1.924277411 -0.615044914
## [1756]  1.001569564  0.982949441 -1.664603755  0.753628952  0.059010440
## [1761]  0.539656679  0.747461867  0.850769665  1.453551237  1.742756437
## [1766] -0.677529841 -0.797036351  0.852421047  0.000000000  0.000000000
## [1771]  1.049084663 -0.162817298 -1.236555930  0.635937857  1.526293360
## [1776] -0.631110240 -1.144813726 -0.935756398 -2.245100778 -2.754635119
## [1781]  2.162228072 -0.529850045  3.096699319  0.000000000  1.841552460
## [1786] -2.089831858  0.735142168 -1.894343751  2.046897417  1.482560842
## [1791] -0.765225520  1.208970915  0.039463960  0.748030837 -1.304875413
## [1796]  1.821597931  1.351038412  0.000000000  0.284340766  1.126001096
## [1801]  0.848106200 -3.067613021  0.740458909  0.901157723  0.000000000
## [1806]  0.482995291  1.013462086 -0.621230334  2.129561243  1.088257129
## [1811] -0.229477886  0.440786522  0.000000000 -2.894872069 -0.889663917
## [1816]  0.725107682  2.154504590 -0.921845153 -0.802651721  0.068920063
## [1821]  1.774575920  0.627311537  1.768895650 -0.275705316  1.077252495
## [1826] -1.548772863  1.175658997 -0.090685914  0.953405079 -0.325256439
## [1831]  0.569162883  0.719726634 -0.299889182  0.006665733  0.367757330
## [1836]  1.304764324  0.068831020  0.031116425  0.898166339  0.376935384
## [1841] -0.032168947 -1.665399977 -0.613210417 -0.053608479 -3.082982098
## [1846]  0.224960926 -0.660926592  1.331162481 -0.764264780 -1.481098548
## [1851] -0.964259366 -1.817371081 -1.543251104  1.269871132 -2.463060347
## [1856] -3.198466055  1.913814044 -0.592358556  2.216420823
## 
## 
## $SMI
## $SMI$x
##    [1]  0.685107711 -0.887271474  0.312439110  0.075580872 -1.215136204
##    [6]  0.764007406  1.409499686 -0.651392890  1.273622589  0.456267049
##   [11]  0.408883624 -0.419166933  0.342314746 -0.062065052 -0.608637221
##   [16]  0.543370600 -1.116704964 -0.075580872 -0.521617717  0.044511053
##   [21]  0.184418986  0.022924375 -0.207786884  0.213301268 -0.726625143
##   [26] -0.714389194  0.395725296 -0.234039548  0.289863864 -0.656402227
##   [31]  0.066118496  0.562222407  0.284243507 -1.039553035 -3.461124681
##   [36]  2.533393817  2.897169268  1.077327344  1.134488812  0.506230285
##   [41] -0.847978932  0.571723349  0.755011527 -0.263245342 -0.490961795
##   [46] -0.278632114 -0.501637496 -0.047210641 -0.735432089 -0.541808390
##   [51] -0.685107711  0.205032071 -0.074228709  0.221585076 -1.255624109
##   [56] -0.206409282 -1.307735956  0.059363328  0.125729300 -0.661428091
##   [61] -0.516988672 -0.710912844 -0.885274487  0.386991129 -0.537129662
##   [66]  0.477317439  1.058251433 -0.270231385 -0.221585076 -0.942601281
##   [71]  0.013484154 -0.504698173 -0.778530978  0.394267521 -0.028319650
##   [76]  0.165250729  1.129371243  0.173457852  1.340125919 -0.400103684
##   [81] -0.767623099  0.371054291 -0.294085140 -1.541543733  0.674913004
##   [86] -0.031017587 -0.698812562 -0.823127102 -0.543370600 -0.590882359
##   [91]  0.648062397  0.229884118  0.306780804  1.713581019 -0.411817256
##   [96]  1.048856395 -0.465263357  0.340885359 -0.291270379 -1.997936847
##  [101] -1.507075579 -0.423587607 -0.602158982 -1.409499686 -1.380950295
##  [106]  1.398659855 -1.074921450 -0.447307518 -1.295156428 -1.815858073
##  [111]  1.187393051  0.885274487 -1.217962298 -0.492483445  0.214680871
##  [116] -0.756805798 -1.021211206  0.985521574  1.179246182 -0.026970760
##  [121]  0.210543276 -0.048560562 -1.067740821 -1.079739490 -0.503167245
##  [126]  1.882932462 -0.205032071 -0.203655249  1.837306881  1.000978901
##  [131] -0.202278813 -0.200902759 -0.199527087  2.084477779  0.478829051
##  [136] -0.970296201 -0.903376738  1.621571613  0.492483445 -0.483370478
##  [141]  1.007677172  2.271268723 -0.996538226 -1.048856395  0.101301081
##  [146]  0.259059897 -0.256272124 -0.438383752 -0.018878365  1.119223863
##  [151] -0.315272007 -1.320525901 -0.405953507  0.375391193 -0.257665760
##  [156] -0.102656486  0.756805798  0.778530978  0.071524788  0.308194453
##  [161]  0.826917147 -0.469775625 -0.036414159 -1.126823516  0.544934137
##  [166]  0.222967175 -0.832624598  1.028048865  0.151596606  0.765814001
##  [171] -0.587674282  0.703985770  0.350905885  0.771248856 -0.078285614
##  [176]  0.242362624  0.124370342 -0.895295078 -1.353484113 -0.535572701
##  [181]  0.268833132 -1.046522062 -1.192868378  0.942601281 -0.707445064
##  [186]  1.238023440  0.041811790  0.793220658  0.133888019 -1.367088290
##  [191]  0.303955341  0.313855244  0.270231385 -0.673220713  0.626586061
##  [196] -0.326629195 -0.863535834  0.683403669 -0.774884781  0.865495146
##  [201]  0.426539323 -1.554954248  0.021575667  1.201149064 -0.693657988
##  [206]  0.811827184  1.255624109 -0.381184749 -0.198151791 -0.196776871
##  [211] -0.875342009  0.861579831  0.252094188 -0.549632774 -0.051260673
##  [216] -1.184668689  0.899328566  0.291270379 -0.195402322  1.601806100
##  [221]  0.751430255  1.018942572 -0.238199023  0.707445064  0.840277002
##  [226] -0.961696145  0.063416084 -0.730141123 -1.528404858  1.072521761
##  [231] -0.867457786  0.240974293 -0.690231824  0.285647748 -0.389899206
##  [236] -0.459261681 -0.817464095 -0.194028142  0.328051780  0.068821391
##  [241]  0.382635132 -1.084582727  0.001348375 -0.397183912 -0.192654329
##  [246] -1.041870422 -0.919719798 -1.346774976  0.644739077 -1.058251433
##  [251]  0.961696145 -0.731902501 -0.857677680  0.373944779 -1.494600149
##  [256] -0.099945863 -0.764007406  0.430973886 -0.851848813  0.663107092
##  [261]  0.465263357 -0.793220658  0.529357768  0.987715314 -0.721367945
##  [266] -0.600543374 -1.360254733  0.524709963  0.565383709 -1.091895656
##  [271] -0.659750952  0.548065218 -0.573311845 -1.915677702 -2.393782545
##  [276]  1.795213515 -1.808890648  0.302543521 -0.624946069  0.257665760
##  [281]  1.089451538  1.978474507 -0.654730623 -0.738970862 -0.416224367
##  [286]  0.638113687  0.940500815 -0.254878985 -0.836444677 -0.819348844
##  [291] -0.082343808 -0.681701610 -0.758602509  0.404489757  0.498581510
##  [296] -0.948927784 -1.016679169 -1.550453053  0.968139475 -2.205284963
##  [301] -1.398659855 -0.565383709  2.161436385  0.261849685  0.348039324
##  [306] -0.507763585  0.658075667  1.067740821 -0.097235975  0.889272006
##  [311] -0.222967175 -0.784019770  0.875342009  1.223643862  2.752336985
##  [316] -1.443055487  1.363663552  0.994325241  0.444329005 -0.749643230
##  [321]  0.680001523  0.773065541 -0.420639577 -0.053961158 -1.830063448
##  [326] -0.045860805 -0.313855244  0.378286384 -1.243847553 -3.001150261
##  [331]  1.899050574  2.108763102  0.723118123  0.450290005  0.091818320
##  [336]  0.686813744 -0.450290005 -0.936312283  0.369610210  1.258595595
##  [341]  1.099267451 -1.044193418  0.078285614  0.538687927  0.535572701
##  [346] -0.391354480 -1.333535586 -0.345175621  0.236812077  0.589277562
##  [351]  0.695374126  0.451782750  0.518530452  0.148869251 -0.002696752
##  [356]  0.202278813 -1.129371243  0.142055660 -1.395082856 -1.157894875
##  [361] -1.545983054 -0.649726742  0.747858595  0.051260673 -0.620036135
##  [366] -0.907439769  0.376838394  0.178935732  1.405868039  0.998756101
##  [371] -0.319526110 -0.510833777  0.067469881  0.438383752  1.212319781
##  [376]  0.353775332  1.094346314  0.366724356  0.271630167  1.264572142
##  [381] -0.811827184  1.091895656  0.166617795  0.919719798 -0.056662036
##  [386]  0.608637221  0.144780288 -0.191280879 -0.189907790  1.616570833
##  [391] -0.322365390  0.825020643 -0.188535059 -0.187162683  0.636461719
##  [396]  0.526257967 -0.403026872 -2.084477779 -0.489441280 -1.616570833
##  [401]  1.737480953 -0.379735168  1.519790077 -0.382635132 -1.124283082
##  [406] -1.276662700 -0.274429329  1.507075579  0.688521779 -1.111688306
##  [411] -0.209164881 -1.387981923  0.441354429  1.032634134  1.564052364
##  [416] -0.101301081 -0.358084978  0.253486340  0.425063002  0.159785525
##  [421] -0.318107437 -0.932140112  0.250702523  0.389899206  0.453276503
##  [426] -0.946814739 -1.168503942  1.003206657 -0.934224165 -1.363663552
##  [431] -2.108763102  0.785854621 -0.468270477  1.969017784  1.101738030
##  [436]  0.520073465  0.579680379 -0.365282575 -0.474297479 -0.329475030
##  [441]  0.970296201  0.299721685  0.384086320 -1.867289179  1.573281819
##  [446] -0.570136293 -0.830719108  0.821236508  1.466361761 -1.282778578
##  [451]  0.174826828 -1.226499513 -0.802489192  1.356861648  0.774884781
##  [456]  0.669841901 -0.032366639 -0.292677470 -0.004045135 -0.554343576
##  [461]  0.590882359 -0.789532284  0.082343808 -0.185790660 -0.184418986
##  [466] -0.579680379 -1.034934930 -0.487921897  0.025621919  0.086403358
##  [471]  0.136609547  0.330898947 -0.250702523 -0.985521574 -1.340125919
##  [476] -1.037241217  0.709177888 -0.992117116  0.278632114  1.240930235
##  [481]  0.329475030  0.234039548 -0.224349699 -0.352340246  0.859627120
##  [486]  0.595705916 -0.091818320 -0.664787965  0.062065052  0.992117116
##  [491]  1.152638890 -0.216060883 -0.183047659  0.224349699  0.127088491
##  [496]  0.235425586  0.109436387  1.005439403  0.123011613 -0.181676676
##  [501] -1.082157935  0.227116039  0.429494761  0.749643230  1.295156428
##  [506] -0.965987242  0.891276104 -0.369610210 -0.239586428 -0.944705914
##  [511] -1.187393051  1.044193418  1.435458325 -0.477317439  0.527807233
##  [516]  0.180306035 -0.762203300  0.546499008  0.521617717  1.106699472
##  [521]  0.000000000  0.112149739 -0.243751421 -0.546499008 -0.428016575
##  [526]  1.298282071 -1.089451538  1.217962298  0.195402322  0.181676676
##  [531]  0.411817256 -0.589277562 -0.733666152 -0.373944779 -0.913562563
##  [536] -2.253834800 -0.755011527  1.333535586  0.460760541  1.731412828
##  [541]  0.410349998  0.469775625 -0.574901790 -0.236812077 -0.213301268
##  [546]  1.395082856 -0.025621919 -0.530909576 -0.277230642 -0.335174740
##  [551] -1.737480953  1.285854591  1.707756416  0.490961795  0.809953940
##  [556] -0.849912281  1.074921450 -0.571723349 -0.495530174 -0.560643862
##  [561]  0.132527628  1.267577427 -1.292043388  0.060714135  0.014832664
##  [566]  0.273029480 -1.023485109 -0.524709963 -1.343443023 -1.941657387
##  [571]  0.475806917 -0.472789121 -0.968139475 -1.070128233 -0.006741924
##  [576]  1.111688306 -1.446885503  0.566966480  0.474297479  1.554954248
##  [581]  0.602158982 -1.003206657  0.484886501  0.955292497  1.636822499
##  [586] -0.404489757  0.249311344 -0.782187555  0.346607117  0.359523002
##  [591]  1.424215576  0.568550673 -0.526257967  0.154325089  0.639767399
##  [596]  0.085050020  0.817464095  0.651392890  1.184668689  2.028630245
##  [601] -0.328051780  0.254878985  0.927984105  0.447307518 -0.909476911
##  [606]  0.616771139  0.634811485  0.114863917 -0.008090336  0.072876682
##  [611]  0.629871114  0.216060883 -1.788499010 -1.959733938  0.903376738
##  [616]  1.988111548  0.594096529 -1.099267451 -0.066118496 -0.366724356
##  [621] -0.430973886 -0.260454538  0.641422863  0.200902759 -1.611610156
##  [626]  0.135248658  0.633162979  0.319526110  0.600543374 -0.363841553
##  [631] -0.098590829  1.490492928  0.486403639  1.314104058  0.681701610
##  [636] -0.271630167  0.294085140  0.549632774  0.016181201  0.586072510
##  [641] -0.594096529 -0.901350805  0.653060847  0.853788545  0.760401672
##  [646]  0.281436703  0.963839475  0.981148261 -0.180306035  0.104012078
##  [651] -1.668520329  0.026970760  0.905406385 -0.178935732  1.486410698
##  [656]  0.018878365  0.339456669  0.439868605  0.787692121 -1.212319781
##  [661]  0.368166900 -1.235127068 -1.822914780  1.550453053  0.776706588
##  [666]  1.023485109  0.413285400 -0.333748798 -0.456267049 -0.029668592
##  [671]  0.957422684  0.923844064  0.040462274  1.606688823  1.384457552
##  [676] -1.246775496  0.721367945 -0.826917147  0.487921897 -2.271268723
##  [681]  0.185790660 -1.641991740 -1.621571613 -0.177565765 -2.161436385
##  [686] -0.176196131 -0.174826828  2.568276871 -0.498581510 -1.249714166
##  [691] -0.780357962  1.647205232 -2.220892296 -1.301420449 -1.673969302
##  [696] -1.679468436 -2.471677151  1.443055487  2.253834800  1.941657387
##  [701] -0.853788545 -1.749812815  0.012135669 -1.373986290  1.545983054
##  [706]  1.446885503 -0.983332566 -0.086403358 -1.768825039 -1.631696630
##  [711]  0.819348844  1.327002669 -0.457763852 -0.974623251  1.235127068
##  [716] -1.519790077 -0.742518914 -0.987715314 -0.173457852 -0.172089202
##  [721]  0.471281838  0.932140112  1.243847553  0.454771268  0.381184749
##  [726]  0.049910572 -0.639767399 -1.482353090  1.192868378 -0.359523002
##  [731] -1.450736862 -0.955292497 -1.582647271  0.163883972 -1.195619501
##  [736]  0.481855566  0.584472241 -1.101738030 -1.478319741  1.215136204
##  [741] -0.616771139 -1.924193887 -1.190126255 -1.756079872 -2.418146732
##  [746]  2.348932362  0.079638199 -0.170720874  1.830063448  1.304571699
##  [751]  0.746076339  0.523163215 -0.825020643  0.211922070 -0.169352865
##  [756] -1.743613740 -0.994325241  0.661428091  0.972457450  1.323757343
##  [761] -1.028048865  0.292677470 -0.448798263  0.005393524  1.997936847
##  [766] -0.338028671  0.953166636 -1.176547886 -0.769434713 -1.005439403
##  [771] -0.384086320 -1.657768635 -1.573281819 -1.719464344 -2.649174982
##  [776] -0.245140689  2.072781954  1.373986290 -1.932851955 -0.917663521
##  [781]  1.788499010  1.195619501 -1.171176839 -1.060614828  1.915677702
##  [786] -1.336823495 -0.703985770 -0.603776164 -1.466361761 -0.005393524
##  [791] -2.096465896 -1.596961269  2.205284963 -0.809953940 -1.106699472
##  [796]  1.232241021  1.725407795  0.744296449  0.869423773 -0.014832664
##  [801]  0.036414159 -2.237060137  0.615141105  0.895295078 -0.167985173
##  [806]  2.007958893 -0.628227740 -0.451782750 -0.846048746  0.710912844
##  [811] -1.515524656  0.167985173 -0.309608718 -0.598929332 -0.676607229
##  [816]  0.796919854  0.435416939 -0.940500815 -1.317308188 -1.270594204
##  [821] -0.275829715  0.428016575  0.416224367  1.360254733  2.121387721
##  [826] -0.089110513  0.388444757 -0.957422684  1.768825039  0.010787206
##  [831] -1.134488812  0.400103684 -0.039112832 -1.131926322 -0.070173025
##  [836]  0.649726742 -1.094346314 -0.631516191 -1.273622589  0.457763852
##  [841] -1.139636266 -0.064767230  0.345175621  0.183047659 -1.203927669
##  [846] -0.445817767  0.356647694 -1.532755121 -1.238023440 -1.626613277
##  [851]  1.055893934 -1.837306881  0.108080014  0.513908791  2.289421602
##  [856]  0.730141123 -0.563802354  1.370529139 -0.584472241 -0.669841901
##  [861] -1.564052364 -0.787692121 -0.059363328 -1.201149064  0.733666152
##  [866] -1.498732738 -0.989913817 -1.053542290  1.474310299  0.712649943
##  [871] -0.320945426 -0.392810584  1.559487170  0.192654329  0.738970862
##  [876] -0.834533115  1.907298228  0.503167245 -0.432453954 -0.520073465
##  [881] -0.063416084  0.762203300 -0.607015276  0.150232789 -0.087756855
##  [886] -1.606688823 -1.327002669  1.034934930  0.076933172  0.232653959
##  [891]  0.131167483  0.419166933 -1.025764317 -0.041811790  1.478319741
##  [896] -1.152638890 -0.425063002  0.118936778 -0.796919854 -0.795068896
##  [901]  0.037763461  0.656402227  0.716130610  0.220203400 -0.386991129
##  [906]  0.578086050  0.934224165  0.555916576 -0.055311546 -0.166617795
##  [911]  0.978968627 -0.953166636 -1.370529139 -0.165250729 -0.163883972
##  [916] -0.930060100  0.873365866 -1.032634134  0.362401286 -0.433934970
##  [921] -0.951045074 -0.355211147  0.056662036 -0.220203400 -0.610260769
##  [926] -0.621671114  0.445817767 -0.021575667 -1.114193130 -1.950615992
##  [931]  0.391354480 -0.658075667  1.343443023 -0.298311662 -0.765814001
##  [936] -0.353775332  1.084582727  0.029668592  1.165839367  1.416819278
##  [941]  0.206409282 -0.691943891  0.836444677 -0.273029480 -0.080990929
##  [946]  0.191280879 -0.494006236 -0.859627120 -1.062984162 -0.375391193
##  [951]  0.507763585 -0.093172475  0.976793633 -0.613512703 -0.905406385
##  [956] -0.532462664  0.813703281 -0.285647748 -1.474310299 -1.568650389
##  [961] -0.686813744 -1.413150018 -2.147701284  0.209164881 -1.000978901
##  [966]  0.563802354  0.504698173  0.758602509  0.177565765  0.832624598
##  [971] -0.712649943 -0.371054291 -1.160534902  1.924193887 -0.618402813
##  [976] -1.220798154 -0.235425586  1.673969302 -1.264572142 -0.001348375
##  [981]  1.155262893 -0.104012078  0.883281024  0.039112832 -0.017529767
##  [986] -0.020226997 -0.240974293 -0.288457923 -0.162517520 -0.161151372
##  [991] -0.800629988 -1.486410698  1.249714166  0.724870519 -0.478829051
##  [996]  0.196776871  0.554343576 -0.551201681  1.346774976 -0.159785525
## [1001]  1.065359478 -0.323786003  1.030338792  0.320945426  0.288457923
## [1006] -0.340885359  0.152960705  1.631696630  1.173858130  0.422113133
## [1011]  0.239586428 -0.500108919 -0.737200322 -1.288942818  1.932851955
## [1016] -0.242362624  1.190126255 -0.158419976 -1.279714656  0.414754435
## [1021]  0.676607229  0.207786884  0.871393127 -0.295493393 -0.157054722
## [1026]  0.083696837  0.363841553 -0.740743723 -0.695374126  0.203655249
## [1031] -0.264641513 -0.308194453 -0.016181201 -1.209512942  1.144814095
## [1036]  0.008090336  0.423587607  1.082157935 -0.444329005 -0.515448120
## [1041]  0.559066713 -0.562222407  0.282839826 -1.009919999 -0.013484154
## [1046]  0.800629988 -0.360961770 -0.643080086  0.551201681 -0.436899865
## [1051]  0.080990929  0.815582246 -0.033715750 -0.460760541  1.181953091
## [1056] -0.897309997 -0.963839475 -1.490492928  0.243751421  0.162517520
## [1061] -0.339456669 -0.454771268 -0.289863864  0.267435404 -0.462260438
## [1066] -0.155689761  1.039553035 -1.592153635 -0.512370678 -0.475806917
## [1071] -0.330898947 -0.871393127  0.867457786  0.693657988 -0.747858595
## [1076]  1.282778578  1.626613277 -0.229884118  0.316689404 -0.302543521
## [1081]  0.515448120 -0.368166900 -0.615141105  0.176196131 -0.653060847
## [1086]  0.064767230  1.137058773 -0.480341759  0.309608718  1.350121948
## [1091]  0.691943891  1.109190438 -0.641422863 -0.105367863 -0.303955341
## [1096]  0.070173025  1.025764317 -0.410349998  0.480341759 -0.865495146
## [1101]  0.974623251 -0.378286384  0.323786003 -1.713581019  0.780357962
## [1106]  1.160534902 -1.470324418 -0.582873468  0.494006236  0.911517835
## [1111]  0.315272007 -0.697092314 -0.106723840  0.623307755  0.311023602
## [1116] -0.744296449  0.847978932  0.355211147  0.946814739  0.169352865
## [1121] -0.348039324  0.834533115 -0.636461719 -0.356647694 -2.308361815
## [1126]  0.767623099  0.582873468 -0.068821391 -1.859635855  1.203927669
## [1131]  1.756079872  0.728382008 -0.398643373  0.472789121 -0.751430255
## [1136]  0.336601363 -0.253486340  0.605394926 -0.927984105 -0.552771947
## [1141]  0.385538318 -0.518530452  0.849912281  0.048560562  1.087013912
## [1146] -0.044511053  0.574901790  0.217441306  0.338028671  1.114193130
## [1151] -0.972457450  0.540247501  0.106723840  0.266038199  0.560643862
## [1156] -0.108080014  0.004045135 -1.431690617 -0.076933172  0.483370478
## [1161]  0.643080086 -0.471281838 -0.249311344  0.576493189 -1.462421997
## [1166] -1.384457552  1.307735956 -0.083696837  0.795068896 -0.154325089
## [1171] -0.152960705  1.377459942 -0.883281024 -0.151596606 -0.150232789
## [1176] -0.148869251  2.501345446  0.325207270 -0.877321577 -0.481855566
## [1181] -0.441354429 -1.647205232 -1.240930235  0.231268816 -1.899050574
## [1186]  0.719619975 -1.427943123  1.380950295 -0.372499146 -0.305367768
## [1191] -1.261578236 -0.024273125 -0.586072510 -0.923844064  0.143417841
## [1196]  1.391523619  0.379735168  1.116704964 -0.581276182 -1.725407795
## [1201]  1.147414556  0.238199023 -0.804351175 -0.296902233  0.298311662
## [1206]  0.147505990  0.113506724  0.116221323  0.198151791 -0.568550673
## [1211] -1.137058773  0.260454538  0.358084978  1.121749883 -0.022924375
## [1216]  0.343744832  1.679468436 -0.408883624  1.051196457  0.468270477
## [1221] -0.791375125  0.828816630  3.461124681 -1.223643862 -1.524083329
## [1226]  1.126823516  0.532462664  0.611885927 -0.771248856  0.705714361
## [1231]  0.654730623  0.095881300  0.534017037  0.537129662  0.915611117
## [1236] -0.798773547  0.365282575 -1.144814095  0.099945863  0.146143003
## [1241] -0.401564849 -1.454609861  0.035064922 -0.147505990 -0.146143003
## [1246] -0.753219684  0.121653111 -1.267577427  0.188535059  0.417695198
## [1251]  0.530909576 -0.306780804 -0.282839826  0.838359300  1.420507713
## [1256] -0.998756101  0.628227740 -0.211922070  0.855731495 -1.356861648
## [1261] -0.442841227 -0.144780288 -0.709177888 -0.981148261 -0.828816630
## [1266] -0.463761374 -1.636822499 -0.646399844  1.163183043 -0.079638199
## [1271]  0.784019770 -0.538687927 -0.143417841  0.624946069 -0.506230285
## [1276]  0.006741924 -1.377459942 -0.280034133  0.789532284 -0.142055660
## [1281]  0.305367768 -1.012167918 -0.873365866  0.557490953 -0.605394926
## [1286]  0.735432089  0.020226997  0.392810584 -1.391523619  0.893283788
## [1291] -0.210543276  0.802489192  0.110792961 -0.666470718  0.102656486
## [1296]  0.887271474  0.448798263  0.301132303  1.012167918  0.403026872
## [1301] -0.266038199  0.717874200 -0.838359300  0.917663521 -0.346607117
## [1306]  0.668155360  0.093172475  0.398643373 -1.402254840 -0.060714135
## [1311]  1.246775496  0.405953507  0.631516191 -0.938404491 -1.104215353
## [1316] -2.072781954 -0.899328566 -0.435416939  0.333748798 -2.348932362
## [1321]  0.570136293 -2.533393817  1.701989181 -0.095881300  0.318107437
## [1326] -1.206715600 -0.978968627 -0.140693743  2.606596640  0.552771947
## [1331]  0.087756855  1.062984162 -0.509298081 -0.544934137 -0.840277002
## [1336]  0.120294834  0.610260769 -0.342314746  0.737200322 -0.407418129
## [1341]  1.060614828 -0.683403669  0.901350805  0.326629195 -0.557490953
## [1346]  0.140693743 -1.096803562 -0.529357768 -1.304571699  0.172089202
## [1351] -1.155262893  0.245140689 -0.439868605  0.264641513  1.462421997
## [1356]  0.225732653 -0.705714361  0.161151372  0.913562563  0.089110513
## [1361] -1.198379702 -0.109436387  0.047210641 -0.139332087 -1.795213515
## [1366]  0.798773547  1.150022800 -0.049910572 -0.287052552  1.229365201
## [1371] -0.072876682  0.671530349  0.275829715 -0.137970689  1.292043388
## [1376]  0.031017587 -0.523163215 -0.540247501  0.137970689  0.157054722
## [1381]  0.155689761 -1.150022800 -0.012135669  0.228499859 -0.688521779
## [1386] -0.626586061 -1.181953091  0.247920647  0.058012629  0.043161383
## [1391] -1.147414556 -0.484886501 -0.040462274  0.256272124  0.360961770
## [1396]  1.104215353  0.921779971 -0.316689404 -0.094526801  0.433934970
## [1401] -0.043161383 -0.325207270  0.909476911  1.226499513 -0.497055264
## [1406]  0.024273125 -0.486403639 -0.855731495  0.597316848  0.170720874
## [1411] -0.633162979 -1.165839367  1.176547886  0.495530174 -1.030338792
## [1416]  1.482353090 -0.648062397 -0.009438762 -1.988111548  1.168503942
## [1421]  0.263245342 -1.014420963 -0.035064922 -0.821236508  0.879304589
## [1426] -0.776706588  0.678303399  0.105367863  0.187162683 -0.671530349
## [1431] -0.376838394 -0.136609547 -0.135248658  1.524083329  0.740743723
## [1436] -0.388444757 -0.133888019 -0.132527628 -0.268833132 -0.702259280
## [1441] -0.232653959  0.607015276  0.581276182 -0.760401672  0.804351175
## [1446]  0.129807580 -0.311023602  0.782187555  0.295493393 -0.513908791
## [1451]  0.335174740  2.308361815  1.276662700 -1.173858130 -0.058012629
## [1456]  1.515524656 -0.578086050  1.096803562  1.652463885  0.199527087
## [1461]  0.296902233  0.139332087  0.017529767  1.288942818  0.664787965
## [1466]  0.592488679  0.925912101 -0.413285400  0.702259280  1.301420449
## [1471] -0.808083534  0.877321577  0.032366639 -0.422113133 -1.577947245
## [1476]  1.046522062  0.881291064 -0.724870519 -1.007677172 -0.915611117
## [1481]  1.387981923  0.830719108  1.458504802  0.823127102  1.131926322
## [1486] -0.394267521 -0.227116039 -1.690621630  0.620036135 -1.852089931
## [1491] -1.109190438  0.332323535 -2.050206632  1.252663668  0.055311546
## [1496]  1.541543733  1.528404858  0.965987242 -0.131167483 -0.129807580
## [1501] -2.697177092 -0.555916576 -0.844121708  0.098590829  2.471677151
## [1506] -0.336601363  1.317308188 -0.417695198 -0.773065541 -0.680001523
## [1511]  1.427943123 -0.674913004  0.996538226  0.806215951  1.009919999
## [1516]  0.218822145  0.666470718  1.336823495 -1.587382521  0.459261681
## [1521]  1.470324418  1.021211206 -0.128447917  1.320525901  1.685018832
## [1526] -1.121749883  0.598929332 -0.127088491 -0.466766389  0.851848813
## [1531]  0.948927784  1.139636266  0.074228709  0.280034133 -0.125729300
## [1536] -1.731412828  1.959733938 -0.259059897  0.002696752  0.274429329
## [1541] -0.350905885 -1.439246522 -0.228499859 -1.882932462  2.190197016
## [1546]  1.279714656  0.659750952  0.189907790  1.494600149  1.053542290
## [1551] -0.349472246 -1.314104058  1.206715600  0.397183912 -0.717874200
## [1556] -0.576493189  1.270594204  2.018186777  1.070128233  0.489441280
## [1561] -0.453276503  1.696278006  0.052610867  0.573311845 -1.663120450
## [1566]  0.673220713  0.349472246  2.328168205  0.808083534  1.815858073
## [1571]  1.261578236 -0.891276104 -1.775306882 -1.696278006  0.863535834
## [1576] -0.225732653  1.587382521 -1.323757343 -2.190197016 -2.039299773
## [1581]  1.171176839  3.001150261 -0.644739077 -0.252094188  0.791375125
## [1586] -1.077327344  1.641991740 -0.806215951 -0.124370342 -2.134359789
## [1591] -0.312439110  0.930060100  1.950615992 -1.285854591 -0.976793633
## [1596] -0.566966480 -2.175591776 -1.907298228 -1.707756416 -1.844648016
## [1601]  2.649174982  2.039299773 -0.668155360 -2.752336985 -0.247920647
## [1606] -2.028630245  0.989913817 -2.897169268 -0.218822145  1.209512942
## [1611]  2.817407051  0.621671114 -0.217441306  1.157894875 -0.785854621
## [1616] -1.435458325 -1.802009946 -1.685018832 -0.085050020  0.846048746
## [1621]  1.890930113  2.444036983  1.582647271 -0.597316848  1.781864184
## [1626]  0.463761374 -0.067469881 -1.458504802  1.016679169 -0.728382008
## [1631] -0.595705916  1.592153635  1.402254840  1.859635855 -0.813703281
## [1636] -1.179246182 -0.719619975 -1.781864184 -0.861579831  1.743613740
## [1641]  0.842197799 -0.638113687 -0.395725296 -1.258595595  0.466766389
## [1646]  1.611610156 -1.350121948 -2.370761549  0.742518914 -2.444036983
## [1651] -3.153406194  3.153406194 -1.978474507  1.867289179  2.134359789
## [1656] -1.072521761  1.330262031 -1.087013912 -2.121387721  0.407418129
## [1661]  0.462260438 -1.229365201 -0.559066713  0.352340246  2.370761549
## [1666]  0.094526801 -0.261849685  1.577947245  1.511286632 -1.652463885
## [1671]  0.372499146  1.454609861  0.646399844 -0.037763461  1.808890648
## [1676]  0.857677680 -0.052610867  0.897309997  0.731902501  1.596961269
## [1681]  0.045860805 -1.065359478 -0.869423773 -0.267435404 -0.815582246
## [1686]  1.852089931  0.510833777 -0.332323535 -2.061362980  1.142221353
## [1691] -0.284243507 -0.071524788 -0.123011613 -0.121653111  2.418146732
## [1696]  1.431690617 -0.246530430 -0.120294834 -0.118936778  2.147701284
## [1701] -0.611885927  0.158419976 -1.252663668 -1.537134586 -2.606596640
## [1706]  1.844648016 -0.592488679 -0.231268816  2.096465896  1.220798154
## [1711]  1.037241217 -0.301132303 -0.842197799  0.587674282  0.287052552
## [1716]  0.128447917  1.502891083  0.322365390  0.907439769  1.719464344
## [1721]  0.516988672 -0.414754435  1.079739490  1.439246522 -0.716130610
## [1726]  0.501637496  1.198379702 -1.424215576  0.698812562  0.009438762
## [1731]  1.413150018 -0.634811485 -0.429494761  0.509298081 -0.214680871
## [1736] -0.889272006  1.822914780  0.844121708  0.512370678  1.775306882
## [1741] -0.426539323 -1.890930113 -1.051196457  1.802009946 -0.362401286
## [1746]  0.936312283  0.442841227 -0.343744832  0.944705914 -1.232241021
## [1751] -0.623307755 -1.701989181  0.090464333  2.220892296  0.603776164
## [1756]  1.041870422  1.014420963 -1.055893934  1.690621630 -0.010787206
## [1761]  0.726625143  0.420639577  0.277230642  1.310913362  1.498732738
## [1766] -1.405868039 -2.018186777  0.500108919 -0.117578942 -0.116221323
## [1771]  0.541808390 -0.911517835 -1.762416670 -0.925912101  0.690231824
## [1776] -1.875053466 -1.119223863 -0.893283788 -0.746076339 -2.289421602
## [1781]  1.875053466  0.983332566  2.237060137 -0.114863917  2.697177092
## [1786] -0.881291064  0.117578942 -1.298282071  0.769434713  1.367088290
## [1791] -0.959557224 -0.879304589 -0.723118123 -0.700534881 -1.969017784
## [1796]  1.663120450  0.097235975 -0.113506724  0.697092314  1.668520329
## [1801]  1.124283082 -1.559487170 -0.663107092  0.753219684 -0.112149739
## [1806] -0.090464333  0.194028142 -1.420507713  1.568650389  0.618402813
## [1811] -0.629871114 -1.142221353 -2.007958893 -1.416819278 -1.330262031
## [1816]  0.700534881  2.393782545 -1.310913362  0.432453954 -0.299721685
## [1821]  1.657768635  0.613512703  1.762416670  0.246530430  0.959557224
## [1826] -0.110792961  2.050206632  0.028319650  0.714389194  0.951045074
## [1831] -0.281436703  0.938404491 -0.527807233 -0.385538318 -0.921779971
## [1836]  0.497055264 -0.534017037 -0.678303399  2.061362980  1.532755121
## [1841]  0.053961158 -1.163183043 -1.601806100 -0.548065218 -2.328168205
## [1846]  1.353484113  0.033715750  1.450736862  0.436899865 -1.502891083
## [1851]  0.401564849 -2.501345446 -1.511286632  1.537134586 -2.568276871
## [1856] -2.817407051  2.175591776 -1.018942572  1.749812815
## 
## $SMI$y
##    [1]  0.619748525 -0.586319218  0.327653997  0.148447242 -0.889363216
##    [6]  0.675999043  1.230019609 -0.358065274  1.107511046  0.436986541
##   [11]  0.388676181 -0.179138977  0.341553780  0.040385392 -0.328719723
##   [16]  0.509170862 -0.805940936  0.029017469 -0.266883268  0.127981385
##   [21]  0.238205903  0.110125775  0.000000000  0.254747568 -0.433125433
##   [26] -0.417609187  0.378589318 -0.023209934  0.313406849 -0.364498959
##   [31]  0.139364729  0.527689185  0.311490540 -0.736055204 -8.040783223
##   [36]  2.721431271  3.366858825  0.937407298  0.981602304  0.477299185
##   [41] -0.556134863  0.535943143  0.672152045 -0.046045816 -0.241851895
##   [46] -0.069268067 -0.248382625  0.052116509 -0.439865725 -0.279037321
##   [51] -0.390579457  0.251653304  0.029188558  0.262620368 -0.948777648
##   [56]  0.000000000 -0.987248046  0.136506618  0.201517307 -0.372648764
##   [61] -0.261236122 -0.416691470 -0.585809074  0.372797787 -0.275564608
##   [66]  0.456538716  0.920887401 -0.053327013 -0.011856770 -0.640341515
##   [71]  0.095476787 -0.250387504 -0.490078891  0.378378378  0.065817029
##   [76]  0.227218369  0.978403532  0.230414747  1.155319776 -0.163160655
##   [81] -0.478608533  0.363615037 -0.087652662 -1.239911101  0.609972758
##   [86]  0.064747778 -0.411764706 -0.537507383 -0.279113962 -0.315626489
##   [91]  0.597407253  0.267236772  0.325752191  1.593954779 -0.174327387
##   [96]  0.913906514 -0.224965390  0.341099613 -0.086425444 -2.006804683
##  [101] -1.218148649 -0.184677708 -0.322291853 -1.071792108 -1.041036194
##  [106]  1.217125382 -0.779503293 -0.200974421 -0.982486117 -1.633181314
##  [111]  1.021239271  0.781443810 -0.892307692 -0.242160820  0.255197311
##  [116] -0.471844540 -0.723598029  0.860823123  1.009220035  0.067842605
##  [121]  0.252696456  0.049182344 -0.768096350 -0.780234070 -0.249641141
##  [126]  1.795657887  0.000000000  0.000000000  1.763982790  0.869722776
##  [131]  0.000000000  0.000000000  0.000000000  2.029818574  0.457746479
##  [136] -0.660123846 -0.599823581  1.484943501  0.472193075 -0.237888019
##  [141]  0.872397348  2.214022140 -0.705099278 -0.744191331  0.171703297
##  [146]  0.291395269 -0.039879223 -0.193776359  0.074234810  0.964336662
##  [151] -0.101729400 -0.995700385 -0.165714286  0.366321332 -0.039920160
##  [156]  0.005705157  0.673170175  0.685668952  0.140702386  0.325970887
##  [161]  0.733852445 -0.228005784  0.061312078 -0.824420677  0.511121096
##  [166]  0.262643196 -0.546204437  0.879847568  0.216654630  0.676274945
##  [171] -0.313842088  0.629660315  0.345792854  0.678262772  0.027165055
##  [176]  0.282439846  0.200400802 -0.594594595 -1.022294725 -0.274695088
##  [181]  0.297487880 -0.741513787 -0.868795307  0.826169476 -0.415236408
##  [186]  1.084116306  0.126498735  0.703103543  0.207276496 -1.028795384
##  [191]  0.324496755  0.328929335  0.300530026 -0.375898889  0.574178378
##  [196] -0.108742932 -0.571521881  0.618601850 -0.484221980  0.765403750
##  [201]  0.401497477 -1.264523102  0.109463084  1.033295063 -0.405844156
##  [206]  0.722629720  1.095048009 -0.149405048  0.000000000  0.000000000
##  [211] -0.577138887  0.763235689  0.288046087 -0.287218765  0.048007681
##  [216] -0.858391981  0.790535090  0.314800982  0.000000000  1.468007021
##  [221]  0.670965036  0.874772195 -0.025809116  0.635068154  0.749063670
##  [226] -0.656923155  0.138404757 -0.435116458 -1.228791774  0.936963198
##  [231] -0.572430509  0.280082988 -0.398262129  0.311575012 -0.155303619
##  [236] -0.217763260 -0.535203949  0.000000000  0.334343329  0.140581068
##  [241]  0.369157178 -0.787401575  0.088763576 -0.161719443  0.000000000
##  [246] -0.736754102 -0.615886719 -1.016949153  0.593964041 -0.755359328
##  [251]  0.836147291 -0.435868814 -0.565906786  0.365100671 -1.198309528
##  [256]  0.010828957 -0.476422500  0.407985639 -0.558023621  0.604739853
##  [261]  0.444059352 -0.512184602  0.498563919  0.862766244 -0.422346966
##  [266] -0.322130355 -1.023376064  0.495211145  0.530676342 -0.791812550
##  [271] -0.369204040  0.512261580 -0.298199957 -1.810865191 -2.713779353
##  [276]  1.679380622 -1.623649292  0.324398156 -0.340367597  0.290300546
##  [281]  0.942164709  1.922968794 -0.364097755 -0.442943359 -0.177965630
##  [286]  0.584990807  0.825301872 -0.038455200 -0.549571334 -0.536030062
##  [291]  0.022223457 -0.388824085 -0.473986505  0.386597938  0.474409778
##  [296] -0.644372847 -0.721234485 -1.250211184  0.838323353 -2.279153942
##  [301] -1.059089068 -0.292466074  2.111932418  0.293002413  0.343701667
##  [306] -0.251184564  0.600927145  0.932984412  0.011272686  0.783363390
##  [311] -0.016775709 -0.497762864  0.770052274  1.070950469  3.316777042
##  [316] -1.105710165  1.188289943  0.864737910  0.418077900 -0.458498024
##  [321]  0.614146548  0.684066512 -0.182920456  0.047122886 -1.653757588
##  [326]  0.053214134 -0.101053079  0.367353458 -0.933587948 -4.262154637
##  [331]  1.817673378  2.070859654  0.651167797  0.433085601  0.165034072
##  [336]  0.621844273 -0.206000423 -0.635155878  0.356895541  1.098726115
##  [341]  0.945030713 -0.738544755  0.151951795  0.507481427  0.504919057
##  [346] -0.155376010 -1.011515717 -0.125766389  0.272836980  0.549421799
##  [351]  0.624479600  0.434422838  0.489186406  0.215219062  0.086925398
##  [356]  0.250332073 -0.825561841  0.210677766 -1.051174239 -0.844690885
##  [361] -1.249085398 -0.354591162  0.669216061  0.131898280 -0.337214816
##  [366] -0.602696273  0.367001755  0.233174351  1.226604631  0.867021832
##  [371] -0.103562552 -0.253991292  0.140310762  0.415153088  1.054263566
##  [376]  0.347754935  0.942819284  0.353410410  0.301856417  1.103475949
##  [381] -0.530832961  0.942643392  0.227283957  0.808479172  0.044011932
##  [386]  0.562127285  0.213872551  0.000000000  0.000000000  1.484212058
##  [391] -0.105147445  0.732022391  0.000000000  0.000000000  0.584212026
##  [396]  0.495820938 -0.164458228 -2.108532969 -0.240396173 -1.373560172
##  [401]  1.632134480 -0.149052794  1.338662301 -0.152055120 -0.823299862
##  [406] -0.964491363 -0.058142352  1.318660009  0.622039332 -0.803652099
##  [411] -0.004793864 -1.045112421  0.416646480  0.882906354  1.396461023
##  [416]  0.009433072 -0.132050556  0.288061957  0.400244856  0.225119595
##  [421] -0.102948058 -0.627693461  0.287545960  0.376028202  0.435495200
##  [426] -0.643416636 -0.849366495  0.870841024 -0.633416225 -1.024648220
##  [431] -2.127761080  0.692176456 -0.227525778  1.921397380  0.947348377
##  [436]  0.490450365  0.539678070 -0.135362211 -0.229025473 -0.112433243
##  [441]  0.839508489  0.320915306  0.370885489 -1.745958430  1.410304626
##  [446] -0.296680883 -0.543983634  0.729278669  1.285561795 -0.966825513
##  [451]  0.231342248 -0.900152333 -0.517048631  1.179941003  0.684899810
##  [456]  0.606701292  0.063959066 -0.086746108  0.086821422 -0.287631831
##  [461]  0.549450549 -0.505464481  0.155613529  0.000000000  0.000000000
##  [466] -0.301603985 -0.733373058 -0.240107125  0.111085397  0.157196357
##  [471]  0.207727462  0.336281555 -0.036729259 -0.688926652 -1.012810433
##  [476] -0.733507756  0.635383819 -0.701524647  0.306141673  1.084659811
##  [481]  0.334448161  0.268518519 -0.018468926 -0.129306364  0.762970498
##  [486]  0.550686063  0.018255671 -0.374172941  0.137406678  0.864474226
##  [491]  0.997641937 -0.008979885  0.000000000  0.264930400  0.201531640
##  [496]  0.272637883  0.178292846  0.872080089  0.198491465  0.000000000
##  [501] -0.783588660  0.266217056  0.407115674  0.669898634  1.116364592
##  [506] -0.658094125  0.784484637 -0.142702703 -0.025983024 -0.641081175
##  [511] -0.863196443  0.905892700  1.255120718 -0.232418008  0.496117343
##  [516]  0.236102168 -0.475374732  0.512070227  0.492336673  0.958548119
##  [521]  0.088615073  0.181289262 -0.029458800 -0.282045885 -0.185748058
##  [526]  1.120791744 -0.790497302  1.058178752  0.246130741  0.237203496
##  [531]  0.390252003 -0.314296348 -0.439742792 -0.145839410 -0.609247204
##  [536] -2.405743555 -0.464616046  1.145351601  0.440133322  1.625186131
##  [541]  0.389333110  0.446205171 -0.298916428 -0.024984385 -0.008330210
##  [546]  1.212146457  0.069964606 -0.271437384 -0.065982102 -0.115544918
##  [551] -1.487296013  1.115537849  1.592634067  0.469483568  0.719219829
##  [556] -0.556743454  0.937157694 -0.297427653 -0.245908248 -0.290967872
##  [561]  0.206703684  1.104190260 -0.980117614  0.137362637  0.096828855
##  [566]  0.302297461 -0.727345791 -0.267163212 -1.014692751 -1.898474660
##  [571]  0.455590387 -0.228842473 -0.658909879 -0.776625666  0.084616686
##  [576]  0.959587420 -1.109575849  0.533491405  0.454851752  1.391916820
##  [581]  0.554085346 -0.707295008  0.463844943  0.828592629  1.492293225
##  [586] -0.165162746  0.286486705 -0.494890159  0.343698193  0.350580271
##  [591]  1.244829940  0.535438068 -0.268265741  0.221518987  0.588095990
##  [596]  0.156955072  0.724779628  0.598988720  1.012991030  1.952078389
##  [601] -0.108875206  0.289397527  0.813221406  0.420058734 -0.607092619
##  [606]  0.566108007  0.581438412  0.184101035  0.084530854  0.143213866
##  [611]  0.579370027  0.255204346 -1.574602713 -1.936008276  0.794966468
##  [616]  1.936231451  0.550034836 -0.802304803  0.036763354 -0.135974422
##  [621] -0.187679399 -0.044242893  0.590166353  0.249349125 -1.368009071
##  [626]  0.207676618  0.581029570  0.331150195  0.553762652 -0.134942923
##  [631]  0.010956103  1.307285010  0.464982158  1.140929966  0.617240156
##  [636] -0.056409533  0.317482715  0.513397567  0.097956899  0.548720816
##  [641] -0.316312698 -0.599762884  0.599873711  0.760191094  0.674857242
##  [646]  0.309384668  0.836189171  0.849646547  0.000000000  0.175237582
##  [651] -1.402812353  0.112593401  0.797491650  0.000000000  1.305112253
##  [656]  0.100126827  0.340090691  0.415365189  0.694927033 -0.887311446
##  [661]  0.354786299 -0.911914359 -1.637212404  1.379707787  0.685481174
##  [666]  0.876756003  0.391769547 -0.114776677 -0.216684724  0.065804626
##  [671]  0.828593036  0.808739605  0.126160515  1.470018093  1.200369344
##  [676] -0.934432419  0.647886429 -0.542740841  0.466385355 -2.425314217
##  [681]  0.239497702 -1.388350768 -1.375155524  0.000000000 -2.161211075
##  [686]  0.000000000  0.000000000  2.928302399 -0.247247313 -0.935258931
##  [691] -0.493728316  1.498591927 -2.282411230 -0.983639805 -1.403065579
##  [696] -1.412644554 -2.770948936  1.260610439  2.204466006  1.867234399
##  [701] -0.558467811 -1.512541345  0.094455134 -1.034530966  1.373781608
##  [706]  1.268071765 -0.681137982  0.020782100 -1.530629913 -1.378582733
##  [711]  0.727454267  1.143484264 -0.217010851 -0.666479585  1.080584787
##  [716] -1.222750140 -0.456249558 -0.699946705  0.000000000  0.000000000
##  [721]  0.447259196  0.815730417  1.084728994  0.436925443  0.368900954
##  [726]  0.131761442 -0.349747212 -1.181499114  1.026831241 -0.132270528
##  [731] -1.115332334 -0.648549575 -1.316209600  0.226488352 -0.875210732
##  [736]  0.459562149  0.543908940 -0.802493462 -1.177362852  1.056170742
##  [741] -0.336322870 -1.825175079 -0.864872856 -1.521139363 -2.722041342
##  [746]  2.315625608  0.152149106  0.000000000  1.735662742  1.131145705
##  [751]  0.668143226  0.495031352 -0.540027731  0.253136694  0.000000000
##  [756] -1.489369488 -0.702080238  0.602296959  0.844117210  1.143109997
##  [761] -0.729155274  0.315839730 -0.205015559  0.091712829  1.942530421
##  [766] -0.118645287  0.827903963 -0.853236229 -0.482500360 -0.709168536
##  [771] -0.153050069 -1.394160584 -1.302835147 -1.462536563 -3.143553052
##  [776] -0.031434185  2.024211933  1.194282852 -1.884493852 -0.613068446
##  [781]  1.678769423  1.029027799 -0.851322590 -0.762802821  1.834756074
##  [786] -1.012744652 -0.413840671 -0.323213667 -1.165798108  0.085927430
##  [791] -2.126829268 -1.335725678  2.174176601 -0.530000396 -0.803212851
##  [796]  1.078285966  1.614054569  0.667369161  0.767620377  0.076946753
##  [801]  0.123020145 -2.284595300  0.565837557  0.789278318  0.000000000
##  [806]  1.946113588 -0.342244362 -0.206051818 -0.554429702  0.642110120
##  [811] -1.222540592  0.228195707 -0.100331867 -0.320611867 -0.383646580
##  [816]  0.704115771  0.409471936 -0.638633478 -0.995082665 -0.962064920
##  [821] -0.059232349  0.403018689  0.393530361  1.183803065  2.088095146
##  [826]  0.018973892  0.375611792 -0.650136075  1.658803835  0.093562874
##  [831] -0.826322677  0.380787212  0.060093897 -0.825794828  0.034063813
##  [836]  0.597805524 -0.793591094 -0.344997536 -0.962489538  0.437905735
##  [841] -0.829923127  0.038565368  0.343099460  0.238195858 -0.881530030
##  [846] -0.197208151  0.348702053 -1.235521236 -0.922595778 -1.377051768
##  [851]  0.920184037 -1.668979187  0.177390743  0.486960721  2.262805879
##  [856]  0.657946268 -0.291806085  1.194053147 -0.308487256 -0.375198236
##  [861] -1.285137444 -0.499508358  0.043481698 -0.881109487  0.661723671
##  [866] -1.207825123 -0.701487153 -0.750847731  1.297486374  0.642441277
##  [871] -0.103730301 -0.155757019  1.392000000  0.244595234  0.665092483
##  [876] -0.547323977  1.827902040  0.474830142 -0.188266031 -0.265609362
##  [881]  0.038596627  0.675180370 -0.325745382  0.215310085  0.019182812
##  [886] -1.350210970 -0.999300101  0.883704489  0.151833684  0.268221574
##  [891]  0.205474141  0.394629938 -0.728351767  0.058229814  1.299709020
##  [896] -0.838759096 -0.185392607  0.193475990 -0.513652338 -0.512422360
##  [901]  0.124863431  0.600155885  0.643061904  0.257890685 -0.153568549
##  [906]  0.538316607  0.818449535  0.519707143  0.045286437  0.000000000
##  [911]  0.848736326 -0.647091827 -1.031548829  0.000000000  0.000000000
##  [916] -0.627662812  0.769436895 -0.733171251  0.352072251 -0.190672311
##  [921] -0.645703588 -0.130749116  0.134770889 -0.011536243 -0.330743789
##  [926] -0.339558574  0.418150844  0.073257249 -0.805239838 -1.914860561
##  [931]  0.376192928 -0.366892852  1.156206692 -0.090030141 -0.477981508
##  [936] -0.129911031  0.942094682  0.113245861  1.002457386  1.235807523
##  [941]  0.251773861 -0.403348554  0.745014136 -0.056884979  0.022766942
##  [946]  0.242792109 -0.242204057 -0.569044006 -0.763067531 -0.146097655
##  [951]  0.477437240  0.015328020  0.846743295 -0.334333802 -0.602294820
##  [956] -0.272291467  0.722965698 -0.076359194 -1.173009323 -1.287454089
##  [961] -0.395582015 -1.073492981 -2.158359170  0.251878936 -0.705110021
##  [966]  0.530547280  0.474972598  0.674747475  0.232772806  0.740740741
##  [971] -0.417329094 -0.143683895 -0.847356009  1.850284194 -0.336420486
##  [976] -0.893530837 -0.024042314  1.527054108 -0.955351151  0.087687831
##  [981]  0.999561945  0.003942907  0.780664748  0.125190720  0.074239050
##  [986]  0.074183976 -0.027310678 -0.081954418  0.000000000  0.000000000
##  [991] -0.515564582 -1.189588159  1.088684043  0.652464429 -0.234301781
##  [996]  0.246594645  0.519308110 -0.287445618  1.176470588  0.000000000
## [1001]  0.931772678 -0.106813153  0.882150768  0.333118825  0.313148463
## [1006] -0.120355047  0.218406387  1.487938679  1.007034432  0.395865406
## [1011]  0.277473530 -0.247578825 -0.441638076 -0.978846647  1.858570900
## [1016] -0.029078220  1.021669575  0.000000000 -0.964549217  0.392484646
## [1021]  0.611764706  0.251852918  0.768016078 -0.089037681  0.000000000
## [1026]  0.156845970  0.352350785 -0.453965101 -0.409719253  0.250420348
## [1031] -0.049958962 -0.099967867  0.075050927 -0.885651025  0.994451250
## [1036]  0.092757760  0.399201597  0.940783868 -0.196954243 -0.260774571
## [1041]  0.522912765 -0.291729640  0.310208686 -0.713382064  0.077867837
## [1046]  0.707338638 -0.133450395 -0.351654535  0.518756396 -0.193090858
## [1051]  0.154771536  0.723492431  0.062763695 -0.219535143  1.009289656
## [1056] -0.594682433 -0.657368439 -1.190392830  0.283466799  0.226132429
## [1061] -0.119861806 -0.215304250 -0.084892646  0.297376713 -0.222371254
## [1066]  0.000000000  0.902080091 -1.332258178 -0.255836265 -0.231555698
## [1071] -0.114261230 -0.575534425  0.765828929  0.624420181 -0.457430588
## [1076]  1.111427757  1.486753100 -0.020828994  0.329861111 -0.096902578
## [1081]  0.488447016 -0.137892995 -0.334852251  0.232066780 -0.362844702
## [1086]  0.138729928  0.983617913 -0.236649861  0.326595160  1.178768461
## [1091]  0.623158465  0.959240685 -0.350046673  0.003345489 -0.097015924
## [1096]  0.140642266  0.879451597 -0.172368072  0.458228184 -0.571825213
## [1101]  0.844386822 -0.148343498  0.333443381 -1.460958836  0.687881925
## [1106]  1.001558717 -1.172221310 -0.305668151  0.473238686  0.802706647
## [1111]  0.329055610 -0.409970482  0.003293265  0.573009287  0.327439424
## [1116] -0.456919060  0.754098361  0.348193947  0.826928690  0.228354561
## [1121] -0.128357347  0.742216367 -0.347643044 -0.131220995 -2.522112550
## [1126]  0.677252852  0.542076217  0.035727045 -1.733766234  1.034163748
## [1131]  1.644919716  0.653111125 -0.163017420  0.454632772 -0.458949516
## [1136]  0.339395492 -0.038292169  0.558641384 -0.625376972 -0.287503194
## [1141]  0.371628116 -0.261729971  0.755248336  0.130224876  0.942109437
## [1146]  0.053422161  0.537077170  0.256169947  0.339648511  0.959597528
## [1151] -0.661334974  0.507818548  0.175606149  0.295239267  0.527413222
## [1156]  0.003050268  0.091505262 -1.090964498  0.027728995  0.462021807
## [1161]  0.591734118 -0.228595812 -0.036659131  0.537864434 -1.161164812
## [1166] -1.042563661  1.137458433  0.021510002  0.703533026  0.000000000
## [1171]  0.000000000  1.195887611 -0.584848211  0.000000000  0.000000000
## [1176]  0.000000000  2.632137550  0.333875018 -0.580128394 -0.236959806
## [1181] -0.195956177 -1.389260747 -0.926149391  0.267957736 -1.791733730
## [1186]  0.646278487 -1.090696817  1.195912155 -0.144269139 -0.098367711
## [1191] -0.950798486  0.071450761 -0.313538013 -0.616591928  0.213072633
## [1196]  1.206928898  0.367647059  0.960384154 -0.301838471 -1.477064220
## [1201]  0.996368377  0.273526338 -0.524105802 -0.089351738  0.320720387
## [1206]  0.215179367  0.184043434  0.186767092  0.247539881 -0.295704661
## [1211] -0.828594142  0.292893479  0.350445742  0.974145325  0.072811116
## [1216]  0.342569575  1.528747092 -0.169617616  0.915106713  0.446019790
## [1221] -0.505793095  0.735946090  5.093448347 -0.898964237 -1.225455672
## [1226]  0.978267070  0.502753848  0.564876486 -0.483456293  0.631827244
## [1231]  0.599955352  0.166430890  0.504001551  0.506984818  0.803245881
## [1236] -0.514005983  0.352642082 -0.836284391  0.170315633  0.213903743
## [1241] -0.164190132 -1.140257106  0.121995176  0.000000000  0.000000000
## [1246] -0.462462961  0.197529490 -0.960710815  0.241105722  0.394350440
## [1251]  0.498662804 -0.099792100 -0.074918838  0.746973231  1.243074888
## [1256] -0.705107263  0.578510131 -0.008177952  0.760611761 -1.022727273
## [1261] -0.196818107  0.000000000 -0.416324295 -0.676604874 -0.542755871
## [1266] -0.222741953 -1.381292555 -0.353696839  1.002385279  0.025302932
## [1271]  0.691438529 -0.276351050  0.000000000  0.573827852 -0.250487058
## [1276]  0.092075893 -1.039779221 -0.073239437  0.699103569  0.000000000
## [1281]  0.324729858 -0.714325576 -0.576134000  0.520111937 -0.323387981
## [1286]  0.662980308  0.109301869  0.377939530 -1.048668247  0.786380676
## [1291] -0.005593154  0.707573554  0.180510428 -0.374230748  0.172514539
## [1296]  0.783311575  0.421685087  0.323855528  0.872681512  0.385105633
## [1301] -0.051330542  0.646015785 -0.550557271  0.807453416 -0.125907471
## [1306]  0.606190655  0.165298070  0.380622837 -1.063293824  0.042881647
## [1311]  1.087655379  0.386918959  0.580781415 -0.635170604 -0.803000687
## [1316] -2.058369282 -0.595416112 -0.191455610  0.337060178 -2.605489553
## [1321]  0.535599114 -2.861765034  1.573537013  0.011307740  0.330714003
## [1326] -0.881814340 -0.676482292  0.000000000  3.153617216  0.518781557
## [1331]  0.157315155  0.925874897 -0.251187681 -0.279191986 -0.551712780
## [1336]  0.195964782  0.564707179 -0.120524831  0.663686477 -0.166189892
## [1341]  0.922388386 -0.389378617  0.792659754  0.333961756 -0.289901756
## [1346]  0.209982232 -0.800558779 -0.270811894 -0.985716613  0.230370513
## [1351] -0.842750431  0.284224178 -0.195366243  0.295001516  1.280994007
## [1356]  0.265986321 -0.414162742  0.225610916  0.802777175  0.158738700
## [1361] -0.878394714  0.002710027  0.130077776  0.000000000 -1.607621316
## [1366]  0.706917893  0.996940894  0.048678909 -0.078388971  1.076665044
## [1371]  0.029440103  0.607357860  0.303175363  0.000000000  1.116237141
## [1376]  0.115373522 -0.267148582 -0.278368655  0.208042557  0.223378535
## [1381]  0.222880667 -0.837214170  0.079151496  0.266265950 -0.397023637
## [1386] -0.340531123 -0.858209944  0.285874589  0.135869565  0.127703727
## [1391] -0.836986847 -0.238478028  0.059090543  0.289909537  0.350633013
## [1396]  0.949535901  0.808497146 -0.102217330  0.013118195  0.409233998
## [1401]  0.057477270 -0.107055199  0.802467522  1.076133181 -0.246286462
## [1406]  0.110588175 -0.238914864 -0.561378209  0.551599120  0.229216030
## [1411] -0.346892104 -0.848331700  1.009024003  0.473726217 -0.730301089
## [1416]  1.303562210 -0.354185247  0.081828875 -2.000613215  1.003780472
## [1421]  0.294269489 -0.715499048  0.062214849 -0.536269430  0.778787800
## [1426] -0.485888556  0.612923333  0.175529169  0.239641311 -0.375311689
## [1431] -0.147077796  0.000000000  0.000000000  1.354075146  0.665442864
## [1436] -0.154496872  0.000000000  0.000000000 -0.053269748 -0.413695084
## [1441] -0.022936949  0.560809605  0.539937641 -0.474005345  0.711860972
## [1446]  0.203747956 -0.100411688  0.691024224  0.319433006 -0.258712903
## [1451]  0.339194413  2.294250702  1.108033241 -0.853160298  0.043631075
## [1456]  1.332590313 -0.301269636  0.944912104  1.499132831  0.248115725
## [1461]  0.319884188  0.209472827  0.099872256  1.116061070  0.605796370
## [1466]  0.549688662  0.809817621 -0.175513602  0.628902464  1.128981676
## [1471] -0.529393523  0.774934865  0.117114131 -0.183190607 -1.311221669
## [1476]  0.911901775  0.779324585 -0.425203789 -0.710224130 -0.612799715
## [1481]  1.201766777  0.739969426  1.277737459  0.731781464  0.980835974
## [1486] -0.155836393 -0.019242693 -1.417817886  0.570511291 -1.719080281
## [1491] -0.803248107  0.336290626 -2.033031245  1.089378559  0.133591610
## [1496]  1.363040046  1.357873031  0.837571691  0.000000000  0.000000000
## [1501] -3.380408654 -0.288779794 -0.552498496  0.170254710  2.605389690
## [1506] -0.117698344  1.141273513 -0.179076140 -0.484156832 -0.388775466
## [1511]  1.245012319 -0.383339794  0.866914562  0.715862572  0.872507501
## [1516]  0.257378536  0.606022347  1.150362887 -1.319244846  0.440039394
## [1521]  1.289299647  0.875368170  0.000000000  1.141375368  1.536287474
## [1526] -0.819150628  0.553283618  0.000000000 -0.225279107  0.755290027
## [1531]  0.826970749  0.985405767  0.144128703  0.307291363  0.000000000
## [1536] -1.483276781  1.920881716 -0.042482524  0.088864848  0.303030303
## [1541] -0.128927974 -1.096339114 -0.019481405 -1.763410690  2.150111076
## [1546]  1.110679612  0.601090797  0.242435812  1.310176722  0.917293233
## [1551] -0.128520340 -0.994050616  1.047357119  0.380299019 -0.419715485
## [1556] -0.300261097  1.105520118  1.948196115  0.934613360  0.467474559
## [1561] -0.209384731  1.547676692  0.132452670  0.536164659 -1.398172026
## [1566]  0.608475963  0.344839782  2.301605484  0.716635945  1.718977166
## [1571]  1.103077182 -0.590426770 -1.534188821 -1.425561559  0.763595622
## [1576] -0.018816928  1.416668092 -0.998734711 -2.235741186 -2.032385700
## [1581]  1.007027844  3.396100122 -0.352646553 -0.037611981  0.701214298
## [1586] -0.779551630  1.496037384 -0.527869129  0.000000000 -2.156590146
## [1591] -0.100502513  0.813501700  1.892603362 -0.967562182 -0.668394489
## [1596] -0.295248558 -2.174437022 -1.805670439 -1.451742988 -1.689551696
## [1601]  3.228133787  1.971290837 -0.374334370 -3.404600621 -0.034698126
## [1606] -2.020497269  0.863274477 -3.554791482 -0.011500201  1.050472521
## [1611]  3.338708148  0.570904084 -0.009126419  1.000346836 -0.498834246
## [1616] -1.093491726 -1.623477989 -1.416917132  0.020830177  0.753516727
## [1621]  1.805813932  2.447487910  1.416114154 -0.319772606  1.677062912
## [1626]  0.443462867  0.036646656 -1.140863498  0.873462618 -0.433824301
## [1631] -0.319758249  1.429427524  1.221610162  1.785407725 -0.532973520
## [1636] -0.856309560 -0.420735775 -1.547498411 -0.570461603  1.636985701
## [1641]  0.750932192 -0.349536521 -0.156467615 -0.950609630  0.445093539
## [1646]  1.483417573 -1.018267410 -2.608905431  0.667044128 -2.741892961
## [1651] -4.586608837  3.774835691 -1.972987771  1.792995587  2.092478783
## [1656] -0.777554823  1.144776281 -0.789060268 -2.137690287  0.387967492
## [1661]  0.443247797 -0.909936359 -0.290761870  0.346978701  2.354239470
## [1666]  0.165318958 -0.044849485  1.412495289  1.329109444 -1.393764737
## [1671]  0.364879466  1.270670455  0.594252653  0.060633359  1.717481258
## [1676]  0.762540212  0.047298096  0.790180154  0.661696960  1.436179065
## [1681]  0.129608059 -0.763533884 -0.574579797 -0.051479624 -0.533337764
## [1686]  1.772291451  0.482544685 -0.114339851 -2.047390885  0.991669310
## [1691] -0.076041856  0.033086836  0.000000000  0.000000000  2.376502886
## [1696]  1.247092272 -0.033505648  0.000000000  0.000000000  2.098794988
## [1701] -0.332968579  0.224289098 -0.935837246 -1.238507472 -3.034326114
## [1706]  1.768364098 -0.316081241 -0.021138899  2.041148248  1.058335990
## [1711]  0.900574096 -0.095349746 -0.552304659  0.549078838  0.312940072
## [1716]  0.202776478  1.318493151  0.333399911  0.799338479  1.601191019
## [1721]  0.488935407 -0.175576949  0.940541669  1.256645009 -0.418544283
## [1726]  0.474488899  1.031949627 -1.090657280  0.625729288  0.092768412
## [1731]  1.233834880 -0.347614620 -0.186615371  0.481792556 -0.008587745
## [1736] -0.588311075  1.733621310  0.752965154  0.484645857  1.676196334
## [1741] -0.185618039 -1.776981886 -0.746090737  1.694148899 -0.134774635
## [1746]  0.820869565  0.416752915 -0.120933940  0.826923871 -0.911572052
## [1751] -0.340164160 -1.438540731  0.159833997  2.193510457  0.554756524
## [1756]  0.904508922  0.873450873 -0.752131262  1.542631373  0.079678100
## [1761]  0.652840253  0.395491398  0.305954960  1.140231450  1.317645841
## [1766] -1.065447066 -2.016967318  0.474427063  0.000000000  0.000000000
## [1771]  0.508912527 -0.608124861 -1.525675197 -0.618658418  0.622509626
## [1776] -1.746643378 -0.816924726 -0.593796604 -0.456954098 -2.472242578
## [1781]  1.794853619  0.859319508  2.203871966  0.000000000  3.234523198
## [1786] -0.583708512  0.192201364 -0.982813896  0.678078556  1.191496092
## [1791] -0.653858678 -0.583430572 -0.424645250 -0.413212195 -1.968242147
## [1796]  1.516672545  0.168377165  0.000000000  0.625683716  1.516698265
## [1801]  0.976871139 -1.272649672 -0.373354294  0.671926364  0.000000000
## [1806]  0.018286073  0.245510937 -1.086460925  1.403943157  0.570166894
## [1811] -0.343518351 -0.831951068 -2.015001437 -1.080230449 -1.007091434
## [1816]  0.626472551  2.354947420 -0.987742473  0.408653846 -0.090442370
## [1821]  1.504299901  0.565260728  1.653647022  0.284808909  0.831531681
## [1826]  0.001268730  1.981730525  0.113209425  0.642451505  0.827262625
## [1831] -0.073475386  0.823529412 -0.269836639 -0.153564899 -0.616424979
## [1836]  0.474090814 -0.273821894 -0.387345093  1.989786501  1.358557950
## [1841]  0.133320636 -0.847598669 -1.336818253 -0.285568464 -2.522636704
## [1846]  1.178941578  0.119856666  1.268712898  0.414356224 -1.217306875
## [1851]  0.380872813 -2.778389758 -1.221170309  1.359893961 -2.912145255
## [1856] -3.540854519  2.142885914 -0.721656260  1.637846569
## 
## 
## $CAC
## $CAC$x
##    [1] -1.295156428 -1.737480953 -0.644739077  0.806215951 -0.581276182
##    [6]  1.087013912  1.206715600 -0.289863864  0.033715750  0.312439110
##   [11] -0.339456669  0.162517520 -0.118936778  0.336601363 -0.127088491
##   [16]  0.343744832  0.498581510  0.118936778 -0.785854621 -0.626586061
##   [21] -0.165250729 -0.211922070  0.649726742 -0.104012078 -0.338028671
##   [26] -0.250702523  1.192868378  0.389899206 -0.416224367 -0.267435404
##   [31]  1.474310299  0.605394926 -0.095881300 -0.094526801 -3.461124681
##   [36]  1.997936847  2.752336985  1.356861648  0.753219684  0.976793633
##   [41] -0.298311662  0.120294834  0.318107437  0.352340246 -0.133888019
##   [46]  0.500108919 -0.738970862  0.411817256 -0.518530452 -0.336601363
##   [51] -0.901350805  0.124370342  0.923844064  0.764007406  0.116221323
##   [56]  0.021575667 -0.554343576  0.578086050  0.274429329  0.169352865
##   [61] -0.263245342 -0.465263357 -0.167985173  0.385538318 -0.264641513
##   [66]  0.358084978 -0.560643862 -0.661428091 -0.885274487 -0.524709963
##   [71]  0.257665760 -0.343744832  0.026970760 -0.610260769 -0.109436387
##   [76]  1.176547886  0.349472246 -0.497055264  0.444329005 -1.023485109
##   [81] -0.568550673 -0.428016575  0.078285614  0.191280879  0.863535834
##   [86] -0.225732653  0.610260769 -0.359523002 -0.093172475 -0.893283788
##   [91]  0.296902233 -0.654730623  0.146143003  0.930060100 -0.091818320
##   [96]  0.059363328 -0.695374126  1.077327344 -0.372499146 -2.471677151
##  [101] -2.061362980 -0.191280879  0.157054722 -1.435458325  0.125729300
##  [106]  1.377459942 -0.702259280 -0.266038199 -0.940500815 -1.696278006
##  [111]  0.744296449 -0.559066713 -0.697092314 -1.084582727 -1.367088290
##  [116] -1.554954248  0.513908791  1.458504802  0.911517835  0.474297479
##  [121]  0.804351175 -0.403026872 -1.330262031 -1.899050574 -0.970296201
##  [126]  2.897169268 -0.090464333  1.264572142 -0.209164881  1.139636266
##  [131]  1.258595595 -0.089110513 -0.963839475  1.067740821  0.885274487
##  [136] -0.566966480  0.384086320  2.289421602  0.213301268 -0.796919854
##  [141]  0.963839475  1.494600149 -0.798773547 -0.087756855  0.302543521
##  [146]  0.108080014 -1.454609861 -0.245140689  0.586072510  0.946814739
##  [151]  1.032634134 -0.651392890 -0.386991129  0.082343808 -1.021211206
##  [156] -0.114863917  0.469775625 -0.366724356  0.068821391  0.236812077
##  [161] -0.172089202 -0.239586428  0.760401672 -0.680001523  0.832624598
##  [166]  1.482353090  0.187162683  1.696278006  0.560643862  0.683403669
##  [171] -1.192868378  1.304571699  0.214680871 -0.180306035 -0.277230642
##  [176]  0.227116039  0.240974293 -0.844121708 -0.392810584  0.451782750
##  [181]  0.817464095 -1.340125919 -1.380950295  0.275829715 -0.978968627
##  [186]  0.703985770 -0.869423773 -0.404489757 -0.247920647 -1.707756416
##  [191]  0.597316848  1.559487170  0.330898947 -0.653060847  0.957422684
##  [196] -0.159785525 -0.819348844  0.686813744  0.052610867  1.519790077
##  [201]  0.043161383 -2.649174982  1.719464344  1.450736862 -0.623307755
##  [206]  0.433934970  0.859627120 -0.703985770 -0.086403358 -0.085050020
##  [211]  0.112149739  0.184418986 -0.368166900  0.339456669  0.530909576
##  [216]  0.534017037  1.398659855 -0.362401286 -0.083696837  0.495530174
##  [221]  0.263245342  0.029668592  0.751430255 -0.082343808  0.644739077
##  [226] -0.751430255 -0.571723349 -1.673969302  0.346607117  1.255624109
##  [231] -1.427943123  0.376838394 -0.774884781  1.279714656  0.071524788
##  [236] -0.887271474 -0.847978932 -0.080990929  0.869423773 -0.859627120
##  [241]  0.366724356 -1.564052364  0.127088491 -0.746076339 -0.079638199
##  [246] -1.028048865 -0.504698173 -1.310913362 -0.112149739 -0.605394926
##  [251]  0.654730623 -1.203927669 -0.959557224  1.070128233 -1.494600149
##  [256]  0.512370678  0.221585076  0.981148261 -0.346607117 -0.489441280
##  [261] -0.430973886 -1.099267451 -0.469775625  0.523163215 -0.875342009
##  [266]  0.554343576 -1.611610156  0.712649943 -0.232653959 -0.078285614
##  [271] -0.076933172 -0.408883624 -0.217441306 -2.271268723 -1.756079872
##  [276] -0.375391193 -1.830063448  0.398643373 -0.075580872  1.104215353
##  [281]  0.738970862  1.679468436 -1.109190438 -1.541543733  1.568650389
##  [286]  0.198151791  0.571723349 -0.326629195 -0.983332566 -1.285854591
##  [291] -1.044193418 -0.516988672 -0.520073465  1.652463885  0.239586428
##  [296] -1.209512942 -0.246530430 -0.646399844  1.060614828 -2.533393817
##  [301] -1.350121948  0.024273125  1.091895656 -0.097235975 -0.253486340
##  [306] -0.707445064  1.932851955  3.001150261 -0.176196131  0.032366639
##  [311] -0.953166636 -0.466766389  0.901350805  1.446885503  2.817407051
##  [316] -1.822914780  1.181953091 -0.460760541  1.502891083 -2.501345446
##  [321]  0.363841553 -0.309608718  0.044511053  0.723118123 -2.897169268
##  [326] -1.941657387  0.278632114 -0.813703281 -2.039299773 -3.153406194
##  [331]  0.094526801  2.220892296  1.096803562 -1.046522062 -0.235425586
##  [336]  1.657768635 -1.074921450 -1.124283082  0.796919854  0.823127102
##  [341]  2.568276871 -0.598929332  0.465263357  1.815858073  0.256272124
##  [346]  0.235425586 -1.424215576 -1.131926322  0.628227740 -0.074228709
##  [351]  2.161436385  0.879304589  0.047210641 -0.686813744 -0.463761374
##  [356]  0.623307755 -0.072876682  1.171176839 -1.409499686 -1.384457552
##  [361] -0.543370600 -0.376838394 -1.882932462  0.110792961 -2.418146732
##  [366]  2.328168205  0.039112832  0.978968627  0.563802354  1.144814095
##  [371]  1.089451538 -0.570136293  0.830719108 -1.032634134  0.382635132
##  [376] -1.307735956  1.320525901 -1.249714166 -0.681701610 -1.187393051
##  [381]  0.368166900 -0.538687927 -0.181676676  1.323757343  1.384457552
##  [386]  1.882932462 -0.271630167  1.673969302 -0.071524788  0.173457852
##  [391]  0.648062397 -0.685107711 -0.142055660 -0.070173025 -0.867457786
##  [396]  0.405953507  0.450290005 -0.881291064  0.420639577 -1.844648016
##  [401] -1.030338792 -0.871393127  1.084582727  1.198379702  0.557490953
##  [406]  0.028319650 -1.087013912 -0.445817767  0.430973886 -1.969017784
##  [411]  0.678303399 -0.915611117  0.200902759 -0.548065218  0.733666152
##  [416]  0.083696837  1.802009946  1.528404858  2.444036983 -0.273029480
##  [421] -0.631516191 -0.131167483  0.613512703  0.329475030 -0.728382008
##  [426] -1.152638890  1.310913362  1.014420963  0.543370600  1.028048865
##  [431] -0.851848813  0.454771268 -0.529357768  1.781864184  0.714389194
##  [436]  0.144780288 -0.395725296 -0.492483445  0.404489757  0.438383752
##  [441]  0.271630167 -0.932140112 -0.268833132 -1.232241021  0.961696145
##  [446] -0.615141105 -0.481855566 -0.288457923 -0.129807580 -1.235127068
##  [451]  0.629871114  0.135248658  2.108763102  1.119223863  0.392810584
##  [456]  0.098590829 -0.318107437 -1.292043388 -0.834533115 -0.877321577
##  [461]  0.940500815 -0.638113687  0.161151372 -0.068821391 -0.067469881
##  [466]  1.454609861 -0.238199023 -1.377459942 -0.202278813 -0.965987242
##  [471] -1.053542290 -0.961696145  0.615141105 -1.462421997 -0.348039324
##  [476]  0.774884781  0.742518914 -1.165839367  0.873365866 -0.206409282
##  [481] -0.780357962  0.155689761 -0.384086320 -1.950615992 -0.166617795
##  [486] -1.246775496  0.893283788  0.378286384 -1.498732738 -0.936312283
##  [491]  0.574901790 -0.597316848 -0.066118496 -0.064767230  1.223643862
##  [496]  1.478319741 -0.120294834  0.709177888 -0.905406385 -0.063416084
##  [501] -0.913562563  0.180306035 -0.495530174 -0.510833777  1.413150018
##  [506]  0.303955341  1.025764317 -0.302543521  0.457763852 -0.280034133
##  [511] -1.041870422  0.992117116 -1.012167918  0.507763585  0.899328566
##  [516]  0.315272007  0.362401286  0.968139475 -0.231268816  1.431690617
##  [521] -0.760401672 -0.369610210 -0.658075667 -1.018942572 -0.883281024
##  [526]  0.475806917  0.422113133  1.707756416  0.268833132  0.326629195
##  [531] -0.137970689 -0.062065052 -1.446885503  0.581276182  0.340885359
##  [536] -0.753219684 -1.114193130  0.861579831  1.391523619  0.549632774
##  [541] -0.475806917 -0.498581510  2.072781954  2.134359789  1.837306881
##  [546] -0.938404491 -0.507763585  0.624946069  1.507075579 -0.600543374
##  [551]  0.074228709  1.184668689 -0.340885359 -0.717874200 -0.060714135
##  [556] -0.621671114  1.039553035 -1.060614828 -0.587674282 -0.863535834
##  [561]  0.555916576  1.564052364  0.626586061  0.448798263  0.909476911
##  [566]  0.460760541 -1.144814095 -0.394267521 -1.373986290  0.093172475
##  [571] -1.009919999 -0.453276503 -1.016679169 -0.106723840  0.480341759
##  [576]  0.668155360 -2.220892296 -0.243751421  1.048856395  0.371054291
##  [581] -0.690231824 -0.771248856 -1.129371243  1.573281819  0.721367945
##  [586]  0.529357768  0.319526110 -0.643080086  0.099945863  0.552771947
##  [591]  1.298282071  0.266038199 -0.865495146  0.407418129 -0.897309997
##  [596] -0.624946069  0.035064922 -0.705714361  1.109190438  0.267435404
##  [601]  0.109436387  0.113506724  2.061362980  1.360254733 -0.281436703
##  [606] -0.855731495 -0.903376738  0.205032071 -0.710912844 -0.059363328
##  [611] -0.634811485  0.080990929 -1.577947245 -2.190197016  0.206409282
##  [616]  1.238023440 -1.252663668 -0.058012629  0.435416939  0.915611117
##  [621] -0.200902759  1.416819278  0.085050020 -0.303955341 -2.444036983
##  [626] -0.611885927 -0.135248658  2.039299773  0.101301081 -0.148869251
##  [631] -0.506230285  1.844648016  0.299721685  1.187393051 -0.170720874
##  [636] -0.563802354  1.229365201  0.277230642 -0.668155360 -0.174826828
##  [641] -1.725407795  0.285647748 -0.210543276  1.541543733  1.142221353
##  [646] -0.422113133  0.425063002  0.731902501  0.375391193  0.996538226
##  [651] -0.603776164  0.717874200 -0.117578942 -0.641422863  0.897309997
##  [656] -0.793220658 -1.134488812  1.021211206  1.317308188  0.408883624
##  [661]  0.582873468 -1.890930113 -1.346774976  0.428016575 -1.255624109
##  [666]  0.551201681  1.116704964 -0.825020643 -0.683403669  1.249714166
##  [671]  0.185790660  0.199527087 -0.150232789  1.295156428  0.838359300
##  [676] -0.236812077  0.955292497 -1.470324418  0.308194453 -1.713581019
##  [681]  0.544934137  0.095881300 -0.323786003 -1.000978901  0.294085140
##  [686] -1.096803562 -0.056662036  0.927984105 -1.327002669 -1.582647271
##  [691]  0.497055264  1.030338792 -1.768825039 -0.494006236  1.641991740
##  [696] -2.084477779 -1.668520329 -0.055311546  1.462421997  1.713581019
##  [701] -0.257665760 -0.838359300 -0.769434713 -0.512370678  1.668520329
##  [706]  1.749812815 -0.789532284  0.245140689 -1.217962298 -0.909476911
##  [711] -0.192654329 -0.110792961 -1.932851955 -0.828816630  0.365282575
##  [716] -1.034934930 -1.743613740 -0.203655249 -0.053961158 -0.052610867
##  [721]  0.809953940  1.220798154 -0.477317439 -0.320945426  1.333535586
##  [726]  0.170720874  0.195402322 -0.693657988  0.875342009  0.037763461
##  [731] -1.150022800 -1.524083329 -0.578086050  1.822914780 -0.957422684
##  [736]  0.651392890  0.724870519  0.154325089  0.693657988  0.857677680
##  [741] -0.410349998 -1.636822499  0.891276104 -0.301132303 -0.944705914
##  [746]  1.101738030  0.527807233 -0.051260673  0.447307518  0.055311546
##  [751]  0.333748798 -0.579680379 -0.925912101 -0.537129662 -0.049910572
##  [756] -1.079739490 -2.018186777  0.355211147 -1.788499010  0.091818320
##  [761] -1.142221353 -2.108763102  1.276662700  1.577947245 -0.316689404
##  [766] -0.742518914  1.034934930 -0.968139475 -0.459261681 -1.915677702
##  [771]  0.688521779 -1.323757343 -1.240930235 -0.429494761 -1.631696630
##  [776] -0.716130610  1.267577427  1.044193418 -1.592153635  0.253486340
##  [781]  0.702259280  0.532462664 -2.007958893 -1.065359478 -0.439868605
##  [786]  0.633162979  0.537129662  1.550453053 -0.048560562  1.405868039
##  [791] -0.474297479  1.545983054 -0.047210641 -0.045860805  2.175591776
##  [796]  1.235127068 -0.490961795  0.466766389 -0.673220713  0.828816630
##  [801]  0.773065541 -1.070128233 -0.214680871  0.948927784 -0.345175621
##  [806]  2.018186777 -0.207786884 -0.948927784  0.477317439 -0.123011613
##  [811] -1.507075579 -0.565383709 -1.273622589 -1.537134586 -0.044511053
##  [816]  0.270231385  1.007677172 -1.243847553 -0.535572701 -1.458504802
##  [821]  1.301420449  0.292677470  0.917663521  1.647205232  0.589277562
##  [826] -0.804351175  0.410349998 -1.596961269 -0.795068896 -1.137058773
##  [831] -1.731412828  0.147505990  0.887271474 -1.663120450  0.846048746
##  [836]  0.143417841 -0.911517835  1.150022800 -2.253834800 -0.185790660
##  [841] -0.278632114 -1.179246182  0.129807580  1.373986290 -1.320525901
##  [846] -0.163883972  0.216060883 -1.511286632  0.183047659 -1.443055487
##  [851]  1.157894875 -1.997936847  0.510833777  0.666470718  1.988111548
##  [856]  0.983332566 -0.136609547  1.743613740 -1.184668689 -1.420507713
##  [861] -0.484886501 -1.212319781 -0.549632774 -1.405868039 -0.116221323
##  [866] -0.994325241  0.386991129  1.346774976  2.190197016 -0.043161383
##  [871] -0.041811790 -1.616570833  1.775306882  0.970296201 -1.370529139
##  [876]  0.765814001  1.065359478  0.249311344 -0.040462274 -0.454771268
##  [881]  0.653060847 -0.315272007 -1.195619501 -0.140693743  0.079638199
##  [886] -0.923844064 -1.005439403  1.915677702  0.568550673  0.328051780
##  [891] -0.709177888  1.690621630 -0.669841901  0.867457786 -0.534017037
##  [896] -0.329475030  0.056662036 -0.873365866 -0.951045074 -0.972457450
##  [901] -0.220203400  0.643080086  0.063416084 -0.436899865  0.224349699
##  [906] -0.270231385  0.782187555  0.566966480 -0.216060883  0.791375125
##  [911] -0.616771139 -1.474310299 -1.657768635 -0.767623099 -0.039112832
##  [916]  0.260454538  0.784019770 -1.559487170  0.756805798 -1.215136204
##  [921] -0.355211147 -0.618402813 -0.358084978  0.520073465  0.925912101
##  [926] -0.919719798  0.207786884 -1.288942818 -1.333535586 -1.978474507
##  [931]  0.403026872  1.155262893  1.209512942 -0.749643230 -0.125729300
##  [936] -0.930060100  1.532755121 -0.714389194  1.336823495  1.490492928
##  [941] -0.194028142 -1.104215353  1.163183043 -0.353775332 -1.094346314
##  [946]  0.323786003  0.311023602 -1.478319741 -0.762203300 -1.147414556
##  [951]  0.211922070 -0.155689761  1.152638890 -1.198379702 -0.291270379
##  [956] -1.439246522  1.626613277 -0.144780288 -0.756805798 -1.261578236
##  [961] -1.431690617  0.445817767 -1.621571613  0.849912281 -1.267577427
##  [966]  2.348932362 -1.641991740  2.308361815  0.188535059  1.168503942
##  [971]  0.133888019  0.250702523 -1.276662700  1.111688306  0.932140112
##  [976]  0.072876682  0.776706588  1.907298228 -1.690621630  0.254878985
##  [981]  0.919719798 -0.602158982  0.847978932  0.526257967 -1.082157935
##  [986] -0.688521779  0.151596606  0.462260438 -0.037763461 -0.036414159
##  [991] -1.398659855  0.934224165  0.373944779  2.147701284 -0.586072510
##  [996]  1.314104058 -0.274429329 -0.649726742 -0.721367945 -0.035064922
## [1001]  