Semana 2

pkges <- c("WDI","tidyverse","tseries","forecast")
#install.packages("pkges")
lapply(pkges,library,character.only=T)
#> -- Attaching packages ----------------------------- tidyverse 1.3.0 --
#> v ggplot2 3.3.0     v purrr   0.3.3
#> v tibble  2.1.3     v dplyr   0.8.5
#> v tidyr   1.0.2     v stringr 1.4.0
#> v readr   1.3.1     v forcats 0.5.0
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#> [13] "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
#> [19] "base"

## -- Attaching packages ---------------- tidyverse 1.3.0 --

## v ggplot2 3.3.0     v purrr   0.3.4
## v tibble  3.0.0     v dplyr   0.8.5
## v tidyr   1.0.2     v stringr 1.4.0
## v readr   1.3.1     v forcats 0.5.0

## -- Conflicts ------------- tidyverse_conflicts() --
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## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

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## [13] "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
## [19] "base"

options(scipen=999)
datos <- WDI(indicator='NY.GDP.MKTP.KN', country=c('CL','PE','BR',"AR"), start=1960, end=2018)
summary(datos)
#>     iso2c             country          NY.GDP.MKTP.KN                 year     
#>  Length:236         Length:236         Min.   :    69946000000   Min.   :1960  
#>  Class :character   Class :character   1st Qu.:   292830863724   1st Qu.:1974  
#>  Mode  :character   Mode  :character   Median :   664997245255   Median :1989  
#>                                        Mean   : 15935318938400   Mean   :1989  
#>                                        3rd Qu.:  7182050744270   3rd Qu.:2004  
#>                                        Max.   :153758254309000   Max.   :2018

df <- datos %>%  rename(GDP=NY.GDP.MKTP.KN) %>% select(-country) %>% mutate(GDP=GDP/(10^9))
datos.rshp<-reshape(data = df,timevar = "iso2c",idvar = "year",v.names = "GDP",direction = "wide") %>%
  rename(AR=GDP.AR,
         BR=GDP.BR,
         CL=GDP.CL,
         PE=GDP.PE)

datos.rshp<- datos.rshp %>% arrange(year) %>% select(-year)
ts <- ts(datos.rshp$AR,start = c(1960,1),end = c(2018,1))
plot(ts,main="PBI real MN (1960-2018)",xlab="",ylab="Miles de millones")

l_ts<-diff(log(ts))
plot(l_ts,main="Variación % PBI",col=2,xlab="",ylab="%")

mean(l_ts)
#> [1] 0.02331694

var(l_ts)
#> [1] 0.002741129

sd(l_ts)
#> [1] 0.05235579

set.seed(100)
y<-rnorm(1000,3,5)
x<-rnorm(1000,10,5)
cov(y,x)/var(x)
#> [1] 0.01480471

cor(y,x)
#> [1] 0.01409256

lm(y~x)
#> 
#> Call:
#> lm(formula = y ~ x)
#> 
#> Coefficients:
#> (Intercept)            x  
#>      2.9357       0.0148

Yi<-l_ts[-1]
Yj<-l_ts[-58]
cor(Yi,Yj)
#> [1] 0.1040253

cov(Yi,Yj)/(sd(Yi)*sd(Yj))
#> [1] 0.1040253

cov(Yi,Yj)/var(Yj)
#> [1] 0.1045314

lm(Yi~Yj)
#> 
#> Call:
#> lm(formula = Yi ~ Yj)
#> 
#> Coefficients:
#> (Intercept)           Yj  
#>     0.02027      0.10453

arima(l_ts,order = c(1,0,0))
#> 
#> Call:
#> arima(x = l_ts, order = c(1, 0, 0))
#> 
#> Coefficients:
#>          ar1  intercept
#>       0.1031     0.0233
#> s.e.  0.1308     0.0075
#> 
#> sigma^2 estimated as 0.002665:  log likelihood = 89.6,  aic = -173.19

acf(ts,lag.max = 20)

pacf(ts,lag.max = 20)

acf(l_ts,lag.max = 20)

pacf(l_ts,lag.max = 20)

model.1 <- arima(ts,c(1, 1, 1))
fmodel1 <- predict(model.1,n.ahead = 3)
ts.plot(ts,fmodel1$pred)

AIC(model.1)
#> [1] 534.1727

model.2 <-auto.arima(log(ts),ic="aic",trace=T)
#> 
#>  ARIMA(2,1,2) with drift         : Inf
#>  ARIMA(0,1,0) with drift         : -174.5762
#>  ARIMA(1,1,0) with drift         : -173.1943
#>  ARIMA(0,1,1) with drift         : -173.4599
#>  ARIMA(0,1,0)                    : -165.9136
#>  ARIMA(1,1,1) with drift         : -173.0501
#> 
#>  Best model: ARIMA(0,1,0) with drift

summary(model.2)
#> Series: log(ts) 
#> ARIMA(0,1,0) with drift 
#> 
#> Coefficients:
#>        drift
#>       0.0233
#> s.e.  0.0068
#> 
#> sigma^2 estimated as 0.002742:  log likelihood=89.29
#> AIC=-174.58   AICc=-174.36   BIC=-170.46
#> 
#> Training set error measures:
#>                         ME       RMSE        MAE         MPE      MAPE
#> Training set 0.00008789483 0.05146518 0.04318507 0.002160526 0.7285139
#>                   MASE      ACF1
#> Training set 0.8872934 0.1037083

fmodel2 <- forecast(model.2,level=c(95),h = 10)
plot(fmodel2)

options(scipen=999)
pkges<-c("pdfetch","tseries","tidyverse","forecast")
#install.packages(pkges)
lapply(pkges,"library",character.only=T)
#> [[1]]
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#> [13] "WDI"       "stats"     "graphics"  "grDevices" "utils"     "datasets" 
#> [19] "methods"   "base"

SP500data.mo <- pdfetch_YAHOO("^GSPC",interval = '1d')  #DATOS DE S&P500
tsSP500 <- SP500data.mo[,4]