0.877321577  1.621571613 -1.304571699 -1.014420963 -0.033715750
## [1006]  2.606596640  0.394267521  0.342314746  0.646399844 -1.314104058
## [1011]  0.463761374  0.189907790 -0.826917147 -1.264572142  0.674913004
## [1016] -0.802489192 -0.328051780 -0.032366639 -1.907298228  0.432453954
## [1021] -0.113506724  0.965987242  0.620036135  0.518530452 -0.031017587
## [1026] -0.360961770  0.426539323 -1.226499513 -2.328168205  0.559066713
## [1031]  0.746076339 -1.515524656  1.307735956 -0.891276104  0.664787965
## [1036] -1.190126255  0.350905885  1.082157935 -1.532755121  0.379735168
## [1041] -1.336823495 -0.724870519 -0.287052552 -0.261849685  1.012167918
## [1046]  0.492483445  0.883281024 -1.007677172  2.649174982 -0.158419976
## [1051]  0.587674282  0.036414159 -0.764007406 -0.029668592  0.181676676
## [1056] -1.181953091  0.123011613 -1.353484113  0.176196131  0.851848813
## [1061]  0.716130610  0.075580872  0.280034133 -0.853788545 -0.740743723
## [1066] -0.218822145  1.924193887 -0.544934137  0.322365390 -0.425063002
## [1071]  0.243751421 -0.633162979  0.287052552 -0.252094188 -0.028319650
## [1076] -0.026970760  1.147414556 -0.256272124  0.242362624  0.611885927
## [1081] -1.116704964 -0.382635132 -0.989913817 -0.161151372 -2.096465896
## [1086]  0.468270477  1.053542290 -1.808890648 -0.188535059  0.913562563
## [1091]  0.105367863 -0.992117116 -1.270594204 -0.448798263  0.758602509
## [1096]  0.231268816  1.201149064 -0.389899206 -0.730141123 -0.513908791
## [1101]  0.565383709 -1.051196457 -0.608637221 -2.568276871  0.541808390
## [1106]  0.800629988 -1.391523619 -1.402254840  1.079739490 -0.501637496
## [1111]  1.009919999  0.196776871 -0.296902233  0.494006236 -1.363663552
## [1116] -0.503167245  0.844121708  0.504698173  0.695374126 -1.486410698
## [1121] -0.671530349 -0.576493189 -0.842197799 -0.998756101 -1.163183043
## [1126]  0.202278813  2.050206632 -0.639767399 -0.747858595  2.533393817
## [1131]  0.938404491 -0.025621919  0.767623099  0.210543276 -0.594096529
## [1136]  1.725407795  0.456267049 -0.817464095 -0.778530978 -0.183047659
## [1141] -0.024273125  1.788499010  1.470324418 -0.849912281 -0.555916576
## [1146] -0.530909576  0.148869251 -0.523163215  1.173858130 -0.152960705
## [1151] -1.091895656 -0.784019770 -1.528404858 -0.480341759 -2.147701284
## [1156]  1.978474507  0.987715314  0.616771139  0.490961795 -0.441354429
## [1161] -0.121653111 -0.889272006  1.959733938 -0.907439769 -1.859635855
## [1166] -0.636461719  1.062984162  0.192654329  1.875053466 -0.022924375
## [1171] -0.438383752  0.538687927  0.114863917 -0.457763852 -0.021575667
## [1176]  1.731412828  1.663120450 -0.678303399 -0.787692121 -0.147505990
## [1181] -0.102656486 -0.405953507 -0.712649943  0.486403639  0.808083534
## [1186]  1.330262031  0.673220713 -0.381184749  0.234039548 -0.573311845
## [1191] -1.101738030  0.592488679  0.238199023  0.785854621  0.671530349
## [1196]  1.016679169  0.819348844  0.167985173 -0.198151791 -1.719464344
## [1201]  0.159785525 -0.349472246 -1.416819278  0.246530430  0.353775332
## [1206]  0.755011527 -1.413150018  0.391354480 -0.659750952 -0.733666152
## [1211] -0.456267049  0.252094188  0.787692121  1.114193130 -0.879304589
## [1216]  0.656402227  1.023485109 -0.388444757  1.215136204 -0.199527087
## [1221] -0.744296449  0.220203400  0.104012078 -1.573281819 -1.387981923
## [1226] -0.934224165  0.600543374  0.855731495 -0.700534881  0.719619975
## [1231]  0.117578942  0.142055660  0.356647694 -0.229884118  1.387981923
## [1236]  0.232653959  1.003206657 -0.590882359  1.134488812  0.509298081
## [1241]  0.685107711 -0.391354480  0.516988672 -0.020226997 -0.018878365
## [1246]  0.320945426  0.576493189 -1.077327344  0.106723840  0.291270379
## [1251]  0.762203300 -1.111688306  0.506230285  0.309608718  1.041870422
## [1256] -0.308194453  0.453276503 -0.356647694  0.936312283 -0.433934970
## [1261]  0.707445064 -0.017529767 -0.541808390 -1.062984162 -1.220798154
## [1266] -0.401564849 -0.016181201  0.089110513  1.285854591 -0.735432089
## [1271]  0.921779971  0.131167483 -0.014832664  0.570136293 -0.846048746
## [1276]  0.416224367 -1.282778578  0.503167245  0.165250729 -0.013484154
## [1281]  0.680001523 -0.821236508 -0.486403639  0.087756855  0.501637496
## [1286] -0.551201681  0.228499859  0.780357962 -1.490492928  0.821236508
## [1291]  0.749643230 -0.099945863 -0.595705916 -0.758602509  0.070173025
## [1296] -0.335174740 -0.420639577 -1.157894875  0.338028671  0.607015276
## [1301]  0.905406385 -0.333748798 -0.105367863  0.487921897 -0.325207270
## [1306] -0.413285400  0.102656486  0.584472241 -1.360254733 -0.996538226
## [1311] -0.222967175  0.261849685 -0.483370478 -1.139636266 -1.089451538
## [1316] -1.802009946  0.282839826  0.590882359 -0.809953940 -1.587382521
## [1321]  0.998756101 -1.450736862  0.953166636 -0.664787965 -0.196776871
## [1326]  0.372499146  1.270594204  0.663107092  0.634811485 -0.574901790
## [1331] -0.776706588 -0.234039548  0.051260673 -0.666470718 -0.444329005
## [1336]  0.132527628 -0.146143003 -0.012135669 -0.010787206  0.335174740
## [1341]  1.537134586 -0.987715314  0.795068896  0.163883972 -0.108080014
## [1346] -0.221585076 -0.830719108 -1.301420449 -0.432453954  0.325207270
## [1351] -0.371054291  0.639767399  0.562222407  0.417695198  0.735432089
## [1356]  0.972457450 -0.294085140  1.226499513  0.691943891  0.281436703
## [1361] -0.342314746 -0.471281838  0.441354429 -0.240974293 -0.663107092
## [1366]  0.658075667  0.951045074  0.048560562  0.158419976  1.121749883
## [1371] -0.527807233  0.802489192 -0.352340246  0.740743723 -0.139332087
## [1376]  0.436899865 -0.765814001 -0.589277562  0.521617717 -0.260454538
## [1381]  1.051196457 -0.532462664  0.313855244  0.842197799 -0.322365390
## [1386] -0.306780804 -1.279714656  0.137970689  0.471281838 -0.628227740
## [1391] -1.173858130 -0.132527628  0.700534881 -0.009438762  0.086403358
## [1396]  1.852089931  1.099267451 -0.162517520 -0.378286384 -0.008090336
## [1401]  0.974623251 -0.613512703  0.060714135  0.907439769 -0.584472241
## [1406]  0.478829051 -0.379735168  0.025621919  0.889272006  0.871393127
## [1411] -0.184418986 -0.282839826  0.793220658  0.994325241  0.136609547
## [1416]  1.203927669 -1.647205232 -0.791375125 -1.988111548  0.638113687
## [1421] -0.292677470 -1.626613277 -0.143417841 -0.468270477  0.798773547
## [1426] -1.343443023  1.046522062  1.232241021  1.212319781  0.388444757
## [1431]  0.097235975 -0.006741924  0.595705916  0.150232789  0.472789121
## [1436] -0.228499859 -0.005393524 -2.175591776  1.037241217  0.944705914
## [1441] -0.312439110  1.190126255  0.705714361 -0.981148261  1.343443023
## [1446]  1.596961269 -0.656402227  0.778530978  0.681701610 -0.861579831
## [1451]  0.177565765  1.240930235  0.726625143 -1.298282071  0.222967175
## [1456]  1.737480953 -0.800629988  1.435458325  0.524709963 -0.400103684
## [1461] -0.313855244  1.420507713  0.636461719  1.427943123 -0.173457852
## [1466] -0.582873468  0.631516191  1.000978901 -0.124370342  0.273029480
## [1471] -0.719619975 -0.942601281 -0.840277002 -0.557490953  0.217441306
## [1476]  1.443055487 -0.305367768  0.942601281 -0.899328566 -0.373944779
## [1481]  1.762416670  0.535572701  1.131926322  0.348039324  0.045860805
## [1486] -0.917663521 -1.601806100 -0.447307518  0.489441280 -1.924193887
## [1491] -0.629871114  0.815582246 -1.606688823  1.195619501 -0.385538318
## [1496]  1.601806100  0.853788545  0.301132303 -0.004045135 -0.002696752
## [1501] -2.393782545 -1.815858073 -0.698812562  0.152960705  1.899050574
## [1506]  0.264641513  1.395082856 -0.450290005 -1.317308188 -0.411817256
## [1511]  1.867289179  0.031017587 -0.319526110 -2.205284963 -1.025764317
## [1516] -0.398643373  0.710912844  0.259059897 -0.242362624  0.540247501
## [1521]  1.808890648  1.282778578 -0.001348375  0.579680379  0.621671114
## [1526] -0.857677680 -0.407418129  0.000000000 -0.435416939  1.969017784
## [1531]  0.895295078  1.795213515  0.066118496  0.298311662  0.001348375
## [1536] -1.238023440  1.179246182 -1.568650389  0.737200322 -2.817407051
## [1541]  0.881291064 -2.752336985 -0.254878985  0.203655249  0.641422863
## [1546]  0.811827184  0.400103684  1.859635855  0.959557224 -1.258595595
## [1551] -0.895295078  1.106699472  2.084477779  1.606688823 -0.526257967
## [1556] -1.229365201 -0.472789121 -0.509298081  0.603776164  0.209164881
## [1561]  0.771248856  2.471677151  0.836444677 -0.187162683 -1.168503942
## [1566]  2.501345446 -1.206715600  0.865495146 -0.177565765  0.429494761
## [1571] -0.676607229  0.669841901 -0.811827184  0.413285400  0.002696752
## [1576]  0.306780804  1.160534902 -1.039553035 -2.308361815 -0.189907790
## [1581]  1.511286632  2.393782545 -1.058251433  1.616570833 -0.224349699
## [1586]  0.062065052  1.409499686  0.229884118 -0.927984105 -1.749812815
## [1591] -0.365282575  1.631696630  0.602158982 -1.781864184 -0.500108919
## [1596]  0.483370478 -2.134359789 -0.169352865  0.004045135 -1.685018832
## [1601]  2.028630245  1.367088290 -0.823127102 -1.701989181 -0.285647748
## [1606] -1.067740821  0.090464333 -1.502891083 -1.837306881  1.165839367
## [1611]  3.153406194 -0.213301268  0.305367768 -0.178935732  0.548065218
## [1616] -0.808083534 -1.519790077 -1.126823516 -0.414754435  2.007958893
## [1621]  1.340125919  0.128447917  1.072521761 -0.128447917  1.243847553
## [1626] -0.755011527  0.813703281 -0.674913004 -0.737200322  0.121653111
## [1631]  0.608637221  1.439246522 -0.195402322  1.261578236 -0.592488679
## [1636] -0.515448120 -1.356861648 -1.875053466 -0.284243507  1.498732738
## [1641] -0.101301081 -0.426539323  0.040462274 -1.201149064 -0.462260438
## [1646]  1.363663552 -1.119223863 -2.606596640 -0.363841553 -2.370761549
## [1651] -3.001150261  3.461124681 -2.348932362 -0.098590829  1.636822499
## [1656] -0.546499008  1.582647271 -1.466361761 -2.289421602  0.005393524
## [1661]  0.006741924 -0.540247501  0.247920647 -0.157054722  2.370761549
## [1666]  0.345175621  0.295493393  0.989913817  1.327002669 -1.852089931
## [1671] -0.648062397  0.834533115  0.594096529  0.825020643  1.950615992
## [1676] -0.275829715 -0.451782750  0.401564849 -0.249311344  0.728382008
## [1681]  0.840277002 -0.976793633 -2.697177092  0.076933172  0.284243507
## [1686]  2.253834800 -0.723118123  0.058012629 -2.121387721  1.524083329
## [1691] -0.478829051  0.546499008  0.008090336  0.049910572  1.941657387
## [1696]  1.126823516  0.747858595  0.009438762  1.217962298  1.005439403
## [1701] -1.171176839 -1.072521761 -1.652463885 -1.223643862 -1.775306882
## [1706]  1.292043388  0.573311845  0.423587607  1.380950295  0.360961770
## [1711]  0.676607229 -0.419166933 -0.397183912 -0.832624598  1.058251433
## [1716]  1.587382521  1.094346314  1.370529139  1.124283082  0.459261681
## [1721]  0.041811790 -0.782187555  0.698812562  0.789532284  0.140693743
## [1726]  0.439868605  0.139332087 -1.762416670  0.289863864  1.074921450
## [1731]  1.592153635  0.053961158 -1.003206657  0.359523002  0.332323535
## [1736] -0.423587607  2.271268723  1.353484113  0.697092314  0.690231824
## [1741] -0.985521574 -1.037241217  0.414754435  2.205284963  1.129371243
## [1746] -0.227116039  0.481855566 -0.442841227  0.381184749  1.515524656
## [1751]  1.611610156 -0.332323535  0.903376738  0.022924375 -0.330898947
## [1756]  1.466361761  1.890930113 -0.974623251  0.661428091 -0.350905885
## [1761]  1.756079872  0.225732653  1.246775496 -0.205032071  1.273622589
## [1766] -1.867289179 -0.836444677  0.515448120  0.010787206  0.012135669
## [1771] -0.773065541  0.419166933 -1.055893934  0.397183912  0.598929332
## [1776] -0.726625143 -0.731902501 -0.417695198 -0.946814739 -2.237060137
## [1781]  2.096465896 -1.395082856  2.697177092  0.013484154  2.418146732
## [1786] -0.921779971  0.067469881 -0.955292497  0.014832664  2.121387721
## [1791] -0.607015276  0.769434713 -0.259059897 -0.620036135 -1.160534902
## [1796]  0.826917147  1.554954248  0.016181201  0.064767230  1.350121948
## [1801]  0.194028142 -2.072781954 -0.151596606  0.618402813  0.017529767
## [1806]  1.018942572  1.424215576 -0.815582246  1.486410698  0.442841227
## [1811] -0.154325089  0.178935732 -1.550453053 -1.959733938 -1.155262893
## [1816]  0.218822145  1.768825039 -1.048856395 -0.691943891 -0.311023602
## [1821]  1.055893934  1.402254840  1.701989181  0.288457923  0.730141123
## [1826] -1.106699472  1.252663668 -0.299721685  1.137058773  0.172089202
## [1831]  0.484886501  0.174826828 -0.552771947 -1.482353090  0.018878365
## [1836]  0.020226997  1.830063448  0.316689404  0.659750952 -0.521617717
## [1841] -1.121749883 -2.028630245  0.369610210 -0.806215951 -1.545983054
## [1846] -0.487921897  0.395725296  1.288942818 -0.562222407 -1.795213515
## [1851] -1.176547886 -1.679468436 -0.295493393  1.685018832 -2.161436385
## [1856] -2.050206632  2.237060137  0.166617795  0.985521574
## 
## $CAC$y
##    [1] -1.257897112 -1.856612396 -0.576251455  0.878168725 -0.510707446
##    [6]  1.178323514  1.320265206 -0.193467623  0.017103763  0.313515362
##   [11] -0.244345948  0.148105953 -0.034127752  0.341394026 -0.039693791
##   [16]  0.346040390  0.520097236  0.112479613 -0.696590079 -0.554392714
##   [21] -0.073951874 -0.108163498  0.689576566 -0.016979851 -0.243419190
##   [26] -0.153217569  1.301506110  0.398339318 -0.335289187 -0.173815531
##   [31]  1.595147158  0.635780628  0.000000000  0.000000000 -7.295500742
##   [36]  2.257777778  3.900092721  1.461319650  0.791600242  1.085355877
##   [41] -0.199633107  0.113531924  0.318608921  0.355278032 -0.042911549
##   [46]  0.520525892 -0.661968823  0.424548581 -0.444159041 -0.241883466
##   [51] -0.829786088  0.114099430  1.009443178  0.805931657  0.111928366
##   [56]  0.005323963 -0.479131175  0.588424093  0.271218890  0.153805357
##   [61] -0.169455624 -0.387226819 -0.074551361  0.389022116 -0.169869413
##   [66]  0.361586728 -0.482144749 -0.596283874 -0.814096728 -0.448188347
##   [71]  0.244087655 -0.254315243  0.010849517 -0.531568670 -0.021812630
##   [76]  1.281771572  0.350045775 -0.423956209  0.468876314 -0.976290098
##   [81] -0.498374865 -0.348432056  0.065559441  0.174710636  0.942882058
##   [86] -0.124183359  0.648718780 -0.273928456  0.000000000 -0.818656757
##   [91]  0.293239207 -0.584763658  0.136158161  1.033394974  0.000000000
##   [96]  0.043066322 -0.624192854  1.175005415 -0.283649987 -2.946543581
##  [101] -2.388984129 -0.090646422  0.141763538 -1.398640997  0.114856716
##  [106]  1.474215568 -0.627473149 -0.170658172 -0.866146219 -1.776168305
##  [111]  0.784176030 -0.481941702 -0.624307136 -1.027477689 -1.322892567
##  [116] -1.593122520  0.531492455  1.579970831  0.999042833  0.503465024
##  [121]  0.878123527 -0.321317988 -1.289415074 -2.119700748 -0.903851987
##  [126]  4.009549461  0.000000000  1.377199694 -0.104499274  1.232056721
##  [131]  1.366324129  0.000000000 -0.894829246  1.165780902  0.977235497
##  [136] -0.497874245  0.387923765  2.704973118  0.190850101 -0.712963971
##  [141]  1.068903141  1.616227357 -0.715200683  0.000000000  0.306418665
##  [146]  0.107186880 -1.424059104 -0.141204584  0.609126013  1.048705335
##  [151]  1.139463970 -0.581825875 -0.303256012  0.074710497 -0.975843865
##  [156] -0.026925148  0.500942634 -0.278700825  0.053746103  0.214868930
##  [161] -0.080403087 -0.134112977  0.800386764 -0.607513989  0.911479277
##  [166]  1.599277403  0.167346512  1.869061293  0.574005740  0.718507949
##  [171] -1.163673160  1.423086767  0.191793267 -0.085638003 -0.186548351
##  [176]  0.207102086  0.216755721 -0.759519139 -0.309173847  0.477909401
##  [181]  0.890553054 -1.298961834 -1.331300813  0.272942631 -0.919315906
##  [186]  0.746423388 -0.792344104 -0.321543408 -0.150884495 -1.797717680
##  [191]  0.620821394  1.687496704  0.337084479 -0.584039694  1.055367819
##  [196] -0.072023871 -0.736202636  0.720916965  0.036045314  1.652339527
##  [201]  0.030382824 -3.437278526  1.892529489  1.569252933 -0.547084747
##  [206]  0.458411858  0.932920955 -0.627919827  0.000000000  0.000000000
##  [211]  0.111212213  0.166633003 -0.282300751  0.343764218  0.544108016
##  [216]  0.546174275  1.500049836 -0.274954583  0.000000000  0.516961253
##  [221]  0.259600313  0.014656310  0.791324736  0.000000000  0.683338180
##  [226] -0.669073406 -0.503973638 -1.763101500  0.347050074  1.363636364
##  [231] -1.389159680  0.380604024 -0.689383494  1.403213011  0.058676837
##  [236] -0.816107120 -0.763697280  0.000000000  0.953279380 -0.781980032
##  [241]  0.371765639 -1.595140501  0.115427080 -0.666700085  0.000000000
##  [246] -0.979006863 -0.433187239 -1.274504786 -0.025922854 -0.528963336
##  [251]  0.693394505 -1.170135653 -0.890611903  1.168199598 -1.468206280
##  [256]  0.530278927  0.200443085  1.089703095 -0.260375983 -0.417689135
##  [261] -0.351281917 -1.036514785 -0.393428678  0.539097945 -0.801656403
##  [266]  0.567299973 -1.665691022  0.757657755 -0.128907509  0.000000000
##  [271]  0.000000000 -0.328062816 -0.113311390 -2.668539326 -1.881451881
##  [276] -0.294134284 -1.996936518  0.410998553  0.000000000  1.199123717
##  [281]  0.774752193  1.842849067 -1.054618117 -1.565129586  1.692597025
##  [286]  0.179331988  0.581785634 -0.233592881 -0.919834987 -1.243459180
##  [291] -0.991340018 -0.443088963 -0.445060979  1.805620065  0.216709438
##  [296] -1.172252888 -0.143951172 -0.576634760  1.159958242 -3.124641670
##  [301] -1.302006273  0.005996282  1.187192709 -0.005925575 -0.154074074
##  [306] -0.635052525  2.221956755  4.037630011 -0.084245998  0.016863406
##  [311] -0.876749283 -0.391222997  0.990437158  1.566903393  3.973362930
##  [316] -1.996157131  1.285263043 -0.381761480  1.630053436 -3.016623294
##  [321]  0.366902141 -0.212789175  0.032806605  0.765236403 -3.970707893
##  [326] -2.169123877  0.277152261 -0.731271953 -2.360788863 -4.295134557
##  [331]  0.093109870  2.586046512  1.190907992 -0.991696039 -0.132746033
##  [336]  1.812579300 -1.020710937 -1.073205828  0.860606061  0.895325081
##  [341]  3.108808290 -0.525616589  0.493554756  2.062749177  0.243432971
##  [346]  0.214604394 -1.386306002 -1.085776330  0.664394246  0.000000000
##  [351]  2.553948577  0.962560860  0.033257580 -0.615060675 -0.384701160
##  [356]  0.660435440  0.000000000  1.278843481 -1.356025254 -1.341273375
##  [361] -0.468212331 -0.294717751 -2.097544338  0.110317599 -2.865096857
##  [366]  2.734654884  0.023247704  1.086577571  0.574811749  1.240212608
##  [371]  1.179857740 -0.502148078  0.902820613 -0.983661220  0.387270584
##  [376] -1.269149055  1.432697208 -1.211478339 -0.610341904 -1.159947689
##  [381]  0.373928551 -0.464236589 -0.086370703  1.434993084  1.488551787
##  [386]  2.132900409 -0.180881386  1.839547526  0.000000000  0.156367950
##  [391]  0.689098250 -0.614874619 -0.053798149  0.000000000 -0.791258478
##  [396]  0.417774402  0.475470067 -0.812002581  0.439143399 -2.051171327
##  [401] -0.980932437 -0.795859305  1.178120617  1.308566676  0.569208035
##  [406]  0.010884354 -1.028459487 -0.362876622  0.452488688 -2.224785761
##  [411]  0.713523232 -0.847930380  0.180038258 -0.471751095  0.773050446
##  [416]  0.078391847  2.058971633  1.661093142  2.901207938 -0.183418929
##  [421] -0.556518087 -0.042236418  0.649659325  0.335852225 -0.653765690
##  [426] -1.121347723  1.426898094  1.128608924  0.555411368  1.135659715
##  [431] -0.770722744  0.478370454 -0.450496570  2.010696287  0.761203811
##  [436]  0.135081049 -0.314763927 -0.421010425  0.417757198  0.461129768
##  [441]  0.269420745 -0.860824999 -0.175667537 -1.191613455  1.058416446
##  [446] -0.538771400 -0.405001772 -0.193158136 -0.040743570 -1.192235186
##  [451]  0.665188470  0.122938224  2.394351786  1.219146597  0.399842038
##  [456]  0.098333251 -0.221032467 -1.255291917 -0.752779301 -0.808720113
##  [461]  1.043196435 -0.566330878  0.146169355  0.000000000  0.000000000
##  [466]  1.570285369 -0.133789208 -1.329760842 -0.095544604 -0.895958122
##  [471] -0.995479709 -0.892628123  0.652207671 -1.434816148 -0.260878639
##  [476]  0.826532747  0.783438830 -1.127413127  0.958033948 -0.103145952
##  [481] -0.691791430  0.140361822 -0.301095364 -2.181723510 -0.074523581
##  [486] -1.209247816  0.981396603  0.384471619 -1.500079791 -0.864070854
##  [491]  0.582883913 -0.519930676  0.000000000  0.000000000  1.339285714
##  [496]  1.595573224 -0.037015494  0.751163775 -0.834820960  0.000000000
##  [501] -0.841848891  0.160187954 -0.421153641 -0.438995664  1.516373609
##  [506]  0.307219662  1.135343507 -0.208855472  0.481372959 -0.187460946
##  [511] -0.986018364  1.101217135 -0.964144257  0.526232700  0.989373397
##  [516]  0.316193241  0.366868186  1.075988468 -0.127336627  1.540187678
##  [521] -0.678051231 -0.283185841 -0.593336376 -0.969288848 -0.813929528
##  [526]  0.503791420  0.444421477  1.888151464  0.267622702  0.327340484
##  [531] -0.050195763  0.000000000 -1.411209321  0.601090113  0.344321231
##  [536] -0.671140940 -1.061776062  0.934531451  1.490563158  0.561403509
##  [541] -0.403748380 -0.430408888  2.337270671  2.450884086  2.066254375
##  [546] -0.864255519 -0.435895006  0.661463786  1.630974330 -0.525630291
##  [551]  0.060790274  1.289840172 -0.253760266 -0.642952958  0.000000000
##  [556] -0.544692737  1.146842672 -0.999629767 -0.514210920 -0.789399493
##  [561]  0.568343279  1.690684751  0.662251656  0.473868237  0.998214204
##  [566]  0.489640477 -1.109857884 -0.310233131 -1.327170381  0.088122072
##  [571] -0.959221501 -0.369625228 -0.967408660 -0.018968134  0.507493834
##  [576]  0.707847671 -2.605313715 -0.139523695  1.151474272  0.376280067
##  [581] -0.616873873 -0.687547746 -1.081730769  1.705953827  0.764599063
##  [586]  0.540643081  0.320754717 -0.573631747  0.099309562  0.566920206
##  [591]  1.414008550  0.264035575 -0.790020790  0.419111484 -0.820812465
##  [596] -0.551737037  0.018806714 -0.629906454  1.201570557  0.266442294
##  [601]  0.107226107  0.111768267  2.325905940  1.463835978 -0.188180474
##  [606] -0.776585716 -0.832428520  0.182481752 -0.637522769  0.000000000
##  [611] -0.563703025  0.069133982 -1.621223287 -2.574906367  0.182604517
##  [616]  1.347851113 -1.211604903  0.000000000  0.459924304  1.001478373
##  [621] -0.094433165  1.517084928  0.079143389 -0.209331535 -2.918142831
##  [626] -0.532987612 -0.043446778  2.308509611  0.103851964 -0.061303405
##  [631] -0.434105601  2.080470120  0.301764160  1.291367739 -0.077682325
##  [636] -0.484748708  1.341850099  0.276606357 -0.601428959 -0.081888904
##  [641] -1.812138597  0.282865755 -0.106353463  1.671064204  1.233837188
##  [646] -0.341803463  0.446771064  0.772755863  0.378956754  1.114812347
##  [651] -0.527101819  0.763931820 -0.030676191 -0.569875504  0.987567234
##  [656] -0.711603947 -1.086048454  1.133534851  1.428508637  0.420350147
##  [661]  0.604151383 -2.118989405 -1.301546956  0.448450404 -1.215577068
##  [666]  0.563808842  1.214737029 -0.742955115 -0.611214457  1.359180036
##  [671]  0.167069686  0.179958741 -0.061338941  1.411661552  0.916479336
##  [676] -0.132796436  1.055205250 -1.438940532  0.310077519 -1.807487549
##  [681]  0.559660706  0.095656333 -0.230224578 -0.944792755  0.285701727
##  [686] -1.034361851  0.000000000  1.027457927 -1.288795371 -1.625366374
##  [691]  0.519140484  1.136210536 -1.940497336 -0.421138432  1.778080946
##  [696] -2.457441580 -1.758966607  0.000000000  1.585303306  1.891035939
##  [701] -0.157664760 -0.753474102 -0.686457244 -0.439439714  1.839080460
##  [706]  1.963882619 -0.699579367  0.227404468 -1.178930510 -0.837347499
##  [711] -0.090797657 -0.022720044 -2.163439687 -0.743287188  0.369746326
##  [716] -0.983912334 -1.860224169 -0.095973895  0.000000000  0.000000000
##  [721]  0.883808060  1.328381660 -0.404097359 -0.226457822  1.442216758
##  [726]  0.153824640  0.176859350 -0.617914886  0.958346968  0.023152436
##  [731] -1.115689088 -1.558988764 -0.508869549  2.065009560 -0.885162982
##  [736]  0.689883287  0.769627857  0.139710334  0.730130679  0.932594645
##  [741] -0.329338578 -1.716383662  0.980575271 -0.203458800 -0.871096284
##  [746]  1.196597177  0.540415704  0.000000000  0.473193366  0.036579790
##  [751]  