R1 <- diff(log(tsSP500))
R1 <- na.omit(R1)

plot.ts(R1)

hist(R1, main="", breaks=20, freq=FALSE, col="grey")

acf(R1)

ts.arch <- garch(R1,c(0,1))
#> 
#>  ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** 
#> 
#> 
#>      I     INITIAL X(I)        D(I)
#> 
#>      1     1.651841e-04     1.000e+00
#>      2     5.000000e-02     1.000e+00
#> 
#>     IT   NF      F         RELDF    PRELDF    RELDX   STPPAR   D*STEP   NPRELDF
#>      0    1 -1.305e+04
#>      1    7 -1.306e+04  1.02e-03  1.21e-03  1.1e-04  1.3e+11  1.1e-05  7.67e+07
#>      2    8 -1.307e+04  5.30e-04  5.88e-04  1.1e-04  2.9e+00  1.1e-05  1.62e+02
#>      3    9 -1.307e+04  4.11e-05  5.15e-05  1.0e-04  2.0e+00  1.1e-05  1.55e+02
#>      4   10 -1.307e+04  3.82e-06  3.95e-06  1.1e-04  2.0e+00  1.1e-05  1.54e+02
#>      5   17 -1.313e+04  5.03e-03  7.01e-03  3.1e-01  2.0e+00  4.6e-02  1.53e+02
#>      6   19 -1.317e+04  3.18e-03  2.08e-03  2.1e-01  0.0e+00  5.0e-02  2.08e-03
#>      7   20 -1.321e+04  2.56e-03  1.73e-03  2.0e-01  0.0e+00  7.2e-02  1.73e-03
#>      8   22 -1.323e+04  1.66e-03  1.16e-03  1.6e-01  0.0e+00  8.4e-02  1.16e-03
#>      9   23 -1.324e+04  7.91e-04  6.29e-04  1.2e-01  1.2e-01  8.4e-02  6.35e-04
#>     10   24 -1.325e+04  3.75e-04  3.20e-04  9.5e-02  0.0e+00  8.1e-02  3.20e-04
#>     11   25 -1.325e+04  6.12e-05  5.56e-05  4.5e-02  0.0e+00  4.4e-02  5.56e-05
#>     12   26 -1.325e+04  4.33e-06  3.80e-06  1.1e-02  0.0e+00  1.1e-02  3.80e-06
#>     13   27 -1.325e+04  9.96e-08  9.66e-08  2.0e-03  0.0e+00  2.1e-03  9.66e-08
#>     14   28 -1.325e+04  1.07e-10  1.07e-10  7.2e-05  0.0e+00  7.5e-05  1.07e-10
#>     15   29 -1.325e+04  1.92e-15  3.11e-15  4.0e-07  0.0e+00  4.2e-07  3.11e-15
#> 
#>  ***** RELATIVE FUNCTION CONVERGENCE *****
#> 
#>  FUNCTION    -1.324688e+04   RELDX        3.964e-07
#>  FUNC. EVALS      29         GRAD. EVALS      16
#>  PRELDF       3.109e-15      NPRELDF      3.109e-15
#> 
#>      I      FINAL X(I)        D(I)          G(I)
#> 
#>      1    9.662103e-05     1.000e+00     1.023e-04
#>      2    5.245821e-01     1.000e+00    -3.448e-08

summary(ts.arch)
#> 
#> Call:
#> garch(x = R1, order = c(0, 1))
#> 
#> Model:
#> GARCH(0,1)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -9.10129 -0.35720  0.05799  0.48886  8.40322 
#> 
#> Coefficient(s):
#>       Estimate  Std. Error  t value            Pr(>|t|)    
#> a0 0.000096621 0.000001421    68.02 <0.0000000000000002 ***
#> a1 0.524582130 0.021572758    24.32 <0.0000000000000002 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Diagnostic Tests:
#>  Jarque Bera Test
#> 
#> data:  Residuals
#> X-squared = 15516, df = 2, p-value < 0.00000000000000022
#> 
#> 
#>  Box-Ljung test
#> 
#> data:  Squared.Residuals
#> X-squared = 3.6125, df = 1, p-value = 0.05735

ts.garch <- garch(R1,c(1,1))
#> 
#>  ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** 
#> 
#> 
#>      I     INITIAL X(I)        D(I)
#> 
#>      1     1.564902e-04     1.000e+00
#>      2     5.000000e-02     1.000e+00
#>      3     5.000000e-02     1.000e+00
#> 
#>     IT   NF      F         RELDF    PRELDF    RELDX   STPPAR   D*STEP   NPRELDF
#>      0    1 -1.306e+04
#>      1    7 -1.308e+04  1.27e-03  1.50e-03  1.2e-04  1.4e+11  1.2e-05  1.08e+08
#>      2    8 -1.309e+04  6.62e-04  1.11e-03  2.3e-04  2.1e+00  2.3e-05  2.54e+02
#>      3    9 -1.309e+04  1.38e-04  1.89e-04  2.2e-04  2.0e+00  2.3e-05  2.32e+02
#>      4   10 -1.309e+04  1.30e-05  1.22e-05  2.3e-04  2.0e+00  2.3e-05  2.36e+02
#>      5   17 -1.324e+04  1.14e-02  1.79e-02  4.8e-01  2.0e+00  9.6e-02  2.33e+02
#>      6   19 -1.336e+04  8.79e-03  9.07e-03  2.9e-01  2.0e+00  9.6e-02  5.44e+01
#>      7   21 -1.345e+04  6.58e-03  7.90e-03  2.2e-01  2.0e+00  9.6e-02  6.49e+01
#>      8   24 -1.376e+04  2.27e-02  2.15e-02  3.3e-01  1.9e+00  2.5e-01  1.64e+00
#>      9   26 -1.382e+04  4.17e-03  4.44e-03  4.7e-02  2.0e+00  5.1e-02  5.78e+00
#>     10   27 -1.383e+04  1.00e-03  8.79e-03  8.2e-02  2.0e+00  1.0e-01  8.81e+00
#>     11   29 -1.386e+04  2.15e-03  2.12e-02  3.5e-02  2.0e+00  4.9e-02  2.87e-01
#>     12   30 -1.389e+04  2.39e-03  2.75e-03  3.5e-02  1.9e+00  4.9e-02  1.48e-02
#>     13   38 -1.391e+04  1.32e-03  1.52e-03  2.0e-06  4.3e+00  2.6e-06  6.70e-02
#>     14   39 -1.391e+04  1.08e-04  2.69e-04  1.5e-06  2.0e+00  2.6e-06  2.37e-02
#>     15   40 -1.392e+04  6.97e-05  8.50e-05  1.9e-06  2.0e+00  2.6e-06  1.79e-02
#>     16   41 -1.392e+04  1.76e-06  1.68e-06  2.0e-06  2.0e+00  2.6e-06  1.86e-02
#>     17   49 -1.394e+04  1.43e-03  1.86e-03  2.9e-02  1.7e+00  3.9e-02  1.87e-02
#>     18   50 -1.395e+04  6.81e-04  6.42e-04  2.7e-02  2.4e-01  3.9e-02  6.65e-04
#>     19   51 -1.395e+04  6.23e-04  3.71e-04  1.8e-02  0.0e+00  3.7e-02  3.71e-04
#>     20   53 -1.398e+04  1.66e-03  1.55e-03  5.8e-02  0.0e+00  1.2e-01  2.00e-03
#>     21   55 -1.398e+04  3.41e-04  4.03e-04  1.4e-02  1.4e+00  2.7e-02  1.67e-03
#>     22   56 -1.398e+04  6.32e-05  1.51e-04  1.4e-02  3.6e-01  2.7e-02  1.64e-04
#>     23   57 -1.398e+04  1.91e-05  6.08e-05  5.8e-03  0.0e+00  1.3e-02  6.08e-05
#>     24   58 -1.398e+04  1.67e-05  1.83e-05  1.1e-03  0.0e+00  2.0e-03  1.83e-05
#>     25   59 -1.398e+04  1.33e-06  1.43e-06  9.7e-04  5.6e-01  2.0e-03  1.80e-06
#>     26   60 -1.398e+04  1.99e-07  2.09e-07  5.5e-04  0.0e+00  1.1e-03  2.09e-07
#>     27   72 -1.398e+04 -7.80e-15  1.26e-15  3.2e-15  3.1e+04  5.3e-15  2.65e-10
#> 
#>  ***** FALSE CONVERGENCE *****
#> 
#>  FUNCTION    -1.398328e+04   RELDX        3.180e-15
#>  FUNC. EVALS      72         GRAD. EVALS      27
#>  PRELDF       1.261e-15      NPRELDF      2.651e-10
#> 
#>      I      FINAL X(I)        D(I)          G(I)
#> 
#>      1    2.967649e-06     1.000e+00     3.321e+03
#>      2    1.446782e-01     1.000e+00    -3.143e-01
#>      3    8.347365e-01     1.000e+00    -1.463e-01

summary(ts.garch)
#> 
#> Call:
#> garch(x = R1, order = c(1, 1))
#> 
#> Model:
#> GARCH(1,1)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -6.6502 -0.4540  0.0713  0.6224  3.7812 
#> 
#> Coefficient(s):
#>        Estimate   Std. Error  t value            Pr(>|t|)    
#> a0 0.0000029676 0.0000002862    10.37 <0.0000000000000002 ***
#> a1 0.1446781773 0.0099975372    14.47 <0.0000000000000002 ***
#> b1 0.8347365095 0.0104825316    79.63 <0.0000000000000002 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Diagnostic Tests:
#>  Jarque Bera Test
#> 
#> data:  Residuals
#> X-squared = 956.99, df = 2, p-value < 0.00000000000000022
#> 
#> 
#>  Box-Ljung test
#> 
#> data:  Squared.Residuals
#> X-squared = 0.65569, df = 1, p-value = 0.4181

ts.garch$residuals
#>    [1]            NA -0.5491353517  0.2100684140 -0.0525487067  0.2118252272
#>    [6]  0.7375795826  0.5785366929  0.1015377313 -0.1182834463 -0.4174097256
#>   [11]  0.4232884870 -0.8058572313  0.5390948403  1.3272407352 -1.6480323934
#>   [16] -0.1547130842 -0.1491863708  0.8279677647  0.9475323913  0.7599738173
#>   [21]  0.2436135056 -0.1462957023  0.1109115172  0.2320998205 -0.2042852428
#>   [26] -1.2752489780 -0.5432625113  1.2849891887  1.2008022024  0.1547206409
#>   [31] -0.1368351859  0.4670065716 -0.2375247829 -0.1505397876 -0.6497955744
#>   [36] -0.2290797810 -6.6501725198  0.3851938276 -0.1934001279 -0.9224857559
#>   [41] -0.7691935211  1.2904756009 -0.1978431920  0.6139702109  0.0613448977
#>   [46]  0.2614476456 -2.1513380369  0.5623940278  0.3265665524 -0.3644770163
#>   [51]  1.0971231762  0.6270477997  1.7528865427 -0.0314989512  0.1066646414
#>   [56]  0.1014609575 -0.6979777930 -0.9267401340  0.4327871775 -0.1434264098
#>   [61]  0.3372126942  1.2649782210  0.1437947401  0.4179740396  0.0844058519
#>   [66]  0.3957469008 -1.0381167608  0.9441479354  0.5228312315  1.6403918145
#>   [71]  0.2914525458  0.0992347278 -0.1818622189  1.4632126664 -0.3315876634
#>   [76] -0.0528675370  1.5985912530 -0.1096750417 -0.0178507139 -1.2276409865
#>   [81]  0.3897758522  0.9896407389  0.6472130339  0.3283489595  0.4082013617
#>   [86] -0.1924263165  0.5531584249 -2.4570299196  1.2507012221 -0.2218755629
#>   [91] -0.1712713774  1.1950266521 -0.1218997287  0.9273856419  0.2151263678
#>   [96] -0.0945643099 -0.1872995840 -1.5837571525  0.7819896358  0.2273853259
#>  [101]  1.2117208387  0.0367582209  0.5681775510  0.2885898054 -0.8737792572
#>  [106] -1.4338933544 -2.5961676282  1.2097890966  0.0989520386 -1.1868547814
#>  [111]  1.6065074784  0.4596224116  0.6587519030 -0.1276238391  0.1948989242
#>  [116] -1.6472474459  0.6575814500 -1.4356110673 -0.3286574009 -0.3533797785
#>  [121]  1.0369654324 -0.0476560832 -0.1911893662  1.3791674289  0.4301773989
#>  [126]  0.0439841284  0.4443831471  0.1295458089 -2.1233619698  0.6804826429
#>  [131]  2.3172985977  0.2953838832 -0.1959988305 -0.0105825109 -0.2422301042
#>  [136]  0.5556746928 -1.5927820184  0.5624304895 -2.4143240762  0.4282201852
#>  [141] -2.3075425624 -1.2325195910  0.7533778918 -0.9730229897  0.5547617407
#>  [146]  0.3531010154 -2.3419541815  1.6143625502  0.3752530399  0.9175466543
#>  [151] -2.0073207021  0.0211009115 -0.0300650801 -1.2091204446 -0.8980018214
#>  [156]  0.2118589559  1.7155000702 -0.0168798196  0.0738485809  0.8596830073
#>  [161] -0.0809311726  0.9369601251 -0.7041951011 -2.0346743361  1.5397032765
#>  [166] -0.2723983718  0.7829041742  0.7546858366 -0.8680202304  0.3248638954
#>  [171] -1.4019504896 -0.0981027164  1.1287666125  0.0038929858  0.7415101123
#>  [176]  0.0184668715 -0.5057656600  2.9888992246  0.4287176533 -0.5091945672
#>  [181]  0.3680993727 -0.4514322988 -0.0311846118  0.5297363773  0.4025963708
#>  [186] -0.3314117035  1.5349590535 -0.0279517742 -0.5164055161  0.2500298557
#>  [191]  1.1988921775 -0.3888546837  1.0260057992 -0.2143336398 -0.6864610477
#>  [196]  0.6441344837 -1.1730679681 -0.8797904476  0.2348272974 -0.1061675265
#>  [201] -3.8668066903  0.3227483673  0.7993219150 -0.2285020553 -0.0979950663
#>  [206]  1.4762379323  0.3670713172 -0.6833981329  1.2990863007 -2.7647743744
#>  [211]  0.0589515346 -0.3957752585  1.0195073727 -2.5290700285 -0.0366242074
#>  [216] -0.9939229540 -0.6962104367  2.0745745815 -0.4228741792 -0.8493982680
#>  [221]  0.3415836865 -1.2405952476  0.3044688328 -1.1763219214  1.1971279361
#>  [226] -1.6344134331  0.9267563629  1.7874318185  0.0264290355  0.4674466393
#>  [231] -0.3807487636 -0.4541345997  1.1130302073  1.0856446606 -0.1281057807
#>  [236]  0.5833598755 -2.1013023795  0.4051911664  0.0880256733 -1.0793084431