0.338239327 -0.510204082 -0.851648352 -0.461808442  0.000000000
##  [756] -1.025331725 -2.292223316  0.359815774 -1.969501410  0.087774906
##  [761] -1.101096224 -2.473028228  1.399201899  1.708677892 -0.220404565
##  [766] -0.662674259  1.141473539 -0.898964237 -0.379609544 -2.127975454
##  [771]  0.723062143 -1.285140562 -1.200162734 -0.350010294 -1.704545455
##  [776] -0.641093011  1.385656865  1.147626500 -1.650335224  0.241216571
##  [781]  0.742833229  0.545227957 -2.287868615 -1.009513742 -0.357733995
##  [786]  0.669810310  0.548251450  1.683430386  0.000000000  1.509787589
##  [791] -0.394912299  1.673446270  0.000000000  0.000000000  2.557479996
##  [796]  1.343143548 -0.419042050  0.494201693 -0.603758886  0.901342216
##  [801]  0.825322847 -1.015986133 -0.111884030  1.051913899 -0.260240964
##  [806]  2.299961345 -0.103910826 -0.874704492  0.505604579 -0.037966874
##  [811] -1.509756445 -0.496505182 -1.225656429 -1.564569130  0.000000000
##  [816]  0.269058296  1.123037170 -1.203931204 -0.457597613 -1.434067856
##  [821]  1.419446416  0.284914526  1.006828490  1.786331113  0.610849857
##  [826] -0.717968486  0.422248107 -1.652892562 -0.712565728 -1.098792318
##  [831] -1.836652988  0.137649758  0.977497200 -1.744479177  0.923645320
##  [836]  0.132194427 -0.837818625  1.249423934 -2.665250594 -0.088330043
##  [841] -0.187217224 -1.151461470  0.115960363  1.474149731 -1.281519145
##  [846] -0.073579650  0.194603692 -1.511811024  0.165227588 -1.410099505
##  [851]  1.257556131 -2.260007462  0.528985112  0.705218618  2.257056669
##  [856]  1.090449349 -0.046899427  1.955059694 -1.155655553 -1.376099327
##  [861] -0.409148133 -1.174549668 -0.474337792 -1.354824890 -0.027142935
##  [866] -0.933970460  0.389169042  1.452361452  2.561756633  0.000000000
##  [871]  0.000000000 -1.684420423  2.001494449  1.077913244 -1.325257545
##  [876]  0.807932427  1.165755920  0.231493390  0.000000000 -0.374666393
##  [881]  0.690330225 -0.220005116 -1.163983181 -0.051880674  0.067479886
##  [886] -0.850710655 -0.957413414  2.197453912  0.578901122  0.334035665
##  [891] -0.635115755  1.850515464 -0.602257199  0.952138493 -0.453926464
##  [896] -0.238131428  0.040629761 -0.797035232 -0.875083158 -0.913784202
##  [901] -0.114625124  0.683323770  0.046627293 -0.357309306  0.202681634
##  [906] -0.176339401  0.841689614  0.577051883 -0.112699145  0.856454177
##  [911] -0.539001322 -1.441717791 -1.742919390 -0.686305564  0.000000000
##  [916]  0.249840527  0.843098786 -1.593227469  0.796152819 -1.176844784
##  [921] -0.268211565 -0.543244406 -0.270401817  0.536847243  1.014023732
##  [926] -0.848996155  0.183100867 -1.247110681 -1.295520113 -2.233496939
##  [931]  0.417418773  1.252668240  1.320388350 -0.668017303 -0.038586627
##  [936] -0.854747987  1.663051338 -0.640113798  1.448158141  1.612027790
##  [941] -0.090807115 -1.042557742  1.269652601 -0.266752027 -1.032416818
##  [946]  0.324306794  0.312483164 -1.444760728 -0.681198910 -1.113854595
##  [951]  0.188658307 -0.066459903  1.252493904 -1.165845649 -0.193830647
##  [956] -1.403839751  1.772750295 -0.055297501 -0.675002766 -1.219919786
##  [961] -1.392883325  0.468946586 -1.690573770  0.926408430 -1.221960874
##  [966]  2.741317226 -1.718485020  2.714828023  0.167991936  1.274597496
##  [971]  0.121439611  0.231558055 -1.226622662  1.202873531  1.034501733
##  [976]  0.059909591  0.827345961  2.191751242 -1.769677760  0.242000538
##  [981]  1.008583691 -0.525812620  0.923701212  0.539625436 -1.026099768
##  [986] -0.616726035  0.139089499  0.491479246  0.000000000  0.000000000
##  [991] -1.350273776  1.034649997  0.378686863  2.465462274 -0.513378967
##  [996]  1.428199114 -0.185004368 -0.581784482 -0.647332988  0.000000000
## [1001]  0.959082617  1.765708090 -1.263254021 -0.965984996  0.000000000
## [1006]  3.180450348  0.402272842  0.345570191  0.683769215 -1.278937193
## [1011]  0.492091388  0.169889572 -0.743253355 -1.221228264  0.712286950
## [1016] -0.717352867 -0.234060958  0.000000000 -2.121691233  0.453337502
## [1021] -0.025936300  1.074041405  0.657084189  0.535495716  0.000000000
## [1026] -0.273930909  0.447632128 -1.190054185 -2.777777778  0.569319979
## [1031]  0.786245938 -1.513417932  1.425780219 -0.817410319  0.703412073
## [1036] -1.162427023  0.353356890  1.177212529 -1.563473925  0.385203947
## [1041] -1.298359966 -0.649731054 -0.192977754 -0.166496590  1.124381321
## [1046]  0.516039794  0.973854134 -0.959220044  3.244244509 -0.071765430
## [1051]  0.610444239  0.020394636 -0.683081001  0.000000000  0.164245753
## [1056] -1.152959262  0.114048730 -1.310066280  0.157405950  0.927235581
## [1061]  0.763002180  0.061814248  0.277992278 -0.775193798 -0.662251656
## [1066] -0.114583333  2.200438002 -0.469387755  0.322944433 -0.342343263
## [1071]  0.220467596 -0.562746201  0.282965478 -0.153909296  0.000000000
## [1076]  0.000000000  1.243448772 -0.157328461  0.218573680  0.649218909
## [1081] -1.063293691 -0.300514440 -0.929804843 -0.072194719 -2.461554340
## [1086]  0.497328184  1.152934983 -1.977724576 -0.090262292  0.999096562
## [1091]  0.105235464 -0.930354796 -1.225594228 -0.365257560  0.797886679
## [1096]  0.208589613  1.312980359 -0.305552629 -0.655252589 -0.441489362
## [1101]  0.577015547 -0.993359894 -0.531172873 -3.409029613  0.552856425
## [1106]  0.871931578 -1.348896107 -1.350597165  1.176736818 -0.430552449
## [1111]  1.123153816  0.177708669 -0.199567604  0.516580570 -1.320733864
## [1116] -0.431203450  0.922384702  0.523851984  0.731788447 -1.458447991
## [1121] -0.603183468 -0.505703208 -0.756762862 -0.944630968 -1.125983800
## [1126]  0.180117367  2.314116692 -0.566861289 -0.667008722  3.036042241
## [1131]  1.041608645  0.000000000  0.810363837  0.185924427 -0.518530648
## [1136]  1.909360255  0.479164423 -0.734072764 -0.690920868 -0.086965975
## [1141]  0.000000000  2.012838647  1.594496587 -0.766363970 -0.481354139
## [1146] -0.451791219  0.138822147 -0.447880565  1.280059986 -0.063458488
## [1151] -1.031855223 -0.695075656 -1.561406343 -0.404747580 -2.526223296
## [1156]  2.253648093  1.096479145  0.654022237  0.514403292 -0.360933039
## [1161] -0.037846021 -0.816701823  2.246700840 -0.837333333 -2.086806863
## [1166] -0.565778632  1.160092807  0.174748799  2.126035761  0.000000000
## [1171] -0.357638518  0.551775861  0.111880661 -0.377840456  0.000000000
## [1176]  1.944444444  1.813037099 -0.607308286 -0.699047225 -0.057360380
## [1181] -0.015652718 -0.323540156 -0.638710015  0.511091206  0.880687775
## [1186]  1.439409686  0.712053686 -0.300101729  0.214274782 -0.503996335
## [1191] -1.038681948  0.615273254  0.215827338  0.846067070  0.711852341
## [1196]  1.130913313  0.893614897  0.153389411 -0.093868880 -1.809909999
## [1201]  0.146051571 -0.261503646 -1.366409519  0.230037828  0.357015352
## [1206]  0.792803781 -1.356325316  0.398691474 -0.595662356 -0.655569782
## [1211] -0.376346858  0.232871041  0.846713821  1.208211744 -0.809347969
## [1216]  0.693559080  1.134464421 -0.305473484  1.326100060 -0.094189966
## [1221] -0.664913412  0.199810180  0.104691161 -1.618525896 -1.346494558
## [1226] -0.862024732  0.631437296  0.930926297 -0.626783530  0.764063381
## [1231]  0.111959288  0.132167548  0.360442685 -0.126460620  1.489059968
## [1236]  0.209601757  1.120517928 -0.517114011  1.227722772  0.528169014
## [1241]  0.719984433 -0.309119011  0.532945736  0.000000000  0.000000000
## [1246]  0.322891566  0.586059471 -1.022016333  0.106151990  0.284378464
## [1251]  0.802653081 -1.058503791  0.525275890  0.311601151  1.146953405
## [1256] -0.212615167  0.478219697 -0.268601857  1.039501040 -0.355405911
## [1261]  0.750891684  0.000000000 -0.465809577 -1.001497566 -1.181809587
## [1266] -0.320512821  0.000000000  0.081585641  1.409801477 -0.657272555
## [1271]  1.009091342  0.117807832  0.000000000  0.578932505 -0.762787215
## [1276]  0.429123833 -1.230220219  0.522937961  0.151336013  0.000000000
## [1281]  0.717759834 -0.740775470 -0.410939493  0.080629862  0.521302308
## [1286] -0.476168026  0.208432023  0.841448426 -1.462591412  0.894386299
## [1291]  0.787438702 -0.009356725 -0.519346839 -0.677264604  0.056823563
## [1296] -0.241362991 -0.341572181 -1.123435045  0.341822734  0.642932540
## [1301]  0.991609458 -0.240747734 -0.018927743  0.511145819 -0.230729387
## [1306] -0.330375684  0.104176532  0.605487228 -1.316531879 -0.938631599
## [1311] -0.120244336  0.255224887 -0.408280897 -1.099643098 -1.028967132
## [1316] -1.970928800  0.281477758  0.611498171 -0.722363374 -1.630871136
## [1321]  1.117175942 -1.417616789  1.054193746 -0.597559123 -0.091701055
## [1326]  0.377339248  1.391922784  0.701437948  0.671675208 -0.504102007
## [1331] -0.690443076 -0.130045516  0.035057845 -0.600781015 -0.362647325
## [1336]  0.121322414 -0.055538726  0.000000000  0.000000000  0.338469310
## [1341]  1.666498842 -0.926063487  0.859742077  0.148676777 -0.019794141
## [1346] -0.118788359 -0.748265610 -1.263168406 -0.353964401  0.324774180
## [1351] -0.283257461  0.679719996  0.574365175  0.430818555  0.773144453
## [1356]  1.079047666 -0.195876793  1.339482852  0.726251574  0.278792540
## [1361] -0.254050427 -0.394060262  0.463163989 -0.134466695 -0.596297187
## [1366]  0.696628126  1.052125871  0.033279452  0.142578775  1.219685824
## [1371] -0.450112528  0.876036172 -0.266131291  0.777117176 -0.051098620
## [1376]  0.460122699 -0.684709692 -0.517072716  0.538490354 -0.163010572
## [1381]  1.152267214 -0.451966979  0.315033588  0.919041241 -0.228812008
## [1386] -0.210989817 -1.227247656  0.125645679  0.501952036 -0.554938957
## [1391] -1.148623512 -0.042338994  0.738893072  0.000000000  0.079420696
## [1396]  2.105312296  1.193251954 -0.072286979 -0.298399494  0.000000000
## [1401]  1.083801923 -0.533847741  0.045101930  0.996303309 -0.513324108
## [1406]  0.506999282 -0.299093790  0.008954957  0.980479943  0.957659056
## [1411] -0.087831013 -0.189002681  0.858728202  1.109025019  0.125232111
## [1416]  1.315448978 -1.719807586 -0.701693594 -2.259541985  0.673896550
## [1421] -0.195052753 -1.692280359 -0.054217684 -0.393291443  0.871380594
## [1426] -1.300278953  1.148744131  1.343007797  1.325210121  0.390607856
## [1431]  0.096179068  0.000000000  0.620195667  0.138900946  0.502817512
## [1436] -0.125075477  0.000000000 -2.534870665  1.143110323  1.046959874
## [1441] -0.216759873  1.299039840  0.750557557 -0.919501086  1.452201933
## [1446]  1.727861771 -0.586986387  0.829145729  0.718498214 -0.783472846
## [1451]  0.157931923  1.352753226  0.769703173 -1.259497014  0.201621199
## [1456]  1.954664915 -0.716932496  1.545638945  0.539331229 -0.317889216
## [1461] -0.219245794  1.526107627  0.672883957  1.528298937 -0.080846968
## [1466] -0.512445095  0.666124472  1.119532182 -0.038045960  0.270229124
## [1471] -0.645283735 -0.867239733 -0.755356868 -0.481515999  0.199001093
## [1476]  1.549904591 -0.210913832  1.045269387 -0.821480186 -0.287598742
## [1481]  1.976694997  0.546819022  1.226464631  0.348290044  0.033231178
## [1486] -0.848959102 -1.656615293 -0.363402355  0.512898446 -2.162080435
## [1491] -0.556328234  0.885780886 -1.659735059  1.307906175 -0.301495883
## [1496]  1.744659404  0.929771749  0.302034961  0.000000000  0.000000000
## [1501] -2.819287085 -1.994732357 -0.624431886  0.139192682  2.156473392
## [1506]  0.260467286  1.496704149 -0.366748166 -1.280674847 -0.330148373
## [1511]  2.123845524  0.015263680 -0.221289584 -2.584888345 -0.977390485
## [1516] -0.317120545  0.751580705  0.244711083 -0.137806126  0.551985175
## [1521]  2.062502451  1.406123939  0.000000000  0.598598219  0.659059240
## [1526] -0.781951512 -0.324295788  0.000000000 -0.355616086  2.247617601
## [1531]  0.983996138  2.022356229  0.050457724  0.298991354  0.000000000
## [1536] -1.192400244  1.283123114 -1.604220500  0.773242879 -3.916175033
## [1541]  0.964327419 -3.622728799 -0.154846702  0.182227047  0.681140911
## [1546]  0.884105324  0.415317203  2.105942172  1.055408971 -1.217225021
## [1551] -0.819000819  1.201111028  2.377420073  1.746187009 -0.448638063
## [1556] -1.191029722 -0.394555853 -0.436094051  0.635106034  0.184976969
## [1561]  0.818188401  2.966101695  0.913719746 -0.089853470 -1.131096506
## [1566]  2.998285694 -1.171875000  0.945179584 -0.085120872  0.449821094
## [1571] -0.607253113  0.709946071 -0.728665356  0.426752245  0.000000000
## [1576]  0.309355453  1.264106822 -0.983935743 -2.768201176 -0.090381340
## [1581]  1.635294527  2.820855157 -0.998834693  1.762233059 -0.122277669
## [1586]  0.046323870  1.511443313  0.208516600 -0.851838606 -1.872438105
## [1591] -0.277369336  1.776079890  0.632182016 -1.963158067 -0.430530988
## [1596]  0.509485822 -2.487827653 -0.075239398  0.000000000 -1.769457184
## [1601]  2.303055643  1.467883659 -0.741784983 -1.792235899 -0.192824186
## [1606] -1.010832816  0.083644094 -1.507817669 -2.047093763  1.274138242
## [1611]  4.112908974 -0.109544023  0.308430432 -0.085411684  0.560779620
## [1616] -0.720867762 -1.544679248 -1.078410909 -0.334083556  2.275854769
## [1621]  1.448975367  0.115622662  1.168478261 -0.040290089  1.353620852
## [1626] -0.672742336  0.884158548 -0.605218772 -0.658814135  0.113879957
## [1631]  0.645700903  1.549047635 -0.091656028  1.372825268 -0.517129929
## [1636] -0.441845354 -1.315102467 -2.096491518 -0.189144459  1.617542554
## [1641] -0.013320457 -0.343047460  0.023394158 -1.166093087 -0.382014875
## [1646]  1.466046764 -1.063580722 -3.421114905 -0.276523504 -2.786942787
## [1651] -4.271374928  6.287481613 -2.785663591 -0.007300602  1.777826452
## [1656] -0.469870875  1.711773397 -1.438492063 -2.685311669  0.000000000
## [1661]  0.000000000 -0.465442725  0.230098348 -0.066649387  2.745563007
## [1666]  0.346195456  0.287500898  1.096538379  1.435559336 -2.068700423
## [1671] -0.578055308  0.911603201  0.615286126  0.897843761  2.245655830
## [1676] -0.185026555 -0.367306306  0.416896362 -0.150969291  0.769732999
## [1681]  0.917306053 -0.919105224 -3.536593684  0.063637971  0.282655549
## [1686]  2.603671212 -0.648993888  0.041475132 -2.473656936  1.657869567
## [1691] -0.404223438  0.559812463  0.000000000  0.034793501  2.239922090
## [1696]  1.224698078  0.786422450  0.000000000  1.327153290  1.122190410
## [1701] -1.142280656 -1.020508938 -1.722819037 -1.187857457 -1.962463182
## [1706]  1.411353712  0.582176444  0.445235975  1.476404801  0.366251134
## [1711]  0.713090057 -0.339061929 -0.316867349 -0.749514823  1.156361675
## [1716]  1.716380603  1.189384010  1.473302464  1.222158402  0.485482803
## [1721]  0.028235294 -0.693137624  0.735874680  0.849636318  0.130568595
## [1726]  0.462603620  0.129797886 -1.891975309  0.283134615  1.173259717
## [1731]  1.717776193  0.036579790 -0.947679556  0.366086261  0.337164751
## [1736] -0.342141439  2.633111608  1.457499552  0.732999706  0.724743564
## [1741] -0.922621638 -0.983923395  0.428829149  2.573767595  1.225884244
## [1746] -0.124790834  0.508306120 -0.361643216  0.385640560  1.641150218
## [1751]  1.750826779 -0.240351788  0.991101985  0.005421964 -0.238553498
## [1756]  1.586913399  2.145245419 -0.913923587  0.697711296 -0.262453415
## [1761]  1.976211778  0.206435631  1.354518065 -0.099087883  1.393692777
## [1766] -2.094411558 -0.753208823  0.531763856  0.000000000  0.000000000
## [1771] -0.688149955  0.436952194 -0.996241569  0.408226943  0.624093640
## [1776] -0.651105335 -0.655372500 -0.338974212 -0.873865153 -2.620951778
## [1781]  2.379790752 -1.350206502  3.802801782  0.000000000  2.880115825
## [1786] -0.849395622  0.050690660 -0.879037365  0.000000000  2.415150276
## [1791] -0.529034512  0.812824565 -0.161751897 -0.543369890 -1.125256879
## [1796]  0.899804831  1.685590836  0.000000000  0.046937918  1.454392810
## [1801]  0.175237910 -2.393158240 -0.062229303  0.655059902  0.000000000
## [1806]  1.133326735  1.526792268 -0.732636044  1.604758437  0.465938687
## [1811] -0.064215383  0.159451677 -1.591978330 -2.192389415 -1.123234917
## [1816]  0.199735351  1.983405178 -0.991961690 -0.616933593 -0.216025625
## [1821]  1.154630966  1.507995080  1.878195962  0.283077216  0.770927723
## [1826] -1.052210348  1.360770786 -0.201844767  1.229980480  0.155654679
## [1831]  0.510310594  0.156931527 -0.476969515 -1.453972958  0.000000000
## [1836]  0.000000000  2.065125458  0.317657620  0.697551685 -0.446621853
## [1841] -1.071207856 -2.359963906  0.374398711 -0.720035884 -1.567032863
## [1846] -0.413093369  0.407529594  1.410900657 -0.483609682 -1.970172121
## [1851] -1.150183150 -1.766347983 -0.196157328  1.846998942 -2.533461986
## [1856] -2.373397639  2.592303692  0.152064272  1.095730951
## 
## 
## $FTSE
## $FTSE$x
##    [1]  0.875342009 -0.755011527  1.160534902  0.747858595 -1.065359478
##    [6]  1.072521761  1.014420963  0.087756855 -0.808083534  1.781864184
##   [11]  1.252663668  0.199527087 -0.826917147 -0.400103684  0.865495146
##   [16]  1.470324418 -0.489441280 -0.150232789  0.465263357  0.277230642
##   [21]  0.016181201 -0.448798263  0.124370342  0.475806917 -0.927984105
##   [26] -0.733666152  1.215136204  0.143417841 -1.559487170 -0.174826828
##   [31]  0.789532284  1.181953091  0.411817256  0.176196131 -3.153406194
##   [36]  0.710912844  2.253834800  0.998756101  0.871393127 -0.098590829
##   [41] -1.157894875  0.206409282  0.680001523  0.360961770  1.621571613
##   [46] -0.623307755 -0.320945426 -0.178935732  0.189907790 -0.823127102
##   [51] -1.217962298 -0.312439110  0.753219684 -0.901350805 -1.104215353
##   [56] -0.693657988 -0.653060847  0.238199023  0.565383709 -1.171176839
##   [61] -0.256272124  1.007677172 -0.220203400  0.155689761  1.109190438
##   [66]  1.165839367 -0.184418986 -1.039553035 -0.158419976 -1.466361761
##   [71]  0.146143003 -0.885274487 -0.796919854 -0.911517835  0.961696145
##   [76]  0.089110513  0.093172475  0.466766389  0.608637221 -1.380950295
##   [81] -0.930060100  0.058012629 -1.707756416 -0.832624598  2.161436385
##   [86] -0.360961770  1.203927669 -0.673220713 -0.963839475 -1.226499513
##   [91]  0.664787965 -0.453276503  0.187162683  1.021211206 -0.313855244
##   [96]  0.994325241 -1.532755121  0.771248856 -0.881291064 -2.147701284
##  [101] -2.061362980  0.472789121 -0.581276182 -1.034934930  0.504698173
##  [106]  0.815582246 -1.370529139 -1.137058773 -0.554343576 -0.382635132
##  [111]  0.275829715  0.181676676 -1.023485109 -1.114193130  1.111688306
##  [116] -1.072521761 -0.760401672  2.237060137  1.507075579 -0.683403669
##  [121] -0.540247501 -1.163183043 -1.282778578 -1.859635855 -0.838359300
##  [126]  2.061362980 -0.097235975 -0.095881300  1.815858073  0.051260673
##  [131]  2.817407051 -0.094526801 -0.117578942  0.573311845 -0.680001523
##  [136] -0.649726742 -0.948927784  1.587382521 -1.173858130  0.629871114
##  [141]  1.353484113  1.018942572  0.214680871 -0.348039324  0.413285400
##  [146] -0.188535059 -1.209512942  0.154325089 -0.883281024  1.524083329
##  [151]  0.602158982 -0.379735168  0.207786884  0.989913817 -0.668155360
##  [156] -0.282839826 -0.595705916 -0.773065541 -0.998756101  1.051196457
##  [161] -0.183047659 -0.817464095 -0.166617795 -0.552771947  1.370529139
##  [166]  0.762203300 -1.099267451  0.336601363 -0.165250729  0.883281024
##  [171] -0.774884781  0.915611117 -0.264641513 -0.006741924 -0.512370678
##  [176]  0.543370600 -0.475806917 -1.147414556 -0.362401286  0.901350805
##  [181]  1.223643862 -2.308361815 -1.564052364 -1.028048865 -0.376838394
##  [186]  1.028048865 -1.439246522  0.135248658 -0.697092314 -0.940500815
##  [191]  0.936312283  0.328051780  0.378286384 -1.384457552  0.246530430
##  [196] -0.809953940 -1.725407795 -0.284243507 -1.327002669  0.963839475
##  [201]  0.162517520 -0.719619975  2.220892296  3.461124681  0.917663521
##  [206]  0.456267049  1.915677702 -0.192654329 -0.093172475 -0.091818320
##  [211] -0.751430255 -1.014420963  0.076933172  1.616570833  0.744296449
##  [216] -0.468270477  0.671530349 -0.643080086  0.266038199 -0.090464333
##  [221]  0.094526801  1.731412828  0.136609547  1.119223863  0.559066713
##  [226] -0.861579831 -0.203655249 -1.330262031 -0.705714361  0.974623251
##  [231] -0.250702523  0.521617717 -0.579680379  0.613512703 -0.089110513
##  [236] -0.600543374 -0.386991129 -0.318107437  0.641422863 -0.582873468
##  [241]  0.394267521 -1.304571699  0.033715750 -0.769434713 -1.223643862
##  [246] -0.616771139  0.020226997 -1.203927669 -0.624946069 -0.611885927
##  [251]  1.114193130 -1.009919999 -1.844648016  1.087013912 -1.795213515
##  [256]  0.503167245 -1.498732738  1.279714656 -1.270594204 -1.067740821
##  [261]  0.264641513 -1.470324418 -1.053542290  1.062984162 -1.528404858
##  [266]  1.314104058 -1.220798154  1.327002669 -0.486403639 -0.771248856
##  [271]  0.294085140  0.102656486 -0.268833132 -2.348932362 -1.577947245
##  [276]  0.636461719 -1.545983054  0.621671114 -1.310913362 -1.626613277
##  [281]  1.384457552  2.370761549 -0.742518914 -0.765814001  1.077327344
##  [286] -0.813703281 -0.903376738 -0.942601281 -1.573281819 -1.424215576
##  [291] -1.021211206 -0.483370478  0.844121708  2.096465896  1.005439403
##  [296] -1.264572142  0.462260438 -0.330898947  0.342314746 -2.568276871
##  [301] -1.756079872  0.211922070  1.502891083  0.040462274 -0.087756855
##  [306] -0.907439769  0.830719108  2.752336985 -1.198379702  0.530909576
##  [311] -1.941657387 -0.681701610  0.719619975  1.647205232  2.418146732
##  [316] -2.393782545  0.442841227  3.153406194  3.001150261 -0.463761374
##  [321]  1.320525901 -0.375391193  1.959733938 -1.134488812 -2.050206632
##  [326]  0.267435404 -0.753219684  0.957422684 -1.243847553 -3.461124681
##  [331]  2.147701284  1.478319741  1.084582727  0.099945863  0.823127102
##  [336]  1.363663552 -0.608637221 -1.490492928  0.877321577 -0.198151791
##  [341]  2.393782545  1.391523619  0.592488679  0.549632774 -0.510833777
##  [346]  0.397183912 -1.070128233 -0.513908791  0.796919854  1.409499686
##  [351]  0.853788545 -0.789532284  0.925912101 -0.523163215 -0.465263357
##  [356]  0.911517835 -0.974623251  1.395082856 -1.435458325 -0.978968627
##  [361] -0.123011613  1.187393051  0.085050020  1.264572142 -0.559066713
##  [366]  0.191280879 -0.961696145  1.532755121  0.863535834  0.873365866
##  [371]  0.600543374 -1.402254840  0.323786003 -0.656402227 -0.335174740
##  [376]  0.714389194 -1.018942572 -1.246775496 -0.590882359  0.250702523
##  [381] -0.294085140  0.707445064  0.352340246  2.205284963  0.842197799
##  [386]  1.564052364 -0.787692121 -0.008090336 -0.086403358 -0.085050020
##  [391]  0.921779971 -0.830719108  0.633162979 -0.083696837  0.674913004
##  [396] -1.373986290 -0.460760541 -0.548065218 -0.909476911 -1.298282071
##  [401] -0.853788545 -0.716130610  0.654730623  0.263245342 -0.206409282
##  [406] -1.301420449  0.506230285  1.142221353  0.362401286 -0.544934137
##  [411]  2.501345446 -0.257665760 -0.846048746 -0.551201681  1.969017784
##  [416] -0.893283788  1.743613740 -0.478829051 -0.243751421  0.320945426
##  [421] -1.802009946 -0.815582246  0.832624598  0.392810584  0.114863917
##  [426] -1.587382521  0.062065052  1.053542290  0.083696837 -0.191280879
##  [431] -1.055893934 -0.151596606  0.515448120  1.737480953  0.659750952
##  [436] -0.113506724  1.606688823 -0.737200322  0.507763585  1.762416670
##  [441] -0.435416939  0.295493393 -0.253486340 -1.673969302  0.284243507
##  [446] -0.247920647 -1.409499686 -0.403026872  0.755011527 -1.641991740
##  [451] -0.232653959 -0.125729300 -0.474297479 -0.009438762 -0.395725296
##  [456]  0.661428091  0.808083534 -0.114863917 -0.497055264 -1.474310299
##  [461] -0.410349998 -0.570136293 -0.116221323 -0.082343808 -0.080990929
##  [466]  1.126823516 -0.322365390 -0.218822145 -0.840277002  0.239586428
##  [471]  1.176547886  0.597316848  0.494006236 -1.731412828 -1.109190438
##  [476]  0.457763852 -1.647205232 -0.584472241  1.217962298 -0.079638199
##  [481] -0.127088491 -0.871393127 -0.578086050  0.339456669  1.641991740
##  [486]  0.287052552  1.104215353 -0.636461719 -0.216060883  0.483370478
##  [491] -0.594096529 -1.367088290 -0.239586428 -0.319526110  0.603776164
##  [496]  0.537129662  0.414754435  0.375391193 -0.782187555 -0.078285614