#>  [241] -1.1677679481  0.4714453338 -0.1090905628  0.4233786782  1.5238760948
#>  [246]  0.6780536763  0.0709405429 -1.3627289796  0.1339059242 -0.6603169018
#>  [251] -1.4521424891  0.0000000000 -2.4750050636  0.2421795795 -1.5031086045
#>  [256]  1.0104077594  0.5914200098 -1.0767917658  0.8417727739 -2.0106576202
#>  [261] -0.3737910996 -2.1047042400 -0.3540457216 -0.7006068278  1.3921016363
#>  [266]  0.6186186377 -1.0411565389  1.1297258886  0.3925833010 -0.3274600242
#>  [271]  1.2269213061  0.8678971476 -0.7664485199 -2.4499764728 -0.4396339954
#>  [276]  0.4830860538 -0.2762241387  0.4155279774  0.5478365758  1.0807312519
#>  [281] -1.0686690532  0.0656231343 -0.0760567248  0.7610922852 -1.2217100739
#>  [286]  0.7135064065  1.2909793363  0.6179906213 -0.0862572231 -0.9072303484
#>  [291] -2.7962526521  0.0384345939 -0.2698549052  0.4393533396 -1.9913088408
#>  [296] -0.6313423258 -1.2218718546  2.7646271204 -0.4897580011  0.2957682474
#>  [301] -1.3119000064 -0.5371072561  2.6321118616 -1.1458554039  1.0859797878
#>  [306]  0.6938266704  0.1100438938 -0.4584776052 -0.6423412763 -0.4679208757
#>  [311]  0.3550824509  2.3747517824 -0.1010536215  0.0738956418  0.0491692796
#>  [316]  0.1048078539 -0.3725714509 -0.6345214323  0.3652373044 -1.8015853736
#>  [321] -0.2575177034  0.3756644141  1.9634261012  0.0458059135  1.4333180325
#>  [326] -0.1155549971 -0.7121152389  0.2419826624  0.5773403975  0.6111550798
#>  [331] -0.1038275070 -0.4133568429 -0.4326775894  2.0122499946  0.3163035213
#>  [336] -0.4749140782  0.8399093340 -2.0420774144  0.3369050576 -0.6630680396
#>  [341]  1.1185697191 -0.0383797634  0.4288929589  1.1937044671  0.1363876071
#>  [346]  0.1048694345 -1.1624030864 -1.9461538527  0.2632653560 -1.4319388607
#>  [351]  0.6804253881  0.4087290454  0.5826591020  0.1730203161 -1.2871962511
#>  [356] -0.6690165680 -0.0388654374  2.4525200311 -3.0101990022  0.0516343248
#>  [361] -0.1725512653 -1.3034101101  0.2390494963  1.1765088316  0.0062070515
#>  [366] -0.5649178601 -0.8546541438  0.3342001677 -1.7859461227  0.0044022667
#>  [371] -0.2528481776  0.5610071549 -3.0120764090 -0.2550547727  0.0936268823
#>  [376]  0.3066109422 -1.5797318443  0.0851952553 -0.7101331741  1.4819702897
#>  [381] -1.8596985867  0.4831001995 -0.8232123052 -0.6872162002 -0.8659183536
#>  [386]  1.9941128345  0.8045838942  0.0198347261 -0.0406549068  1.0940762878
#>  [391]  0.3266187629 -2.0205904514  0.2985323783 -1.4505582215  1.6586875450
#>  [396]  1.0633017900 -0.8463845744 -0.3670457900 -0.6346633567  2.0941412408
#>  [401]  0.2032150452 -1.1899851055  1.5134851618  0.4085456148 -0.7678683696
#>  [406] -0.1915673121  0.3912065342  0.3094871383 -1.2439705545 -0.7368907758
#>  [411]  0.5039869176  0.2153199202  1.0478210464 -1.8255003036  0.2925381440
#>  [416]  0.6793200551  1.3099372799 -1.1681924546 -0.3377802240 -0.1797522176
#>  [421] -2.8862797398  0.2921715803  1.4468088219 -2.3055221878  0.3200203050
#>  [426]  0.7728967369  0.1238319625 -3.0653010014  0.7425128955 -2.1519381813
#>  [431]  1.5384192384  1.3167929805 -1.2465282077 -0.4887125969 -0.0657515724
#>  [436]  0.7059851760  0.1283272282 -3.8194678825  1.2725266538 -0.1061598388
#>  [441] -1.0471843891 -0.3470809839 -1.0847936599 -1.6265183900 -0.2839794245
#>  [446] -2.1432702417 -0.2611583111  2.6300135102 -0.0944989211 -1.8329813321
#>  [451]  0.7008393642 -0.1101916567  0.9000389402 -0.6191569086 -1.3196794785
#>  [456]  0.2523185153 -0.7677753762 -0.7351354156  2.4400384826 -0.2036246990
#>  [461]  0.5075357956  0.3250875342 -0.0585083219  1.0106797035 -1.3776125320
#>  [466] -1.2454096456  0.6669570852 -0.3145857262 -0.5969015913 -1.5141757690
#>  [471]  1.7588749993 -0.9877808216 -0.6133672967  0.2433129224 -1.7059796675
#>  [476] -1.6747213134  1.3262566231  1.2986757037  0.1301048320  0.7555491359
#>  [481]  0.2178914081 -2.3128163907  0.7630788194  0.5181362243 -0.6460226091
#>  [486]  0.8222629847  0.8939530220 -0.5688761948  0.3059951511 -0.8121779715
#>  [491]  0.2035543923 -0.4040665353  1.7080119346 -0.2928159367 -0.7048285194
#>  [496]  0.1013088198 -0.6963396610 -0.3860835611  0.2456316175  0.2470590296
#>  [501] -0.1946540763  1.3139244728  0.7326274603  1.6902470948 -0.2267091651
#>  [506]  0.4094071669 -1.7202937169  0.1697485618 -1.1715860130 -1.2163923797
#>  [511]  0.0910489844 -1.9202983573  0.0638550177  0.3946127160 -3.0554889147
#>  [516]  1.6181011683 -0.5262199655  0.1971015105  0.2214817450  0.4723299909
#>  [521]  1.5358677387 -1.4412714235 -0.9236284810 -0.0217586361  0.6999647598
#>  [526] -0.3508367810  0.8173829168  1.3791736505  0.0729385812 -2.6966661997
#>  [531]  0.3081332106  0.0731680782 -0.4614224297 -2.2933561556 -0.0369370173
#>  [536] -0.5129215599 -0.5193795994 -1.7035604665  1.6887378329 -0.4111487766
#>  [541] -0.6567664099 -1.0366478069 -2.0797720251 -0.2312375022  0.9180598335
#>  [546] -1.7336891608  0.0429436372 -0.3887023770  2.5663500459  0.0758637146
#>  [551]  1.3539710965  0.2489178182 -0.1235833060  1.2106501020  0.7705716303
#>  [556] -0.5070998733 -0.8279060820  2.9252812002 -0.6122120111  0.3011483090
#>  [561]  0.7856130127 -0.7262972575 -1.3111921269  0.4627815818  0.6247932382
#>  [566]  1.1387481605  0.3842125805 -0.3577884747 -1.1141123289  0.5350765601
#>  [571]  1.8160438335  0.1071301475 -0.9354094154  0.5850858995  0.7664725927
#>  [576]  0.2559176943 -2.4458351954  0.8995344477 -0.3371403913  0.4663342925
#>  [581]  0.8421414066 -0.5261919727 -0.1519015101  1.2857336226 -0.0548863903
#>  [586]  0.3380587362  2.2521453417 -0.2042194308  1.0064653010 -0.7785876691
#>  [591]  1.4427830476 -1.2318929387 -0.0537857626 -1.6297260628  0.5551696076
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#>  [601] -0.0922167615  1.7359941338 -1.1302316599  0.8897205271  0.8004804429
#>  [606]  1.5625722591  0.1109161310 -0.8420942624  0.7137034609 -0.1640780364
#>  [611] -0.0714124723  0.2678657474 -0.2875442739  0.5397576259  0.1303392095
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#>  [626]  0.6641076154 -0.6592529041  0.3500931639 -2.5482297737  0.1647218375
#>  [631] -1.3853506156 -0.1096276910  0.2522432943 -0.3097431945  2.0339272855
#>  [636]  0.3631946139  2.1472322602  0.5135990068 -0.0243048517  0.7844076855
#>  [641]  0.2580036572 -0.0410778088  1.9165868428  0.2147323974  0.2274643334
#>  [646] -0.2150597038 -0.4060094119  1.1178501449  0.0684807754  1.5196127404
#>  [651]  0.2742044413 -0.2851613879 -0.5893632288  1.4563220916 -0.3369251429
#>  [656] -1.3648607135  1.1505703241  0.6698658693 -0.8689513545 -2.5232158344
#>  [661]  0.7757646947  0.5421637021  0.9122126967  1.5646440086 -0.0420817898
#>  [666]  0.1975613257  0.0105000781  0.2696660586 -0.2067602426 -0.9016350623
#>  [671] -2.5012391229 -0.2769289320  0.7656263294  1.2086170809  0.7889221478
#>  [676]  0.7130816228  0.9871461309 -0.1284903767  0.6464220623  0.3327375801
#>  [681]  1.7189127358 -0.3037694325  0.2787667772 -0.3852550467  0.7823248824
#>  [686] -1.2293968847 -1.1083773065 -0.6907060899  2.0566397752 -0.2132547977
#>  [691] -0.3418038299 -2.8476416557 -0.3447096477  1.2089534217  1.0794471506
#>  [696]  0.2124143586  0.6296721255  0.4979744352  0.4098411139 -0.2778517462
#>  [701]  1.8504939629  0.3779677614 -0.7896273289  0.9312903175 -0.6258923083
#>  [706] -0.9266746624  1.1080919840 -1.2546016084 -1.1540201945 -0.3166611400
#>  [711] -2.0088581385  1.8830567732 -2.0571733287  0.3845807644  0.1555311236
#>  [716]  0.0725311628  1.4384940775  0.1759403679  1.6750316915 -0.0043451361
#>  [721]  0.3700162213 -0.8147106671  0.4640460956  1.2377987759  0.0762578636
#>  [726] -0.0420056534 -1.3081238191 -0.2957758855  1.3299334674 -0.0495840145
#>  [731]  0.4502441812 -1.8421430385  0.3441335903  1.1654786543  0.0323265465
#>  [736] -0.8577523940  0.5665739947 -0.2667592075 -1.1859138025  0.4064104541
#>  [741]  0.6823413687  0.4436786220  0.8791232211 -0.7071354482  0.1466834453
#>  [746] -1.6400417825  0.7091264075  1.3066561282  0.4188052319  0.2847447094
#>  [751]  0.6883376028  0.1550172934 -0.1995330712  0.0293047339 -1.5952261457
#>  [756]  2.2245116202  0.3428038419  0.0637837632  0.4990094718  0.3754947963
#>  [761]  0.2393011406 -1.3631952048  1.1107069120  0.3143647235 -1.4887944685
#>  [766]  1.5443733659 -1.1964540888 -2.0674839369 -1.9841530853  0.3402519347
#>  [771] -0.3353518445  0.4155926217 -1.0810125552 -0.8857441235  1.2883014362
#>  [776]  1.1180178307 -0.4673624769 -2.8585293354  0.1829627429 -0.6101995506
#>  [781]  0.9347073996 -0.1631721475  0.7608941895 -0.2242461699  1.5680715724
#>  [786]  0.3374353833  0.5614095016  0.1967210463 -0.1013659226 -1.2689515482
#>  [791]  0.9612116081 -0.2072360051  0.1497552200  1.1543483779  0.2574603701
#>  [796]  0.0505764222  0.4695225356  1.8322549938 -0.0197485837  0.2060458564
#>  [801]  0.5781473054  0.5351271817 -0.0299308097  0.0659441529  1.1924341075
#>  [806]  0.8475612511 -0.0475387460 -0.7848688465  0.7845352526  1.1060377457
#>  [811] -0.8193962391 -0.2540282709  0.1151424833  0.9280781663  0.0068537992
#>  [816] -0.5517258786  1.2669004477  1.2606754035  0.2515924470 -0.9236002908
#>  [821]  0.5198689410  1.0578275977  0.2707701360  0.1098716853  1.8611031539
#>  [826]  0.1186447189 -2.4201026234  0.5079258233  0.9474805254 -0.1199968090