##  [501]  0.384086320  0.616771139 -0.568550673 -1.176547886  0.673220713
##  [506] -0.120294834  0.983332566 -0.423587607  0.059363328  1.023485109
##  [511] -0.828816630  0.571723349 -0.436899865  0.148869251  1.034934930
##  [516]  0.173457852 -0.417695198 -0.369610210 -0.433934970  0.416224367
##  [521] -0.597316848  0.620036135 -0.605394926 -1.458504802 -0.994325241
##  [526]  0.425063002 -0.002696752 -0.217441306 -0.228499859 -0.676607229
##  [531]  0.274429329 -0.325207270 -0.135248658  0.044511053  0.439868605
##  [536] -0.989913817 -0.555916576  0.260454538  0.343744832  0.758602509
##  [541]  1.573281819  0.205032071  1.490492928  0.389899206  0.666470718
##  [546]  0.125729300 -0.275829715  0.068821391  1.144814095  0.716130610
##  [551] -0.764007406  1.498732738  0.106723840  0.029668592 -0.189907790
##  [556]  0.712649943  2.007958893 -0.451782750 -0.442841227 -0.778530978
##  [561]  0.309608718  1.285854591 -0.076933172  0.903376738 -0.075580872
##  [566] -0.131167483 -0.746076339 -0.641422863 -0.767623099 -0.194028142
##  [571] -0.844121708 -0.246530430 -0.289863864  0.231268816 -0.631516191
##  [576]  0.118936778 -1.685018832  0.618402813  0.049910572 -0.147505990
##  [581] -0.231268816  0.236812077 -0.368166900  0.151596606  0.907439769
##  [586]  0.444329005 -0.392810584  0.315272007  0.055311546  1.206715600
##  [591]  0.735432089  0.653060847 -0.469775625  0.669841901 -0.366724356
##  [596] -0.428016575 -0.698812562  0.210543276  1.420507713  0.686813744
##  [601] -0.438383752  1.067740821  1.323757343  0.420639577 -0.688521779
##  [606] -0.905406385 -0.557490953  0.356647694  0.329475030 -0.372499146
##  [611] -0.112149739 -0.187162683 -0.658075667 -2.289421602 -0.445817767
##  [616]  0.776706588  0.080990929  0.036414159 -0.132527628 -0.343744832
##  [621]  0.159785525  0.938404491  0.213301268 -0.855731495 -1.601806100
##  [626] -0.163883972 -0.200902759  1.058251433  0.767623099  0.976793633
##  [631]  1.310913362  2.348932362 -0.490961795  0.408883624  0.101301081
##  [636] -0.074228709  1.577947245 -0.333748798 -0.530909576 -0.363841553
##  [641] -0.346607117  1.212319781  1.298282071  0.972457450  1.032634134
##  [646] -0.992117116  0.492483445  1.559487170  0.590882359 -0.072876682
##  [651] -0.071524788  1.837306881 -1.356861648 -0.509298081 -0.070173025
##  [656] -0.492483445 -1.229365201  0.909476911  1.611610156 -0.311023602
##  [661] -1.144814095 -1.621571613 -0.566966480  1.554954248  0.256272124
##  [666]  1.074921450  1.405868039 -0.299721685  0.509298081 -0.214680871
##  [671] -1.454609861 -0.405953507 -0.439868605  0.764007406  1.631696630
##  [676] -0.495530174  1.416819278 -1.187393051 -0.726625143 -2.072781954
##  [681]  0.804351175 -0.538687927 -0.965987242 -1.195619501 -0.712649943
##  [686]  1.121749883  0.932140112  0.281436703 -1.631696630 -1.353484113
##  [691] -0.762203300  0.318107437 -2.471677151  0.524709963  1.795213515
##  [696] -2.161436385 -1.016679169 -0.180306035  1.273622589  1.065359478
##  [701] -1.657768635 -0.842197799 -0.620036135 -1.743613740  1.657768635
##  [706]  1.350121948 -1.096803562  0.487921897 -1.568650389 -0.925912101
##  [711]  0.121653111 -1.924193887 -1.443055487  0.299721685  0.009438762
##  [716] -0.355211147 -1.398659855 -0.350905885 -0.068821391 -0.067469881
##  [721]  1.261578236  0.628227740 -0.213301268 -0.450290005  1.171176839
##  [726]  0.395725296 -0.661428091 -0.703985770  1.515524656 -1.340125919
##  [731] -0.541808390 -1.333535586  0.098590829  1.346774976 -1.249714166
##  [736]  0.806215951  0.981148261 -0.955292497 -0.301132303 -0.066118496
##  [741] -1.181953091 -1.343443023  1.482353090 -0.064767230 -0.454771268
##  [746]  1.582647271 -0.342314746  0.298311662 -0.887271474 -0.263245342
##  [751]  0.332323535 -0.394267521  0.242362624  0.172089202 -0.897309997
##  [756] -0.921779971 -2.444036983 -0.146143003 -2.205284963 -0.063416084
##  [761]  0.165250729 -1.749812815  2.084477779  0.733666152  0.480341759
##  [766] -0.305367768  1.413150018 -0.515448120  1.131926322 -1.737480953
##  [771]  0.968139475  0.245140689 -0.800629988 -0.420639577 -2.134359789
##  [776] -1.427943123  0.887271474 -0.899328566 -2.501345446  0.996538226
##  [781]  0.400103684  1.626613277 -1.292043388  0.765814001  1.486410698
##  [786] -0.339456669 -0.919719798  0.782187555 -0.199527087  0.934224165
##  [791] -0.987715314  1.768825039  1.882932462  0.992117116  0.302543521
##  [796]  0.388444757 -0.714389194  0.751430255  0.828816630 -0.480341759
##  [801]  0.451782750 -1.515524656  0.555916576 -0.671530349  0.611885927
##  [806]  2.308361815  0.095881300 -0.529357768  0.693657988  0.166617795
##  [811] -0.242362624 -0.181676676 -1.279714656  0.152960705 -0.102656486
##  [816]  0.198151791  1.725407795 -0.425063002  0.358084978 -0.932140112
##  [821]  0.137970689  1.232241021  1.157894875  1.243847553 -0.062065052
##  [826] -0.738970862  0.048560562 -1.450736862  0.234039548  0.756805798
##  [831] -1.507075579 -0.176196131 -1.089451538 -1.701989181 -0.546499008
##  [836] -0.416224367 -1.788499010  1.360254733 -2.018186777  0.576493189
##  [841] -1.830063448 -1.082157935  0.257665760  0.296902233 -1.320525901
##  [846]  0.371054291  1.317308188 -1.997936847  1.446885503 -1.882932462
##  [851]  0.800629988 -1.988111548  1.235127068  0.610260769  1.424215576
##  [856]  1.707756416  1.139636266  1.701989181 -1.524083329  0.541808390
##  [861] -1.511286632 -1.165839367  0.078285614 -1.395082856 -0.273029480
##  [866] -1.314104058 -0.148869251  1.304571699  2.175591776  0.554343576
##  [871] -0.152960705 -0.749643230  0.951045074 -0.384086320 -1.413150018
##  [876] -0.196776871  1.511286632  0.144780288 -1.255624109  0.826917147
##  [881]  1.652463885  0.450290005 -0.895295078  0.123011613 -0.537129662
##  [886] -1.815858073 -2.096465896  0.386991129 -0.238199023  0.566966480
##  [891]  0.584472241  0.857677680 -1.822914780 -1.074921450  0.685107711
##  [896] -0.873365866 -0.267435404  0.039112832 -1.611610156 -1.537134586
##  [901]  0.113506724  1.494600149 -0.426539323  1.713581019  0.895295078
##  [906]  0.970296201  0.498581510  0.899328566 -0.462260438 -0.060714135
##  [911] -0.059363328  0.497055264 -1.377459942 -0.104012078 -0.058012629
##  [916] -0.004045135 -0.724870519 -0.934224165  1.373986290 -0.503167245
##  [921]  0.188535059 -0.571723349 -0.821236508  0.643080086  1.201149064
##  [926] -1.079739490  0.024273125 -1.235127068 -1.462421997 -1.852089931
##  [931]  0.646399844  0.560643862  1.048856395  0.638113687 -1.238023440
##  [936] -0.295493393  1.079739490  0.746076339  1.012167918  0.072876682
##  [941]  0.438383752 -0.108080014  1.089451538  0.447307518 -1.307735956
##  [946] -0.535572701  0.133888019 -1.139636266 -0.397183912 -1.206715600
##  [951]  0.196776871 -0.280034133  1.292043388 -0.598929332 -0.644739077
##  [956] -0.819348844  1.356861648 -0.235425586 -0.674913004 -1.124283082
##  [961] -1.201149064  0.656402227 -0.332323535  1.466361761 -0.518530452
##  [966]  1.636822499 -0.266038199  1.941657387 -0.306780804  1.450736862
##  [971]  0.435416939  0.185790660 -0.245140689  0.698812562 -0.260454538
##  [976] -1.007677172  0.562222407  1.380950295 -1.606688823  0.202278813
##  [981]  1.808890648  0.064767230  0.419166933  0.398643373 -0.373944779
##  [986] -0.651392890  0.769434713 -0.144780288 -0.056662036 -0.055311546
##  [991] -0.695374126 -1.119223863  0.174826828  0.987715314  0.373944779
##  [996]  0.209164881  0.445817767 -0.457763852 -0.142055660  0.129807580
## [1001]  1.094346314  0.557490953  0.047210641 -0.603776164 -0.053961158
## [1006]  0.372499146  1.129371243  1.060614828 -0.404489757  0.005393524
## [1011] -0.500108919 -0.240974293 -0.560643862 -1.106699472  0.923844064
## [1016]  0.280034133  1.377459942  0.021575667 -0.791375125 -0.052610867
## [1021] -0.154325089  0.365282575  0.836444677  0.157054722  1.220798154
## [1026]  0.109436387 -0.471281838  0.381184749 -1.690621630  0.252094188
## [1031]  0.110792961 -0.430973886  1.168503942 -0.278632114  0.568550673
## [1036] -0.270231385  0.028319650  0.955292497 -1.060614828 -2.370761549
## [1041]  0.140693743 -1.295156428  0.433934970  0.819348844  0.353775332
## [1046]  0.965987242  1.719464344 -0.353775332  2.444036983 -0.401564849
## [1051]  0.333748798 -0.607015276 -0.234039548 -0.811827184  0.484886501
## [1056] -0.946814739 -0.707445064 -0.296902233  0.460760541  0.700534881
## [1061]  0.035064922  0.817464095  0.131167483  0.391354480 -0.316689404
## [1066] -0.610260769  1.830063448 -1.030338792  0.235425586  0.025621919
## [1071] -0.664787965 -0.121653111  0.222967175 -0.371054291 -1.101738030
## [1076]  0.090464333  0.785854621  0.195402322  1.443055487  0.946814739
## [1081] -0.308194453 -0.639767399  0.132527628  0.167985173 -0.051260673
## [1086] -0.936312283  0.037763461 -1.091895656  1.163183043  0.468270477
## [1091]  0.355211147  0.919719798 -0.549632774  0.325207270 -0.298311662
## [1096] -0.589277562  1.295156428 -0.303955341 -0.136609547 -1.240930235
## [1101]  0.292677470  0.726625143 -0.236812077 -1.616570833 -0.388444757
## [1106]  0.589277562 -1.482353090 -0.326629195  1.041870422  0.428016575
## [1111]  0.128447917  0.723118123  0.002696752 -0.776706588 -0.723118123
## [1116] -1.907298228  0.510833777  1.788499010  1.601806100 -0.501637496
## [1121]  0.163883972  1.096803562 -0.626586061 -1.111688306 -0.857677680
## [1126]  0.120294834  0.067469881 -0.795068896 -0.917663521  0.436899865
## [1131]  0.705714361 -0.494006236  0.142055660 -0.959557224  0.512370678
## [1136]  0.271630167  0.520073465  0.147505990 -0.793220658  0.469775625
## [1141]  0.401564849  0.855731495  1.402254840 -0.169352865  0.703985770
## [1146] -1.003206657  0.978968627 -1.192868378  0.774884781  0.891276104
## [1151] -0.106723840  0.220203400  0.311023602 -0.049910572  0.177565765
## [1156] -0.302543521 -0.159785525 -0.944705914 -0.447307518  0.798773547
## [1161]  0.075580872  0.247920647  0.326629195 -1.152638890 -1.696278006
## [1166] -0.825020643  1.333535586  0.702259280  0.889272006 -0.048560562
## [1171] -0.047210641  0.634811485  0.001348375  0.429494761 -0.045860805
## [1176] -0.157054722  0.953166636 -0.162517520 -0.444329005  0.544934137
## [1181] -0.044511053 -1.768825039 -0.710912844  0.063416084  0.178935732
## [1186]  1.663120450 -0.328051780  1.541543733 -0.110792961  0.192654329
## [1191] -0.784019770  0.811827184 -0.957422684  0.006741924 -0.101301081
## [1196]  0.012135669  0.838359300 -0.329475030  0.959557224 -1.288942818
## [1201]  0.017529767 -0.869423773 -0.740743723  0.259059897  0.359523002
## [1206]  0.721367945 -0.202278813  1.195619501 -0.414754435 -1.041870422
## [1211] -1.160534902  0.376838394  0.477317439  0.000000000 -1.363663552
## [1216]  0.407418129  0.780357962 -0.484886501  0.867457786  0.532462664
## [1221]  0.285647748 -0.747858595 -0.129807580 -1.679468436 -1.360254733
## [1226] -1.346774976  0.013484154  1.462421997 -1.405868039  0.879304589
## [1231]  0.834533115 -0.365282575  0.441354429  0.305367768 -1.000978901
## [1236] -0.867457786  0.404489757 -0.005393524  0.944705914  0.651392890
## [1241]  0.348039324 -0.227116039  1.003206657 -0.043161383 -0.041811790
## [1246]  0.079638199  0.301132303 -0.915611117  0.791375125  0.821236508
## [1251]  1.173858130 -0.798773547  0.490961795  1.240930235 -0.259059897
## [1256] -0.780357962 -0.633162979  0.043161383  0.448798263 -0.913562563
## [1261]  0.288457923 -0.526257967 -1.142221353 -0.976793633 -0.040462274
## [1266] -1.116704964 -0.663107092  0.724870519  0.905406385 -0.638113687
## [1271]  0.709177888  0.551201681 -0.889272006  1.249714166 -0.504698173
## [1276]  0.379735168 -0.985521574 -0.717874200  0.161151372 -0.039112832
## [1281]  0.270231385  0.513908791 -1.126823516  0.022924375 -0.407418129
## [1286]  0.535572701 -0.177565765  0.221585076 -1.899050574  0.773065541
## [1291]  0.930060100  0.453276503 -0.358084978 -0.378286384  0.253486340
## [1296] -0.287052552 -0.221585076 -1.012167918 -0.292677470 -0.520073465
## [1301] -1.215136204  0.546499008 -0.709177888  1.116704964  0.486403639
## [1306] -0.010787206 -0.524709963  1.596961269 -0.730141123 -0.172089202
## [1311]  0.368166900  0.454771268 -0.700534881 -0.847978932 -1.179246182
## [1316] -2.220892296  0.913562563  1.258595595  0.587674282 -1.150022800
## [1321]  0.940500815 -1.446885503  0.538687927 -0.521617717  0.184418986
## [1326] -0.481855566  1.229365201  1.055893934  1.267577427  0.594096529
## [1331] -0.012135669  0.778530978 -0.001348375 -0.128447917 -0.352340246
## [1336]  0.676607229  0.216060883  0.227116039  1.184668689 -0.419166933
## [1341]  0.649726742 -0.487921897  0.626586061  0.526257967 -0.037763461
## [1346] -0.173457852  0.417695198 -1.232241021 -0.702259280  0.540247501
## [1351] -1.077327344  0.548065218  0.463761374  0.183047659  0.578086050
## [1356]  0.158419976 -0.459261681  0.897309997  1.147414556  0.303955341
## [1361] -0.274429329 -0.654730623  0.595705916 -0.441354429 -1.519790077
## [1366] -0.413285400  0.840277002 -0.195402322  0.422113133  0.225732653
## [1371]  1.276662700  0.740743723 -0.586072510  0.809953940  0.203655249
## [1376]  0.112149739 -0.968139475 -0.573311845  1.039553035  0.335174740
## [1381]  0.385538318 -0.970296201  0.552771947  0.350905885  0.631516191
## [1386] -0.613512703 -1.046522062 -1.062984162  0.742518914  0.070173025
## [1391] -1.155262893 -1.084582727  0.471281838 -1.129371243 -0.804351175
## [1396] -0.336601363  0.459261681 -1.261578236  0.340885359  0.097235975
## [1401]  0.658075667 -0.345175621 -0.133888019  1.000978901  0.104012078
## [1406]  0.501637496 -0.602158982 -0.398643373  2.050206632  1.137058773
## [1411]  0.426539323 -0.735432089  0.018878365  0.232653959 -0.744296449
## [1416]  0.728382008 -0.628227740  0.180306035 -2.418146732  1.568650389
## [1421]  0.784019770 -1.762416670  0.249311344 -0.721367945  0.690231824
## [1426] -0.565383709  1.270594204  1.009919999  0.846048746  0.306780804
## [1431]  0.150232789 -0.036414159 -0.035064922 -0.155689761  0.793220658
## [1436]  0.066118496 -0.033715750 -1.969017784  0.985521574  0.518530452
## [1441] -0.996538226  0.261849685 -0.118936778 -1.087013912  1.592153635
## [1446]  1.859635855 -0.389899206  1.192868378  0.312439110 -0.543370600
## [1451]  0.031017587  0.717874200 -0.032366639 -0.109436387 -0.315272007
## [1456]  0.787692121 -1.044193418  0.639767399  1.427943123 -0.659750952
## [1461]  0.071524788  0.615141105 -0.576493189  1.288942818 -0.099945863
## [1466] -0.211922070 -0.031017587  0.678303399  0.410349998 -0.209164881
## [1471] -0.277230642  0.749643230 -0.143417841 -0.685107711 -0.281436703
## [1476]  0.403026872 -0.563802354  0.289863864 -1.051196457 -0.140693743
## [1481]  1.519790077  0.052610867  1.152638890  0.605394926  0.478829051
## [1486]  0.194028142 -0.756805798 -0.859627120  0.795068896 -1.554954248
## [1491] -0.587674282 -0.865495146 -2.121387721 -0.210543276 -1.323757343
## [1496]  1.690621630  0.927984105  0.338028671 -0.029668592 -0.028319650
## [1501] -1.978474507 -0.466766389 -0.806215951  0.668155360  1.025764317
## [1506] -0.185790660  0.691943891  0.623307755 -1.387981923 -0.691943891
## [1511]  1.016679169  0.217441306  0.108080014  0.345175621  0.529357768
## [1516]  0.495530174  1.246775496  0.010787206 -0.669841901  0.579680379
## [1521]  1.307735956  0.060714135  0.243751421  0.308194453 -0.026970760
## [1526]  1.802009946  0.500108919  1.226499513  1.398659855  1.037241217
## [1531]  0.582873468 -0.224349699 -0.271630167  0.346607117 -1.420507713
## [1536] -1.184668689  0.948927784  0.254878985  0.268833132 -0.025621919
## [1541]  0.534017037 -0.225732653 -0.252094188 -1.494600149 -1.663120450
## [1546] -0.249311344 -0.124370342  0.523163215  1.890930113  1.150022800
## [1551]  1.435458325 -0.527807233  0.893283788  0.695374126 -1.168503942
## [1556] -1.775306882 -0.834533115 -0.205032071 -1.719464344 -0.618402813
## [1561]  0.563802354  1.238023440  0.474297479 -0.592488679 -1.131926322
## [1566]  2.697177092  0.624946069  2.121387721 -0.615141105 -0.167985173
## [1571] -1.478319741  0.086403358  0.127088491  0.859627120  1.550453053
## [1576]  1.091895656  1.679468436 -0.516988672 -1.932851955 -1.950615992
## [1581]  1.070128233  0.738970862 -0.422113133 -0.411817256  0.291270379
## [1586]  0.366724356  1.340125919 -0.634811485 -0.323786003 -0.207786884
## [1591]  1.685018832  1.668520329  1.545983054 -1.486410698  0.004045135
## [1596]  1.106699472 -1.890930113 -0.432453954 -2.697177092 -0.938404491
## [1601]  2.039299773  1.155262893  0.489441280 -2.028630245 -0.024273125
## [1606] -0.506230285  0.527807233 -1.652463885 -0.875342009  1.387981923
## [1611]  2.108763102  0.644739077  0.369610210  0.053961158 -0.338028671
## [1616] -1.032634134 -1.285854591 -1.416819278 -0.288457923  1.431690617
## [1621]  1.875053466  0.942601281  0.851848813 -0.690231824  1.336823495
## [1626] -1.336823495  1.301420449 -0.408883624  2.897169268 -0.261849685
## [1631]  0.581276182  1.749812815 -0.621671114  0.849912281 -0.877321577
## [1636]  0.117578942 -1.190126255 -1.212319781  0.218822145  1.756079872
## [1641] -0.137970689 -0.983332566  0.586072510 -0.534017037 -1.541543733
## [1646]  0.363841553 -1.959733938 -3.001150261 -0.666470718 -2.752336985
## [1651] -2.190197016  2.568276871 -1.915677702  1.046522062  1.673969302
## [1656] -0.340885359  0.282839826 -1.267577427 -2.328168205  1.134488812
## [1661] -0.472789121 -2.007958893 -0.359523002  0.847978932  2.649174982
## [1666] -0.686813744 -0.532462664  2.018186777  1.950615992 -2.175591776
## [1671] -1.058251433  0.730141123 -0.170720874 -1.582647271  2.271268723
## [1676]  1.454609861 -0.291270379  2.471677151  1.537134586  1.099267451
## [1681] -0.356647694 -1.258595595 -2.253834800  0.224349699  1.899050574
## [1686]  1.978474507 -0.429494761 -0.678303399 -2.897169268 -0.161151372
## [1691]  0.825020643 -1.048856395 -0.022924375 -0.021575667  2.328168205
## [1696]  0.481855566  0.056662036 -0.020226997  1.439246522  1.696278006
## [1701]  0.032366639 -1.121749883  0.322365390 -2.271268723 -1.808890648
## [1706]  0.382635132  0.570136293  1.474310299  2.289421602  0.240974293
## [1711]  0.091818320 -0.254878985 -0.574901790 -1.837306881  1.367088290
## [1716]  2.134359789  1.101738030  1.190126255  0.861579831  2.606596640
## [1721]  0.319526110 -0.507763585  0.229884118  0.516988672 -0.785854621
## [1726]  0.278632114 -0.229884118 -1.391523619  0.683403669  0.869423773
## [1731]  1.988111548  0.313855244 -0.222967175 -0.018878365 -0.477317439
## [1736] -1.276662700  2.072781954  0.430973886  0.041811790  1.179246182
## [1741] -0.385538318 -1.713581019 -0.972457450  1.924193887  0.813703281
## [1746]  0.200902759  0.014832664 -0.891276104 -0.381184749  0.045860805
## [1751]  1.082157935  1.528404858  1.997936847 -1.025764317 -0.309608718
## [1756]  0.802489192 -0.456267049 -1.431690617  0.737200322 -0.728382008
## [1761]  0.432453954  1.822914780  0.760401672  0.228499859  0.885274487
## [1766] -0.349472246 -0.951045074  1.030338792 -0.017529767 -0.016181201
## [1771] -0.139332087 -0.758602509 -1.592153635 -1.781864184  0.688521779
## [1776]  0.008090336 -0.629871114 -0.849912281 -0.879304589 -2.649174982
## [1781]  1.844648016  0.574901790  2.028630245  1.775306882 -0.014832664
## [1786] -0.648062397  0.105367863 -1.273622589  0.681701610  1.282778578
## [1791] -1.596961269  0.349472246 -0.646399844 -0.802489192 -2.039299773
## [1796]  1.124283082  0.648062397  0.607015276  0.423587607 -0.013484154
## [1801]  0.330898947 -2.108763102 -0.285647748  0.170720874 -0.851848813
## [1806]  0.074228709  1.255624109 -0.953166636  1.852089931  1.907298228
## [1811] -0.498581510 -0.836444677 -2.533393817 -1.875053466 -1.317308188
## [1816]  0.316689404  2.190197016 -0.562222407 -1.502891083 -0.923844064
## [1821]  1.343443023  0.731902501  1.198379702  0.405953507  0.139332087
## [1826] -1.252663668  1.867289179  0.881291064  0.598929332  0.026970760
## [1831]  0.273029480  0.116221323 -0.981148261 -1.037241217  0.663107092
## [1836]  2.533393817  1.044193418 -0.863535834  1.209512942  0.082343808
## [1841] -1.094346314 -2.606596640 -0.391354480 -1.867289179 -1.350121948
## [1846] -0.105367863  0.169352865  1.458504802 -1.636822499 -0.731902501
## [1851] -1.668520329 -2.237060137 -1.005439403  1.932851955 -2.084477779
## [1856] -2.817407051  0.697092314 -1.550453053  1.330262031
## 
## $FTSE$y
##    [1]  0.679325585 -0.487765222  0.906788661  0.578853627 -0.720408902
##    [6]  0.855359170  0.823988102  0.083718705 -0.521808405  1.405461680
##   [11]  0.959526160  0.164267835 -0.534947286 -0.227692066  0.668896321
##   [16]  1.149110807 -0.285946134 -0.034876962  0.376027291  0.220136716
##   [21]  0.023121387 -0.261981815  0.112021014  0.385847127 -0.626513434
##   [26] -0.468012687  0.936540629  0.123200123 -1.153579943 -0.046681709
##   [31]  0.603253678  0.924600565  0.321987121  0.145193336 -3.071346814
##   [36]  0.551072623  1.855549031  0.810945847  0.674799848  0.000000000
##   [41] -0.791456811  0.167951752  0.533495923  0.284284740  1.281324413
##   [46] -0.395581430 -0.164855751 -0.048787811  0.153944355 -0.532353603
##   [51] -0.844263531 -0.159647256  0.582502094 -0.609409894 -0.754055907
##   [56] -0.445126631 -0.416281221  0.197398978  0.448101364 -0.799907703
##   [61] -0.112424889  0.822789723 -0.084687043  0.130990908  0.873412851
##   [66]  0.911622230 -0.052918053 -0.703426367 -0.038086533 -1.082069649
##   [71]  0.127108851 -0.592421620 -0.514685964 -0.614594679  0.763209393
##   [76]  0.085453486  0.089261458  0.376114773  0.479004906 -0.976509938
##   [81] -0.628955235  0.062512209 -1.280699699 -0.537910849  1.741758460
##   [86] -0.203244088  0.932127051 -0.430716697 -0.643024162 -0.851147284
##   [91]  0.518237202 -0.263686095  0.149948702  0.827423168 -0.160218835
##   [96]  0.806293788 -1.125994952  0.592970744 -0.585571518 -1.716013508
##  [101] -1.590155420  0.385692826 -0.368033649 -0.698193627  0.404692801
##  [106]  0.622913444 -0.971070200 -0.772216547 -0.345878284 -0.218990166
##  [111]  0.219470786  0.148748037 -0.693126496 -0.760282509  0.874952903
##  [116] -0.730411687 -0.493311037  1.810772204  1.167828994 -0.440528634
##  [121] -0.323664372 -0.793291956 -0.911501492 -1.400735909 -0.538569187
##  [126]  1.662829368  0.000000000  0.000000000  1.438517027  0.053747881
##  [131]  3.020661157  0.000000000 -0.012033212  0.453305520 -0.435286131
##  [136] -0.413123696 -0.636352652  1.248429330 -0.800672565  0.492352395
##  [141]  1.052166580  0.826610500  0.177367861 -0.192791942  0.323254622
##  [146] -0.058941412 -0.841393410  0.130848533 -0.590028907  1.175111536
##  [151]  0.476396709 -0.215517241  0.168859219  0.799749098 -0.427815806
##  [156] -0.132802125 -0.379380476 -0.502532292 -0.674742532  0.842205625
##  [161] -0.051213363 -0.528162075 -0.043586797 -0.344882264  1.078006285
##  [166]  0.586383314 -0.751203099  0.264122679 -0.043249194  0.684419620
##  [171] -0.503965308  0.714622271 -0.116959064  0.003903201 -0.304437766
##  [176]  0.434561328 -0.272861932 -0.785647280 -0.204861521  0.694800837
##  [181]  0.944838672 -2.035109523 -1.153663178 -0.693859544 -0.214054927
##  [186]  0.829724370 -1.063744380  0.117661379 -0.445777273 -0.635024017
##  [191]  0.725112659  0.252165779  0.296158059 -0.982930184  0.204256710
##  [196] -0.521831302 -1.290930700 -0.132857261 -0.943709986  0.763839342
##  [201]  0.137448457 -0.457532651  1.805114491  5.590215071  0.715229729
##  [206]  0.366653802  1.526629494 -0.060601470  0.000000000  0.000000000
##  [211] -0.485105738 -0.685505370  0.076692998  1.272128132  0.575104048
##  [216] -0.270859980  0.524330441 -0.405268490  0.214762066  0.000000000
##  [221]  0.090232348  1.371046503  0.118575610  0.880861616  0.443922662
##  [226] -0.562495434 -0.069791361 -0.948355082 -0.449029577  0.782822635
##  [231] -0.110963160  0.418425535 -0.365057709  0.481125093  0.000000000
##  [236] -0.383057090 -0.221844265 -0.163047506  0.497364709 -0.369330773
##  [241]  0.307680902 -0.923907018  0.037300906 -0.499645774 -0.850665168
##  [246] -0.393075818  0.026561433 -0.834566215 -0.397842470 -0.387909513
##  [251]  0.875231339 -0.684172304 -1.373922414  0.862371717 -1.334726091
##  [256]  0.403874054 -1.093493712  0.975282319 -0.907206820 -0.722149876
##  [261]  0.214643453 -1.082817706 -0.713741529  0.848107912 -1.125305354
##  [266]  1.000405022 -0.846132253  1.023214430 -0.284238761 -0.501846796
##  [271]  0.229996368  0.096618357 -0.120656371 -2.073769832 -1.159587154
##  [276]  0.495070100 -1.146713032  0.485782487 -0.929360283 -1.228335857
##  [281]  1.081771721  2.098255667 -0.478705844 -0.497594958  0.858476413
##  [286] -0.524750021 -0.610591900 -0.635239050 -1.156628533 -1.038253691
##  [291] -0.692264695 -0.281434015  0.646954105  1.673856773  0.818906993
##  [296] -0.900635495  0.373720644 -0.173471546  0.267017038 -2.307984952
##  [301] -1.302410108  0.175361683  1.164113786  0.043260080  0.000000000
##  [306] -0.614027502  0.635224504  2.978815391 -0.827070826  0.423334180
##  [311] -1.454346177 -0.436326304  0.562835661  1.294539862  2.159517483
##  [316] -2.151025969  0.350210970  4.440146323  3.345545312 -0.268796260
##  [321]  1.011679231 -0.212683681  1.577213718 -0.770639402 -1.576316801
##  [326]  0.214843750 -0.487234457  0.755973365 -0.878591144 -4.055379064
##  [331]  1.720966357  1.153351551  0.862103214  0.094532850  0.629623800
##  [336]  1.075394963 -0.386892096 -1.091389288  0.679337155 -0.066305238
##  [341]  2.138786980  1.096675583  0.468685036  0.436401941 -0.303404877
##  [346]  0.308085362 -0.726646191 -0.305614247  0.605533058  1.109731783
##  [351]  0.662251656 -0.513749261  0.720734109 -0.309837335 -0.270100270
##  [356]  0.712324701 -0.655713549  1.097597152 -1.060005869 -0.663577386
##  [361] -0.014927601  0.925649448  0.081360947  0.968147218 -0.347679696
##  [366]  0.154247310 -0.641707308  1.188367287  0.667444744  0.677511684
##  [371]  0.475025191 -0.999283668  0.249629174 -0.418621436 -0.177574835
##  [376]  0.555454710 -0.689580475 -0.879776057 -0.377773703  0.206170385
##  [381] -0.143287530  0.548217374  0.274443794  1.802722330  0.645230670
##  [386]  1.221640489 -0.513722730  0.003536818  0.000000000  0.000000000
##  [391]  0.717948718 -0.537256830  0.494263019  0.000000000  0.526962937
##  [396] -0.975013105 -0.268210051 -0.336164190 -0.614237529 -0.921691912
##  [401] -0.558880796 -0.456869357  0.506319892  0.213830096 -0.072330115
##  [406] -0.922876479  0.405464641  0.894968531  0.284859193 -0.334388034
##  [411]  2.301670334 -0.112846916 -0.550750221 -0.344350172  1.581647193
##  [416] -0.603170150  1.390064917 -0.274897348 -0.104679158  0.248000279
##  [421] -1.348432056 -0.526260022  0.635563130  0.306954098  0.102004924
##  [426] -1.184159668  0.064006827  0.842217484  0.081051556 -0.059859155
##  [431] -0.715216855 -0.035486160  0.415335463  1.389330788  0.509065551
##  [436] -0.010407271  1.259410887 -0.472829439  0.406224181  1.395460468
##  [441] -0.250228249  0.230516289 -0.111610918 -1.269723031  0.222915738
##  [446] -0.106077197 -1.007090741 -0.228381605  0.582665696 -1.248232820
##  [451] -0.097768777 -0.017475796 -0.272670069  0.003505328 -0.224333135
##  [456]  0.509397506  0.618664803 -0.010421371 -0.295302946 -1.083661452
##  [461] -0.232492603 -0.356613234 -0.010630382  0.000000000  0.000000000
##  [466]  0.885959317 -0.165097654 -0.084444601 -0.538789309  0.198272199
##  [471]  0.922261484  0.472672525  0.400752718 -1.294644407 -0.756030663
##  [476]  0.368493782 -1.249691107 -0.375361956  0.943734750  0.000000000
##  [481] -0.017773986 -0.572424092 -0.364741641  0.265585185  1.288613666
##  [486]  0.226172386  0.870914284 -0.401985459 -0.080721581  0.389884089
##  [491] -0.377873412 -0.969339374 -0.102847821 -0.163305879  0.476495271
##  [496]  0.428227633  0.324206223  0.295057782 -0.511329808  0.000000000
##  [501]  0.299222023  0.484346483 -0.356269647 -0.802720135  0.526520372
##  [506] -0.014060742  0.791027985 -0.240678084  0.062937063  0.828150115
##  [511] -0.537168602  0.452961672 -0.253208463  0.128664325  0.833506981
##  [516]  0.144657987 -0.237309121 -0.206846623 -0.248730438  0.329004329
##  [521] -0.379703141  0.485100485 -0.386206897 -1.076571587 -0.671868986
##  [526]  0.338206799  0.007022225 -0.084260787 -0.094873327 -0.432611142
##  [531]  0.219011622 -0.169186846 -0.021184197  0.045908818  0.349452877
##  [536] -0.668331633 -0.347037785  0.213212039  0.269493990  0.583513103
##  [541]  1.237606357  0.166701396  1.158033423  0.305045243  0.519391765
##  [546]  0.112180032 -0.125636672  0.071397001  0.896921927  0.558960199
##  [551] -0.495579962  1.160990712  0.099797079  0.033232528 -0.059798678
##  [556]  0.555130805  1.606611570 -0.263534617 -0.257706736 -0.510204082
##  [561]  0.239973702  0.980552914  0.000000000  0.694985711  0.000000000
##  [566] -0.019351093 -0.480645161 -0.405173252 -0.497949619 -0.062146338
##  [571] -0.549846174 -0.105311657 -0.138367266  0.191343362 -0.401712216
##  [576]  0.105792118 -1.274768824  0.485047167  0.053264090 -0.033272334
##  [581] -0.096521884  0.196561834 -0.206151288  0.129943691  0.702116332
##  [586]  0.350262697 -0.223912542  0.244216362  0.059259259  0.934425690
##  [591]  0.570459954  0.505639829 -0.270897833  0.523864959 -0.205880461
##  [596] -0.241763909 -0.445923676  0.175273459  1.117843372  0.538323507
##  [601] -0.254971953  0.853144172  1.013845325  0.335602045 -0.443888715
##  [606] -0.612283346 -0.347518403  0.275813968  0.252924439 -0.208136235
##  [611] -0.009480470 -0.056888215 -0.420579958 -2.013337567 -0.259268862
##  [616]  0.597868469  0.080749354  0.038728417 -0.019356712 -0.187151108
##  [621]  0.135777325  0.726392252  0.176282051 -0.559910414 -1.203346203
##  [626] -0.042337003 -0.068419509  0.844418362  0.591639456  0.784212895
##  [631]  0.991772434  2.093529950 -0.287640727  0.319488818  0.095850597
##  [636]  0.000000000  1.238686560 -0.176969549 -0.314830664 -0.205439549
##  [641] -0.190499601  0.935845339  0.988166402  0.782193767  0.833058644
##  [646] -0.668667717  0.397917664  1.215841702  0.465184749  0.000000000
##  [651]  0.000000000  1.456495619 -0.958983247 -0.303313112  0.000000000
##  [656] -0.289609174 -0.859615667  0.704308712  1.263590949 -0.156703424
##  [661] -0.778933907 -1.224441971 -0.355871886  1.208333333  0.211727342
##  [666]  0.856857797  1.108524876 -0.146758367  0.409221902 -0.080362781
##  [671] -1.074280462 -0.229384437 -0.256104304  0.586467482  1.287927133
##  [676] -0.294976803  1.114462157 -0.818112093 -0.461119863 -1.619957415
##  [681]  0.617121465 -0.322655660 -0.644483975 -0.824772527 -0.455769629
##  [686]  0.883008771  0.722032300  0.222371770 -1.246606137 -0.954886773
##  [691] -0.495478017  0.245972943 -2.226278464  0.419280796  1.429355114
##  [696] -1.727712509 -0.687947166 -0.049259567  0.970275682  0.851128737
##  [701] -1.255331377 -0.542212964 -0.394246466 -1.298741458  1.300166045
##  [706]  1.051524711 -0.749831670  0.394708440 -1.154897564 -0.624592151
##  [711]  0.109443402 -1.443073559 -1.064874972  0.233846942  0.015979546
##  [716] -0.194919316 -0.992508164 -0.194024059  0.000000000  0.000000000
##  [721]  0.965526179  0.490982607 -0.079833945 -0.262064557  0.916431684
##  [726]  0.307995174 -0.421005983 -0.448216670  1.168694319 -0.950036297
##  [731] -0.325027086 -0.949488491  0.093599716  1.047981427 -0.880747998
##  [736]  0.618138502  0.790324129 -0.638095238 -0.146969552  0.000000000
##  [741] -0.809522286 -0.951612903  1.156163491  0.000000000 -0.264005151
##  [746]  1.242817483 -0.184931288  0.233189586 -0.592772006 -0.115414209
##  [751]  0.253562717 -0.224107572  0.202149848  0.144101447 -0.604355195
##  [756] -0.620898211 -2.214237156 -0.033104909 -1.765076001  0.000000000
##  [761]  0.138214671 -1.299444538  1.667860432  0.570316694  0.386950430
##  [766] -0.152854390  1.111554846 -0.306102297  0.891412724 -1.295853922
##  [771]  0.772469582  0.203974207 -0.515463918 -0.237615920 -1.713586291
##  [776] -1.040018848  0.687028093 -0.608025942 -2.236269712  0.809984009
##  [781]  0.313803924  1.282227570 -0.919797712  0.589202521  1.157880398
##  [786] -0.181793698 -0.617200675  0.600671938 -0.067467278  0.722387254
##  [791] -0.666934781  1.396808259  1.500682128  0.799895096  0.234161571
##  [796]  0.301752109 -0.456118785  0.581697647  0.633259022 -0.276110059
##  [801]  0.357361321 -1.119594508  0.441228952 -0.429600439  0.480114189
##  [806]  1.940337057  0.091844814 -0.313251487  0.539596889  0.138910813
##  [811] -0.104038589 -0.050495487 -0.909377960  0.130648142 -0.003182382
##  [816]  0.162306664  1.366250437 -0.241356612  0.276503488 -0.629817635
##  [821]  0.119824678  0.948001638  0.904779733  0.955414013  0.000000000
##  [826] -0.474717467  0.052314131 -1.070341094  0.192756101  0.583361777
##  [831] -1.113681937 -0.046796032 -0.745965854 -1.279874214 -0.334469468
##  [836] -0.236512401 -1.332735311  1.068251185 -1.529219006  0.456755081
##  [841] -1.357539541 -0.740789517  0.212286055  0.231696015 -0.937850869
##  [846]  0.290019335  1.003822503 -1.520387008  1.129490393 -1.414268248
##  [851]  0.613373555 -1.515757212  0.950512465  0.479158290  1.120485544
##  [856]  1.342215480  0.894890986  1.335268505 -1.120341195  0.434544694
##  [861] -1.118518044 -0.794088095  0.078410873 -0.992426221 -0.121999472
##  [866] -0.930969595 -0.033323336  0.990033001  1.789015051  0.441014333
##  [871] -0.035513657 -0.484449181  0.749683575 -0.219043938 -1.026601240
##  [876] -0.065235828  1.168483582  0.125822687 -0.889318511  0.630709711
##  [881]  1.295512551  0.354021815 -0.603845543  0.111910472 -0.319386777
##  [886] -1.355334829 -1.663039595  0.300578035 -0.102087861  0.448327015
##  [891]  0.459453251  0.663160302 -1.356526254 -0.733649164  0.536903854
##  [896] -0.573594857 -0.119359438  0.043153527 -1.211095627 -1.138615524
##  [901]  0.101922946  1.160738528 -0.241562102  1.351987624  0.690204407
##  [906]  0.781044028  0.402210523  0.693720688 -0.268460717  0.000000000
##  [911]  0.000000000  0.402153467 -0.975515214 -0.003262004  0.000000000
##  [916]  0.006524221 -0.459927586 -0.632455106  1.078389341 -0.300163132
##  [921]  0.150533412 -0.359430140 -0.531252050  0.497824080  0.931666831
##  [926] -0.737803491  0.029469548 -0.860911977 -1.079706795 -1.391902266
##  [931]  0.500981653  0.444594139  0.841660519  0.495461045 -0.870226987
##  [936] -0.143529490  0.859072068  0.576674510  0.823804659  0.075170768
##  [941]  0.349444807 -0.006508934  0.862489829  0.351726363 -0.926074793
##  [946] -0.318068222  0.117214209 -0.774008911 -0.226147947 -0.840943433
##  [951]  0.159014113 -0.128993848  0.986918364 -0.380415177 -0.408203575
##  [956] -0.528873170  1.060047187 -0.098645272 -0.431176354 -0.766916796
##  [961] -0.829474666  0.507222036 -0.173790983  1.144999833 -0.307834895
##  [966]  1.288266153 -0.118009572  1.545782737 -0.155133965  1.129705759
##  [971]  0.345688496  0.149920255 -0.105105583  0.542022701 -0.114162491
##  [976] -0.682583021  0.447527411  1.078827610 -1.205843461  0.165715925
##  [981]  1.431707550  0.065869954  0.335402169  0.312412134 -0.208664237
##  [986] -0.415080207  0.592309380 -0.031154589  0.000000000  0.000000000
##  [991] -0.445649464 -0.763812803  0.145105833  0.793775790  0.293759180
##  [996]  0.174492880  0.351488382 -0.266567479 -0.027971159  0.115024715
## [1001]  0.863246802  0.443322456  0.052105683 -0.385993934  0.000000000
## [1006]  0.292154873  0.886176867  0.844959120 -0.229060550  0.012083497
## [1011] -0.299030417 -0.103005332 -0.351792321 -0.754762919  0.720637841
## [1016]  0.222256051  1.078437329  0.027048959 -0.513791239  0.000000000
## [1021] -0.036241732  0.287017735  0.638669639  0.131712866  0.944693572
## [1026]  0.100693005 -0.272189349  0.296665480 -1.274846190  0.206729185
## [1031]  0.101656401 -0.244922342  0.916222528 -0.127581296  0.451561154
## [1036] -0.121255139  0.032571361  0.754817512 -0.716845878 -2.077291827
## [1041]  0.120875136 -0.920560184  0.344228836  0.625379478  0.274542931
## [1046]  0.767217258  1.364504956 -0.194409261  2.201694065 -0.228132490
## [1051]  0.260492041 -0.386836028 -0.098533588 -0.522162915  0.390761694
## [1056] -0.636147098 -0.450200251 -0.143893343  0.373485472  0.542029240
## [1061]  0.037883203  0.623379650  0.115797701  0.306508978 -0.161434460
## [1066] -0.386914215  1.449317372 -0.694305552  0.195649672  0.031587411
## [1071] -0.421989378 -0.014414207  0.184528443 -0.207212133 -0.752703677
## [1076]  0.087173825  0.600975496  0.158725578  1.129487697  0.737933785
## [1081] -0.155556184 -0.405076200  0.116613100  0.139204545  0.000000000
## [1086] -0.632642061  0.039970308 -0.747716895  0.908620392  0.378982162
## [1091]  0.275356971  0.716226928 -0.340107373  0.251015343 -0.146293431
## [1096] -0.377539233  0.987018864 -0.151226616 -0.022437875 -0.878078887
## [1101]  0.229247446  0.567572147 -0.101081005 -1.211388741 -0.221918744
## [1106]  0.464784716 -1.087049073 -0.172166428  0.839321644  0.342055755
## [1111]  0.113629907  0.564667159  0.008464772 -0.505022007 -0.459378988
## [1116] -1.430077201  0.410392763  1.424747431  1.254327714 -0.299887892
## [1121]  0.137744919  0.864634215 -0.400779293 -0.760073772 -0.560342400
## [1126]  0.107603002  0.070715357 -0.514444005 -0.616547335  0.345921839
## [1131]  0.544159544 -0.294692698  0.122204223 -0.641498723  0.411381556
## [1136]  0.216228519  0.417329094  0.127222866 -0.513892026  0.380314469
## [1141]  0.313843022  0.662363652  1.103208826 -0.044311510  0.543056633
## [1146] -0.680665785  0.785216836 -0.823147230  0.596807772  0.689845475
## [1151] -0.005480954  0.183622013  0.240733142  0.000000000  0.147367847
## [1156] -0.149876012 -0.038207521 -0.636125369 -0.261024866  0.608815427
## [1161]  0.076668218  0.205203973  0.251201398 -0.789846388 -1.276560698
## [1166] -0.533911738  1.028823842  0.542380386  0.688079707  0.000000000
## [1171]  0.000000000  0.494765328  0.008160157  0.342698616  0.000000000
## [1176] -0.037947578  0.751104965 -0.040370330 -0.258474462  0.434606560
## [1181]  0.000000000 -1.319679622 -0.452131281  0.065665271  0.147649906
## [1186]  1.307778415 -0.172478844  1.201339021 -0.008002774  0.154732686
## [1191] -0.511427202  0.621151272 -0.638603587  0.013389749 -0.002677591
## [1196]  0.018743641  0.642518673 -0.172904530  0.759432957 -0.917673816
## [1201]  0.024021780 -0.571047365 -0.475027509  0.213029878  0.277157388
## [1206]  0.563516342 -0.069377735  0.929238985 -0.235462194 -0.705401893
## [1211] -0.793205673  0.296128789  0.386514924  0.008021390 -0.965163222
## [1216]  0.315857675  0.600123792 -0.283558932  0.673355510  0.423694940
## [1221]  0.225547949 -0.481851156 -0.018622469 -1.274546325 -0.964881546
## [1226] -0.952510546  0.021981041  1.140015933 -1.004943234  0.680421422
## [1231]  0.637671681 -0.205794747  0.350029848  0.235243220 -0.677097383
## [1236] -0.570357696  0.314130405  0.005446030  0.737896858  0.505446388
## [1241]  0.271622203 -0.091189486  0.818769966  0.000000000  0.000000000
## [1246]  0.079880711  0.234129729 -0.615809311  0.603600235  0.629181268
## [1251]  0.918084685 -0.514992288  0.396783687  0.952705002 -0.114075342
## [1256] -0.511329717 -0.401774067  0.044530595  0.353467913 -0.615737842
## [1261]  0.228394414 -0.311689672 -0.777719390 -0.656710094  0.000000000
## [1266] -0.762341401 -0.421702928  0.566449977  0.700050962 -0.404858300
## [1271]  0.548245614  0.438864803 -0.598485250  0.959079284 -0.300823306
## [1276]  0.296437457 -0.665012931 -0.456936401  0.136108887  0.000000000
## [1281]  0.215879108  0.412212116 -0.768069497  0.029359169 -0.229467955
## [1286]  0.427899016 -0.047933532  0.183833324 -1.422758822  0.593503831
## [1291]  0.721411714  0.359453630 -0.198981216 -0.215328176  0.210464621
## [1296] -0.135584208 -0.085187946 -0.684749014 -0.139503689 -0.308948768
## [1301] -0.843483885  0.434841690 -0.451900961  0.875285419  0.393424953
## [1306]  0.002684131 -0.311350887  1.251985676 -0.462692124 -0.045415687
## [1311]  0.288654283  0.359779335 -0.446120346 -0.552147239 -0.804656278
## [1316] -1.784603737  0.713046830  0.962221858  0.462988033 -0.786955936
## [1321]  0.736152989 -1.067845971  0.433384213 -0.309387467  0.149729126
## [1326] -0.279982603  0.945890691  0.842514582  0.969365895  0.469421312
## [1331]  0.002639706  0.599197550  0.007871743 -0.018365955 -0.194190044
## [1336]  0.528488418  0.180467647  0.185364071  0.925105540 -0.237548091
## [1341]  0.504697570 -0.285846724  0.490689807  0.421474647  0.000000000
## [1346] -0.046065259  0.332846865 -0.859979075 -0.447876448  0.434377909
## [1351] -0.733704047  0.435695946  0.374415782  0.149207656  0.457230927
## [1356]  0.135522144 -0.268123899  0.691315035  0.897624981  0.234380907
## [1361] -0.123202253 -0.417893915  0.470207549 -0.256648970 -1.120052471
## [1366] -0.234711840  0.644418872 -0.063521102  0.335604597  0.184978715
## [1371]  0.973771404  0.573618556 -0.376080297  0.620000000  0.166467899
## [1376]  0.101699119 -0.651699871 -0.364153343  0.836107843  0.263151362
## [1381]  0.299601357 -0.651723116  0.439817116  0.272135771  0.493449458
## [1386] -0.390366060 -0.709849157 -0.719888790  0.575086263  0.072096261
## [1391] -0.790003230 -0.741204457  0.383460733 -0.769018120 -0.516651893
## [1396] -0.178203203  0.372344495 -0.896917956  0.266639319  0.092052777
## [1401]  0.508379317 -0.188089368 -0.020372304  0.817605257  0.098529635
## [1406]  0.403826254 -0.384605716 -0.227112143  1.641458850  0.893323712
## [1411]  0.340354166 -0.471929997  0.024696236  0.192583082 -0.480532282
## [1416]  0.569518386 -0.401329558  0.148323939 -2.177132701  1.226343679
## [1421]  0.600757802 -1.318234755  0.205900816 -0.458566166  0.538717148
## [1426] -0.355551104  0.969946728  0.823751929  0.649174339  0.235432607
## [1431]  0.129673126  0.000000000  0.000000000 -0.036652413  0.603764361
## [1436]  0.068032169  0.000000000 -1.483549836  0.791147040  0.415698741
## [1441] -0.674540363  0.213298029 -0.012232416 -0.743821874  1.249815116
## [1446]  1.482725878 -0.223117893  0.928130034  0.243001787 -0.325593555
## [1451]  0.035765379  0.562507448  0.000000000 -0.007110521 -0.161183275
## [1456]  0.603038936 -0.705621372  0.496732026  1.120991392 -0.420973853
## [1461]  0.072807553  0.483465934 -0.364358286  0.982207740 -0.002321371
## [1466] -0.078928430  0.000000000  0.529702855  0.321231310 -0.073715734
## [1471] -0.126792383  0.579368926 -0.029834305 -0.443056863 -0.131433315
## [1476]  0.314007989 -0.354454853  0.228674382 -0.712112832 -0.027853214
## [1481]  1.174804393  0.055074925  0.899061948  0.477348669  0.386851571
## [1486]  0.155496462 -0.490515942 -0.560768796  0.604861632 -1.152724725
## [1491] -0.377289461 -0.564634594 -1.710447348 -0.077499354 -0.940114694
## [1496]  1.326278827  0.721193247  0.265023829  0.000000000  0.000000000
## [1501] -1.502469336 -0.270709258 -0.519284332  0.521994970  0.828494548
## [1506] -0.056183721  0.538730003  0.486918435 -0.985347306 -0.444891938
## [1511]  0.825552132  0.181953905  0.100125739  0.269836470  0.422224800
## [1516]  0.401968258  0.957180000  0.018232787 -0.428392389  0.457697325
## [1521]  0.990956102  0.063159794  0.202885482  0.238470191  0.000000000
## [1526]  1.429661550  0.402717235  0.945454545  1.102523797  0.835690686
## [1531]  0.458283365 -0.087401407 -0.121615567  0.271297958 -1.037516777
## [1536] -0.811590459  0.748779164  0.211115898  0.214970549  0.000000000
## [1541]  0.424728646 -0.087576897 -0.111170497 -1.091539499 -1.265877567
## [1546] -0.109581836 -0.015358287  0.419126199  1.503430794  0.897739505
## [1551]  1.128725969 -0.312262638  0.689976295  0.540211040 -0.794463841
## [1556] -1.325577965 -0.538208534 -0.070861069 -1.284999033 -0.394000740
## [1561]  0.448009091  0.950764746  0.385775862 -0.377852680 -0.769346809
## [1566]  2.686443991  0.488547681  1.690028202 -0.391166670 -0.043633644
## [1571] -1.085081173  0.081958600  0.113388208  0.664876882  1.206375664
## [1576]  0.862601392  1.324679036 -0.306192337 -1.450798141 -1.466005085
## [1581]  0.853153547  0.573586151 -0.237973125 -0.234428016  0.228795218
## [1586]  0.287911817  1.039658779 -0.401842794 -0.167091187 -0.073479885
## [1591]  1.325653124  1.322420675  1.205682225 -1.091059212  0.011925347
## [1596]  0.872433872 -1.422435872 -0.245823007 -2.514375013 -0.632989436
## [1601]  1.638055843  0.899434292  0.395288803 -1.544797107  0.000000000
## [1606] -0.301973026  0.421586886 -1.253337138 -0.575803855  1.093928386
## [1611]  1.683709088  0.498768224  0.289336736  0.058101096 -0.180209042
## [1616] -0.696060339 -0.915059085 -1.027481041 -0.135947928  1.128253785
## [1621]  1.499112770  0.737480910  0.660270092 -0.443898379  1.033082527
## [1626] -0.949622712  0.988562904 -0.230441976  3.174415161 -0.114803972
## [1631]  0.457828094  1.390107166 -0.394952136  0.655199109 -0.577774443
## [1636]  0.105660377 -0.819888420 -0.841869216  0.182069071  1.392688386
## [1641] -0.022641082 -0.664288815  0.459752645 -0.317706462 -1.140179469
## [1646]  0.285933602 -1.475343960 -3.055080796 -0.426725433 -2.605528953
## [1651] -1.762141839  2.447743618 -1.434787963  0.841333639  1.323751110
## [1656] -0.183433882  0.222567076 -0.906627549 -2.045725564  0.892051298
## [1661] -0.272530582 -1.529090264 -0.199135666  0.653789004  2.640347547
## [1666] -0.443805219 -0.315763404  1.621084450  1.576888599 -1.748967066
## [1671] -0.716531254  0.569548679 -0.044978737 -1.169973410  1.862659878
## [1676]  1.133731562 -0.138621022  2.245156618  1.192373532  0.865270567
## [1681] -0.198558044 -0.896254660 -1.847701093  0.184674040  1.518274796
## [1686]  1.593189894 -0.242149364 -0.433459197 -2.865545731 -0.039839050
## [1691]  0.629707863 -0.710919244  0.000000000  0.000000000  1.964538583
## [1696]  0.389249667  0.062350213  0.000000000  1.129393438  1.328583807
## [1701]  0.036104513 -0.765519337  0.248846691 -1.886540261 -1.352587432
## [1706]  0.297900884  0.452408584  1.153341558  1.883541755  0.199502195
## [1711]  0.087226942 -0.111780531 -0.364167441 -1.364908340  1.076929015
## [1716]  1.701290766  0.869271352  0.926925511  0.665756860  2.573967207
## [1721]  0.246472584 -0.302879133  0.189427785  0.415596461 -0.511572553
## [1726]  0.221392990 -0.096200096 -0.987892081  0.536695182  0.673557494
## [1731]  1.594334419  0.243453893 -0.085613447  0.000000000 -0.274547521
## [1736] -0.908325735  1.665192001  0.342900907  0.043366639  0.924175958
## [1741] -0.221626636 -1.284501610 -0.654096388  1.532762132  0.622525031
## [1746]  0.164979635  0.022304195 -0.600363649 -0.215710637  0.048423638
## [1751]  0.860832138  1.177398070  1.597330442 -0.693576085 -0.156137199
## [1756]  0.617117875 -0.265721878 -1.042260129  0.570644812 -0.461333827
## [1761]  0.343375226  1.439600823  0.584950811  0.188342585  0.685993206
## [1766] -0.193258869 -0.636691828  0.830690976  0.000000000  0.000000000
## [1771] -0.022930145 -0.491472944 -1.187007129 -1.329556814  0.538651177
## [1776]  0.015115635 -0.401343409 -0.556389203 -0.579847748 -2.413069800
## [1781]  1.471410597  0.456377226  1.632065283  1.400064099  0.000000000
## [1786] -0.412556352  0.098555082 -0.907816568  0.535533850  0.979932326
## [1791] -1.187731201  0.271962664 -0.408511778 -0.516096495 -1.547872520
## [1796]  0.885654457  0.503589778  0.477367370  0.336949929  0.000000000
## [1801]  0.253542884 -1.683219723 -0.134578038  0.143288470 -0.558706798
## [1806]  0.075369568  0.960238262 -0.637461006  1.475907726  1.521698922
## [1811] -0.298121832 -0.538223861 -2.253064769 -1.413071337 -0.937640819
## [1816]  0.244939378  1.797650837 -0.353181203 -1.101151047 -0.621074790
## [1821]  1.043344304  0.569993070  0.930248583  0.315758931  0.120801715
## [1826] -0.883677458  1.498499786  0.680754742  0.473138485  0.031728007
## [1831]  0.218686877  0.103274811 -0.663937700 -0.700202690  0.511142226
## [1836]  2.383270115  0.840956034 -0.564090059  0.935129479  0.080984775
## [1841] -0.749312186 -2.333393122 -0.223721117 -1.403902145 -0.953787146
## [1846] -0.005140419  0.142225573  1.139610890 -1.246891231 -0.467706013
## [1851] -1.266846825 -1.806105193 -0.681757656  1.542696770 -1.633687768
## [1856] -2.770420216  0.541157414 -1.147889129  1.027872951