#>  [831]  0.2840581597  0.9434388905 -0.5677700015 -3.2299870825  0.5677471850
#>  [836]  1.1917865699 -1.5070386338  1.0739418139 -1.9665130768 -0.4529662950
#>  [841] -2.4053554870 -0.8684852204  2.4814309306 -0.1489524897  0.6502865957
#>  [846] -0.6129032614 -1.0053652829  0.0590502937 -0.8290256770 -0.3069302939
#>  [851] -2.5597894881  0.7166716435 -0.6524083066  0.0186919854 -0.3265875182
#>  [856]  2.0066260488 -0.6462365886 -0.9455453537  1.4126009619  0.2103454658
#>  [861] -1.9769510560 -0.6478521947  0.5464953473 -0.3170654751  1.6706123501
#>  [866]  0.2247054467 -0.1007461213  1.4086635867 -0.0316940324  0.0795204083
#>  [871]  0.0886976301 -0.2825504971 -1.2757958134 -0.2256610239 -1.3799707883
#>  [876]  0.2187353312 -0.1682806902 -2.8096667434 -0.6408409363 -0.2149931173
#>  [881] -0.3348832460  0.4115177656  2.5366517058  0.5764645120  0.4671126686
#>  [886]  0.0508555532  1.1494743938 -0.0114430213  0.0955819757 -2.5286955130
#>  [891]  0.3863310414  0.7889128148 -0.9253002755  1.6178895845  0.5365990430
#>  [896]  0.7742356448 -0.0754447046 -0.5411018973 -0.3431301775  0.0055992896
#>  [901]  2.0739813761 -0.3757690841  0.5045574519 -0.1123824575 -0.3543234445
#>  [906]  0.5565752584 -0.6385290950 -3.1663073663 -0.3920984178 -0.3137664887
#>  [911]  0.0100677665  1.0951254551  0.1317735491 -1.6373494781 -0.3146631007
#>  [916] -0.3719826975 -1.4320099865  0.2986904322 -0.7513194073  1.6485050194
#>  [921] -1.3249999260  0.0331010798  2.6622762709  0.6028265111  0.9228491037
#>  [926] -0.8221092862  0.4697992658  0.3756123787  0.4045441250  0.9844482263
#>  [931] -0.0634949342  0.3395031002 -0.0373350774  0.0909905016  1.7797268369
#>  [936] -0.2620432614 -0.5276375842 -0.9564804871  2.3907299100 -0.4968658886
#>  [941]  0.4475957861 -0.2541955995 -0.3243457949  0.4925772314 -0.9469083759
#>  [946]  2.4169555280 -0.0599928907 -0.1586852430  0.6316340009  0.0156972138
#>  [951]  0.4400794918  0.8624966186 -0.4465100671  0.2601583764  0.9807768141
#>  [956] -2.1442537069  1.1254434569  0.1857353832  0.2677659424  0.2561654545
#>  [961]  0.0021419966 -0.3638143877  0.1593146214 -0.0657066845  0.1489905956
#>  [966]  1.2749147015  0.5645342618  3.0115732172  0.4142594436 -0.2377661519
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#>  [976] -2.0359750966  0.0217261451  1.6773325916  0.2470274104 -0.1644142829
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#> [1891]  0.7587004561 -0.6786506228  0.2432720515  0.8316890116 -0.3291649303
#> [1896]  0.7373766204 -2.0884537453  1.4357792622 -0.2991695521  0.6804365094
#> [1901]  0.2437225579  0.0714990472 -0.7510130253  0.0448015040 -0.7410512995
#> [1906]  0.0099799159 -3.4614077192 -0.3010629941  0.8026252988 -1.1100009859
#> [1911]  0.0017392234 -0.6638455637  1.4084151809  0.3134131760 -0.1977707641
#> [1916]  0.8586119280  0.5596860075 -0.0082164083  1.2069532456  0.6740421072
#> [1921]  0.3422563435  0.4274024690 -0.3011399461  0.7536755877  0.1665333622
#> [1926]  0.0082913783 -0.2930667476  0.5936233613 -0.0984009020 -0.1458936362
#> [1931] -0.2961779099  0.9899561854 -0.5805107081 -1.2453374588  0.6392419984
#> [1936]  0.1559741260 -1.0965772852 -0.1237224906  1.3488004692  0.2142515651
#> [1941]  0.8405407401 -0.0812280353 -1.4260128553 -0.9287986598  1.2290247499
#> [1946] -2.4189246975  0.9588062645 -0.2855900067 -0.3323555472 -1.6815241895
#> [1951]  0.0005707348  1.3199790689 -0.1752672874 -1.8217882516  1.7760219284
#> [1956] -1.8627051293 -0.8810006961 -1.2934392659  0.1174474904 -0.6555231574
#> [1961]  0.0122067591  1.1652399905  0.8062225136  1.7599533691 -0.5817114060
#> [1966]  1.0221165501  0.5855661936 -0.1316019934  1.1208097685 -0.1281951437
#> [1971]  0.6184142394  1.2110816437 -0.0118890683 -0.3047032856  0.6506172304
#> [1976]  0.4461002480  0.0434911978  0.4129991836  0.0967033490 -0.1030370323
#> [1981]  0.0820135059  0.0390599434  0.1250524351  0.9068194367 -0.2600195603
#> [1986]  0.3520569959  0.9610978634  0.5090093962 -0.2083482319  0.5237625067
#> [1991] -0.4811323888 -1.3121961530  1.1158709083  0.6264558524 -0.1963868783
#> [1996]  0.2922343507 -1.3203334078 -0.0396199878 -2.8672685671  0.5413327334
#> [2001] -2.0390559227 -0.6518726293 -0.9069801250  2.1572001651  2.0461390503
#> [2006]  0.3250810853  0.2915260106  0.1438487651 -0.0123994617  0.3174496656
#> [2011]  0.0883891024 -0.5400115887 -1.1952858954 -0.0377172353 -2.1920030033
#> [2016] -0.8466843976  1.1155364705  1.6754017201 -0.7083805556 -0.7080068630
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#> [2056]  0.1979819525 -2.4625786204  0.5061095108 -2.2918812986 -0.2003284400
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#> [2796]  0.6943865660  0.6780989623  0.1343530025  0.7455782439  0.6987543982
#> [2801]  0.0227308164 -0.3877863690 -0.3912496772  0.0739777229  1.3091589567
#> [2806]  0.9163584465 -1.0156381492 -0.8849537013 -1.0820597623  0.4033742934
#> [2811]  0.9341072680  0.2263634482 -0.0447231525  0.4436292123  1.8166999381
#> [2816] -0.1158918224 -0.6253813956 -0.5864038727 -0.0835088150  0.1948506041
#> [2821] -1.7467745928  0.1573367265 -0.2100415048 -3.0924151840 -1.7096070498
#> [2826]  1.9131237008 -1.0594351255 -0.1768537296  0.8980515882 -1.5107459074
#> [2831]  0.7723380018  0.7337921534  0.4538218072 -1.5698827549  0.2148246233
#> [2836]  1.1578511983 -0.3786453728  0.6022578803 -0.2229518838  0.6718376535
#> [2841]  0.9194622651  0.0728050585 -0.5430530520 -0.8527202705  0.0056807306
#> [2846] -1.4632455958  0.1835662667  1.1134929774  0.1166125595 -0.9238529492
#> [2851]  0.2867011287 -0.8661013144 -0.2721408241  1.6288265685  0.3923779411
#> [2856] -0.0319148039  1.2355054578  1.1380149793  0.2015965935  0.1111045219
#> [2861] -0.9189708034  0.5396924114 -0.1182789258 -0.3851965160  1.1216297041
#> [2866] -0.4593770808  0.4922205920 -0.3173502783 -0.3850913102 -1.9626170102
#> [2871]  1.7518489731 -0.8293526093  1.3115003580  0.5116101366  0.0842067495
#> [2876]  1.0912874168 -0.0889535274  0.4137963340  0.1483186166  0.2556456448
#> [2881] -0.6213211452  0.3878189471 -0.1658056803 -0.3620449299 -0.7074817861
#> [2886]  0.3004238618 -1.1534655357  0.3178375258 -2.4406685486  0.2907609043
#> [2891] -1.2035778684  0.8172800007  0.1014226498  0.4345600393 -0.7328263403
#> [2896]  1.2830306894  1.1827159095  1.1754156174  0.4448395659 -0.9563538677
#> [2901]  1.1582641261  0.1379270852 -0.1397400208  0.5703197532  0.3195790197
#> [2906] -0.6132875693 -0.1499318006  0.3038200603  0.8185575084  1.5403456645
#> [2911] -0.4592655585 -1.0307242480 -0.8770111006  0.7352137062 -0.1586040896
#> [2916]  0.7861478217  0.7411742701  0.5677871886  0.4631788430 -0.0443150538
#> [2921] -0.2540574434 -1.2994103087 -0.6733212172  1.0770786638 -1.2375688026
#> [2926]  1.2010946391  0.4789838674  0.3631023370  0.3225103757 -0.0647264474
#> [2931] -0.2878150076  1.0881121033  1.2839694906  0.0420596033  0.9323276141
#> [2936] -0.7139027597  0.0217821181 -0.2807377137 -0.4931638303 -0.6555723892
#> [2941] -0.3985604253  0.3492168406  0.7042618150  0.0668752907  1.0191612903
#> [2946]  0.0508957693 -1.0664879994  0.9715624980  0.2197979253  1.4188398382
#> [2951] -0.0605283982 -0.6045027020 -0.2270070003 -0.5932717542  0.5014577488
#> [2956] -0.0012682225  0.6935180329 -0.0752455148  0.1389580032 -1.6435430251
#> [2961] -0.9577826563 -0.0664455309 -0.2488219959 -6.0603592035 -1.5084782387
#> [2966]  0.9425026044 -0.4004407008  1.5403632137 -0.0167520842 -1.0437214032
#> [2971] -0.0259083941 -0.3351750848 -0.4612266801 -2.7791138306  1.1638746801
#> [2976] -1.0796911637 -0.4035644743  1.0223100564  0.7102086609  0.7203023453
#> [2981] -0.4521757196  0.4249537174  0.5067028914  1.8050391904 -0.1874800330
#> [2986] -0.7453220240 -1.6601290951 -0.1104852660 -0.6127532162  0.8919043559
#> [2991]  0.1907422323 -1.5526639484 -1.5412841149  0.2334529571 -0.5447803358
#> [2996]  1.3473197165  0.2689691351  2.0166963372 -0.1613353385  0.6497898550
#> [3001]  0.9085272908 -2.7820236426 -0.0916453181 -1.5427003991  0.1054403836
#> [3006] -0.0231929680  0.3820784111 -0.0151480902 -1.5818876353 -1.5621471043
#> [3011]  0.0058587666 -1.1422864094 -1.1479273061 -1.4723465580 -1.8037164086
#> [3016]  2.7664900162  0.3488216265 -0.0548938165  0.4074608634  0.0656496776
#> [3021] -1.4136701430  1.7883123327  0.3238509304  0.4833613630  0.2189010572
#> [3026]  0.2617058222 -0.0091871956 -0.3597807414  0.7815846559  0.1678587799
#> [3031]  0.6182735641  1.1224834015 -1.1989824988  0.1794108412  0.1209303719
#> [3036]  0.8018696792 -0.7649308532 -0.1453817772  1.6528050802  0.8156374829
#> [3041]  0.0874381058  0.7072902070  0.5075102887 -0.2526829445 -1.1357322090
#> [3046]  0.0791435139  0.0886562923  1.7053889607  0.3515179530 -0.3271357076
#> [3051]  1.4089235944  0.1801157258  0.2273299922 -0.4792098257  0.9025423579
#> [3056]  0.1728522528 -0.1171920345 -0.0849228586 -0.4633665157  1.1573652563
#> [3061] -0.6208046914 -0.1839107795 -1.1097591358 -1.3200009129 -0.3199330542
#> [3066]  2.2804075046  0.3585035127  0.8888642361 -0.1115709655  0.6789033423
#> [3071]  0.5163335726 -0.0188874585 -0.4503929166  1.7065885525 -2.6260122628
#> [3076] -0.0837345995  0.7675466657 -0.5111004294  0.4127729237  0.8155789226