qqline(eu_percentreturns)

Plotting pairs of data

DAX<-eu_stocks[,1]
FTSE<-eu_stocks[,3] 
# Make a scatterplot of DAX and FTSE
plot(DAX, FTSE)

# Make a scatterplot matrix of eu_stocks
pairs(eu_stocks)

# Convert eu_stocks to log returns
logreturns <- diff(log(eu_stocks))

# Plot logreturns
plot(logreturns)

# Make a scatterplot matrix of logreturns
pairs(logreturns)

Calculating sample covariances and correlations

x<-read.csv("x1.csv")
x<-ts(x)
n<-length(x)
n

## [1] 150

# Define x_t0 as x[-1]
x_t0 <- x[-1]

# Define x_t1 as x[-n]
x_t1 <- x[-n]

# Confirm that x_t0 and x_t1 are (x[t], x[t-1]) pairs  
head(cbind(x_t0, x_t1))

##            x_t0       x_t1
## [1,]  1.2996380  2.0655438
## [2,]  0.0335780  1.2996380
## [3,] -0.3425806  0.0335780
## [4,]  0.2325613 -0.3425806
## [5,]  0.4681201  0.2325613
## [6,]  4.3411156  0.4681201

# Plot x_t0 and x_t1
plot(x_t0,x_t1)

# View the correlation between x_t0 and x_t1
cor(x_t0,x_t1)

## [1] 0.7630314

# Use acf with x
acf(x, lag.max = 1, plot =FALSE)

## 
## Autocorrelations of series 'x', by lag
## 
##     0     1 
## 1.000 0.758

# Confirm that difference factor is (n-1)/n
cor(x_t1, x_t0) * (n-1)/n

## [1] 0.7579445

The autocorrelation function

# Generate ACF estimates for x up to lag-10
acf(x, lag.max =10, plot = FALSE)

## 
## Autocorrelations of series 'x', by lag
## 
##     0     1     2     3     4     5     6     7     8     9    10 
## 1.000 0.758 0.537 0.345 0.227 0.198 0.140 0.114 0.124 0.118 0.100

# Type the ACF estimate at lag-10 
acf(x, lag.max =0.100, plot = FALSE)

## 
## Autocorrelations of series 'x', by lag
## 
## 0 
## 1

# Type the ACF estimate at lag-5
acf(x, lag.max =0.198, plot = FALSE)

## 
## Autocorrelations of series 'x', by lag
## 
## 0 
## 1

Visualizing the autocorrelation function

# View the ACF of x
acf(x)

# View the ACF of y
acf(y)

# View the ACF of z
acf(z)

##4. Autoregression Simulate the autoregressive model

# Simulate an AR model with 0.5 slope
x <- arima.sim(model = list(ar=0.5), n = 100)

# Simulate an AR model with 0.9 slope
y <- arima.sim(model=list(ar=0.9),n=100)

# Simulate an AR model with -0.75 slope
z <- arima.sim(model=list(ar=-0.75),n=100)

# Plot your simulated data
plot.ts(cbind(x,y, z))

Estimate the autocorrelation function (ACF)

# Calculate the ACF for x
acf(x)

# Calculate the ACF for y
acf(y)

# Calculate the ACF for z
acf(z)

Compare the random walk (RW) and autoregressive (AR) models

# Simulate and plot AR model with slope 0.9 
x <- arima.sim(model = list(ar=0.9), n = 200)
ts.plot(x)

acf(x)

# Simulate and plot AR model with slope 0.98
y <- arima.sim(model=list(ar=0.98),n=200)
ts.plot(y)

acf(y)

# Simulate and plot RW model
z <-arima.sim(model = list(order = c(0, 1, 0)), n = 200)
ts.plot(z)

acf(z)

Estimate the autoregressive (AR) model

# Fit the AR model to x
arima(x, order =c(1,0,0))

## 
## Call:
## arima(x = x, order = c(1, 0, 0))
## 
## Coefficients:
##          ar1  intercept
##       0.9179     0.0680
## s.e.  0.0270     0.8579
## 
## sigma^2 estimated as 1.103:  log likelihood = -294.49,  aic = 594.98

# Copy and paste the slope (ar1) estimate
0.8575

## [1] 0.8575

# Copy and paste the slope mean (intercept) estimate
-0.0948

## [1] -0.0948

# Copy and paste the innovation variance (sigma^2) estimate
1.022

## [1] 1.022

# Fit the AR model to AirPassengers
AR <-arima(AirPassengers,order=c(1,0,0))
print(AR)

## 
## Call:
## arima(x = AirPassengers, order = c(1, 0, 0))
## 
## Coefficients:
##          ar1  intercept
##       0.9646   278.4649
## s.e.  0.0214    67.1141
## 
## sigma^2 estimated as 1119:  log likelihood = -711.09,  aic = 1428.18

# Run the following commands to plot the series and fitted values
ts.plot(AirPassengers)
AR_fitted <- AirPassengers - residuals(AR)
points(AR_fitted, type = "l", col = 2, lty = 2)

Simple forecasts from an estimated AR model

# Simulate an AR model with 0.5 slope
x <- arima.sim(model = list(ar=0.5), n = 100)

# Simulate an AR model with 0.9 slope
y <- arima.sim(model=list(ar=0.9),n=100)

# Simulate an AR model with -0.75 slope
z <- arima.sim(model=list(ar=-0.75),n=100)

# Plot your simulated data
plot.ts(cbind(x,y, z))

# Simulate and plot AR model with slope 0.9 
x <- arima.sim(model = list(ar=0.9), n = 200)
ts.plot(x)

acf(x)

# Simulate and plot AR model with slope 0.98
y <- arima.sim(model=list(ar=0.98),n=200)
ts.plot(y)

acf(y)

# Simulate and plot RW model
z <-arima.sim(model = list(order = c(0, 1, 0)), n = 200)
ts.plot(z)

acf(z)

# Fit an AR model to Nile
AR_fit <-arima(Nile, order  =c(1,0,0))
print(AR_fit)

## 
## Call:
## arima(x = Nile, order = c(1, 0, 0))
## 
## Coefficients:
##          ar1  intercept
##       0.5063   919.5685
## s.e.  0.0867    29.1410
## 
## sigma^2 estimated as 21125:  log likelihood = -639.95,  aic = 1285.9

# Use predict() to make a 1-step forecast
predict_AR<- predict(AR_fit, n.ahead = 1)

# Obtain the 1-step forecast using $pred[1]
predict_AR$pred[1]

## [1] 828.6576

# Use predict to make 1-step through 10-step forecasts
predict(AR_fit, n.ahead = 10)

## $pred
## Time Series:
## Start = 1971 
## End = 1980 
## Frequency = 1 
##  [1] 828.6576 873.5426 896.2668 907.7715 913.5960 916.5448 918.0377
##  [8] 918.7935 919.1762 919.3699
## 
## $se
## Time Series:
## Start = 1971 
## End = 1980 
## Frequency = 1 
##  [1] 145.3439 162.9092 167.1145 168.1754 168.4463 168.5156 168.5334
##  [8] 168.5380 168.5391 168.5394

# Fit an AR model to Nile
AR_fit <-arima(Nile, order  =c(1,0,0))
print(AR_fit)

## 
## Call:
## arima(x = Nile, order = c(1, 0, 0))
## 
## Coefficients:
##          ar1  intercept
##       0.5063   919.5685
## s.e.  0.0867    29.1410
## 
## sigma^2 estimated as 21125:  log likelihood = -639.95,  aic = 1285.9

# Use predict() to make a 1-step forecast
predict_AR<- predict(AR_fit, n.ahead = 1)

# Obtain the 1-step forecast using $pred[1]
predict_AR$pred[1]

## [1] 828.6576

5. A simple moving average

# Generate MA model with slope 0.5
x <- arima.sim(model = list(ma=0.5), n =100)

# Generate MA model with slope 0.9
y <- arima.sim(model=list(ma=0.9),n=100)

# Generate MA model with slope -0.5
z <- arima.sim(model=list(ma=-0.5),n=100)

# Plot all three models together
plot.ts(cbind(x,y,z))

Estimate the autocorrelation function (ACF) for a moving average

# Calculate ACF for x
acf(x)

# Calculate ACF for y
acf(y)

# Calculate ACF for z
acf(z)

Estimate the simple moving average model

# Fit the MA model to x
arima(x, order = c(0,0,1))

## 
## Call:
## arima(x = x, order = c(0, 0, 1))
## 
## Coefficients:
##          ma1  intercept
##       0.4321    -0.0146
## s.e.  0.0939     0.1400
## 
## sigma^2 estimated as 0.9617:  log likelihood = -140.04,  aic = 286.09

# Paste the slope (ma1) estimate below
0.7928

## [1] 0.7928

# Paste the slope mean (intercept) estimate below
0.1589

## [1] 0.1589

# Paste the innovation variance (sigma^2) estimate below
0.9576

## [1] 0.9576

# Fit the MA model to Nile
MA <- arima(Nile, order =c(0,0,1))
print(MA)

## 
## Call:
## arima(x = Nile, order = c(0, 0, 1))
## 
## Coefficients:
##          ma1  intercept
##       0.3783   919.2433
## s.e.  0.0791    20.9685
## 
## sigma^2 estimated as 23272:  log likelihood = -644.72,  aic = 1295.44

# Plot Nile and MA_fit 
ts.plot(Nile)
MA_fit <- Nile - resid(MA)
points(MA_fit, type = "l", col = 2, lty = 2)

Simple forecasts from an estimated MA model

# Make a 1-step forecast based on MA
predict_MA <-predict(MA,n.ahead=1)

# Obtain the 1-step forecast using $pred[1]
predict_MA$pred[1]

## [1] 868.8747

# Make a 1-step through 10-step forecast based on MA
predict(MA,n.ahead=10)

## $pred
## Time Series:
## Start = 1971 
## End = 1980 
## Frequency = 1 
##  [1] 868.8747 919.2433 919.2433 919.2433 919.2433 919.2433 919.2433
##  [8] 919.2433 919.2433 919.2433
## 
## $se
## Time Series:
## Start = 1971 
## End = 1980 
## Frequency = 1 
##  [1] 152.5508 163.1006 163.1006 163.1006 163.1006 163.1006 163.1006
##  [8] 163.1006 163.1006 163.1006

# Plot the Nile series plus the forecast and 95% prediction intervals
ts.plot(Nile, xlim = c(1871, 1980))
MA_forecasts <- predict(MA, n.ahead = 10)$pred
MA_forecast_se <- predict(MA, n.ahead = 10)$se
points(MA_forecasts, type = "l", col = 2)
points(MA_forecasts - 2*MA_forecast_se, type = "l", col = 2, lty = 2)
points(MA_forecasts + 2*MA_forecast_se, type = "l", col = 2, lty = 2)

AR vs MA models

AR= arima(x = Nile, order = c(1, 0, 0))
MA=arima(x = Nile, order = c(0, 0, 1))
# # Find AIC of AR
AIC(AR)

## [1] 1285.904

# 
# # Find AIC of MA
AIC(MA)

## [1] 1295.442

# 
# # Find BIC of AR
BIC(AR)

## [1] 1293.72

# 
# # Find BIC of MA
BIC(MA)

## [1] 1303.257