#> [3081]  1.4156558925  0.0019864906  0.2613641819  0.2690404124  0.6317860462
#> [3086]  0.1468697715 -0.9018508653  0.5100124647  0.0057871707  1.0522982847
#> [3091] -0.0971913800  0.0825534837 -0.3860698352  0.2757623876  0.1826885568
#> [3096]  1.6429250576 -0.3552925786 -0.0619385058  0.8184185550  0.1854240264
#> [3101]  0.1708560609 -1.3993865523 -0.3576467872  1.6666268758 -0.6760776918
#> [3106] -2.5526382623 -0.1812462626 -0.3644487390  0.4722178255 -3.2473132024
#> [3111]  0.6833143925  0.5183583895  0.8324626171 -0.5613102919 -0.6815598752
#> [3116]  0.8819220247 -0.2979177097 -1.3454097263  0.1425822207 -0.9501771506
#> [3121] -0.7822807444  0.2411789757 -1.6268721668 -0.3018735287  2.4599212672
#> [3126]  0.7127692977  0.5558603400  0.9981404001  0.4430480792 -0.0353467931
#> [3131] -0.2214905971  0.4741968477 -0.1963710173  0.1205835882  1.3297752555
#> [3136]  0.3827616059  1.2726713229 -0.1604988449 -0.2344899538 -1.3628913868
#> [3141] -0.1634603231  0.5353065280  0.8330637911  1.1103885367  0.4095507822
#> [3146]  1.1178492608 -0.2545005560 -0.7182263626  0.1854906732  0.7094795389
#> [3151]  0.3632491686  0.7610701182  0.0290429691 -0.5884233595 -1.1463084428
#> [3156]  0.5921952460 -1.0435999097  0.4585601713  1.1405945168  0.7433922204
#> [3161] -0.8429837776  1.1682357128 -0.2439949784 -0.4081123441 -1.7910792923
#> [3166] -1.2599704717 -0.9618010273 -3.9387123227  0.9525133274  0.0569707902
#> [3171]  1.4969940178 -0.4925405756 -0.9768143340  1.1888984895 -2.2883054587
#> [3176]  0.1493026904  0.9430317954  0.8018387596 -0.5458678857  0.5974228359
#> [3181] -0.0387689581 -2.1808186282  0.7294181576 -0.2227664937  0.4895560438
#> [3186]  1.0049867943  0.0512295917 -0.5972615035  0.9760941592  1.1718165015
#> [3191]  0.0802288820 -0.0089426538  0.0330228768  0.7932299952  0.3228148970
#> [3196] -0.0863853265 -0.3995328425  0.3446478401  0.0481437258  0.0029689486
#> [3201] -0.7687738530 -0.0152386322 -1.3942218359  0.9258108772 -0.3619895128
#> [3206] -0.8274893920  0.7795278882 -1.9155845205 -2.3403490329  0.7943399503
#> [3211]  1.4445701929 -0.4250300986 -1.5764705030  0.8233740406  0.5937974701
#> [3216]  1.0581746360 -0.1333639194  1.0235460252 -0.2049667357  0.3025736542
#> [3221] -0.4581376749  0.8395731065 -0.4424493457  0.3691548235  0.2619394050
#> [3226]  0.5849233739  0.8236678757 -0.1233669885  0.5066308738 -0.4860001678
#> [3231]  1.5876239851  0.5394841478 -0.1785508509  0.1109998467  0.4515826003
#> [3236]  0.4355959129 -0.3435929823  0.2816608323  0.1319906151  0.1601883640
#> [3241]  1.5080242013  0.0875109265 -0.1071844627 -0.7043184512 -0.2949194555
#> [3246]  0.4149683053  1.4520435705  0.3805866895  0.7436089801 -0.7141540392
#> [3251] -1.5385281384 -1.0486546804  0.9606639153  0.2243314293  1.4277854803
#> [3256] -0.4534798532 -0.1633324575  0.4544436096  1.3802103013  0.0107641773
#> [3261]  1.1134322485  0.0502748816 -0.0682830894  0.7368025436  0.8190119287
#> [3266]  0.1427851859 -0.0336386298  0.9163544950  0.0059373574 -1.0529694779
#> [3271]  0.5110304695  1.4777918497 -1.1251389745  0.5358434959 -0.4387539775
#> [3276]  0.7904550326  1.0707120712 -0.4445380697  1.1177494911 -0.2331794600
#> [3281]  0.3008612489  1.3950896813  0.5893247886 -0.4155798652  0.0468441194
#> [3286]  0.1934185371 -1.6014647462 -2.4536751194  1.1613220176 -0.0973391277
#> [3291]  0.3758222321 -2.2639762446  0.7188502855  1.5261179221  1.0469251855
#> [3296]  0.3077368434 -0.5369327976  0.7605252706  0.1802730503  0.7365907537
#> [3301] -0.1912271905  0.2299881881 -0.3873427941  0.6524287316 -0.5440183038
#> [3306] -1.5539604867 -4.4840341873 -2.0762140742 -0.2106975167 -2.7261288035
#> [3311] -0.3602567642  2.1147658692 -1.0979966710  1.5812606656 -1.2047178009
#> [3316] -0.5864535406 -2.8587267010  1.2271289343 -1.2417740285 -2.4063469554
#> [3321]  1.6525175060 -2.1410023606  0.7977044984 -0.7571687884  0.0697284104
#> [3326] -0.7197110942 -0.5059064198  1.6336191294  0.1889992860  1.0881321602
#> [3331] -0.6137395424  0.6257936270 -0.3243600454 -0.9832858209  0.4976326705
#> [3336] -0.3600954236  1.7352058327 -0.0363118559  0.8287811858  0.3679381463
#> [3341] -0.2807581195  0.9038181526 -0.6839415912  0.1871580472  0.9293574059
#> [3346] -0.6461245881 -1.1767243727  0.8399447523 -0.0206088052  0.5763238976
#> [3351]  0.6463319017 -0.2450241941  1.3266984228 -0.4468351603 -1.4726780168
#> [3356]  0.2040585926  0.4703709797 -0.3913563814  0.6867848996  1.0508848100
#> [3361]  0.0083323829 -1.4098053167 -1.1249769744

hhat <- ts(ts.garch$fitted.values[-1,1]^2,start = c(2007,3),frequency = 365.25)
plot.ts(hhat)