Semana 2

juan alberto zapata May 26, 2020

lapply devuelve una lista de la misma longitud que X, cada elemento del cual es el resultado de aplicar FUN al elemento correspondiente de X.

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   0.3.4
## v tibble  3.0.1     v dplyr   0.8.5
## v tidyr   1.1.0     v stringr 1.4.0
## v readr   1.3.1     v forcats 0.5.0

## -- Conflicts --------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## [[1]]
## [1] "WDI"       "stats"     "graphics"  "grDevices" "utils"     "datasets" 
## [7] "methods"   "base"     
## 
## [[2]]
##  [1] "forcats"   "stringr"   "dplyr"     "purrr"     "readr"     "tidyr"    
##  [7] "tibble"    "ggplot2"   "tidyverse" "WDI"       "stats"     "graphics" 
## [13] "grDevices" "utils"     "datasets"  "methods"   "base"     
## 
## [[3]]
##  [1] "tseries"   "forcats"   "stringr"   "dplyr"     "purrr"     "readr"    
##  [7] "tidyr"     "tibble"    "ggplot2"   "tidyverse" "WDI"       "stats"    
## [13] "graphics"  "grDevices" "utils"     "datasets"  "methods"   "base"     
## 
## [[4]]
##  [1] "forecast"  "tseries"   "forcats"   "stringr"   "dplyr"     "purrr"    
##  [7] "readr"     "tidyr"     "tibble"    "ggplot2"   "tidyverse" "WDI"      
## [13] "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
## [19] "base"

Importación de datos

Importa datos de World Development Indicators (WDI), que es la principal colección de indicadores de desarrollo del Banco Mundial

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   : 15935456430700   Mean   :1989  
##                                        3rd Qu.:  7182049960520   3rd Qu.:2004  
##                                        Max.   :153758254309000   Max.   :2018

1) Promedio de vector de datos (variable)

Importa datos de serie de tiempo del PBI del peru.

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$PE,start = c(1960,1),end = c(2018,1))
plot(ts,main="PBI real MN (1960-2018)",xlab="",ylab="Miles de millones")

Aplica un logaritmo y lo diferencia la serie de tiempo del PBI del peru.

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

Estimación de Parámetros de la media (mean), varianza (var) y la desviacion estandar (sd) de los retornos de la serie de tiempo del PBI del peru.

mean(l_ts)
## [1] 0.03506753
var(l_ts)
## [1] 0.002230807
sd(l_ts)
## [1] 0.04723142

Regresión

El modelo [ y = XB+\varepsilon ]

Se le conoce como el modelo lineal clásico si cumple los siguientes supuestos.

  1. (E(\varepsilon)=0)
  2. (Cov(\varepsilon)=E(\varepsilon\varepsilon^{\prime})=\sigma^2I)
  3. La matriz de covariables (X) es una matriz de rango completo. Es decir, (rk(X)=k+1=p) (Las covariables son linealmente independientes) El modelo lineal normal clásico se obtiene si:
  4. (\varepsilon \thicksim N(0,\sigma^2I)). En el caso de procesos estocasticos (\varepsilon |X \thicksim N(0,\sigma^2I)).

Estimación de parámetros (OLS)

Minimzando (LS(\beta))

set.seed es la forma recomendada para especificar semillas de 100. LA función de distribución,realiza la generación aleatoria para la distribución normal con media igual a media y desviación estándar igual a sd.

#Ejemplo con 
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

cov y cor calculan la varianza de x y la covarianza o correlación de x e y si son vectores.

#Ejemplo con series de tiempo
Yi<-l_ts[-1]
Yj<-l_ts[-58]
cor(Yi,Yj)
## [1] 0.4304888
cov(Yi,Yj)/(sd(Yi)*sd(Yj))
## [1] 0.4304888
cov(Yi,Yj)/var(Yj)
## [1] 0.4282983

El arima realiza un ajuste un modelo ARIMA a una serie temporal univariante.

#-------------------------------
#Comparación MCO - AR(1)
lm(Yi~Yj)
## 
## Call:
## lm(formula = Yi ~ Yj)
## 
## Coefficients:
## (Intercept)           Yj  
##     0.01945      0.42830
arima(l_ts,order = c(1,0,0))
## 
## Call:
## arima(x = l_ts, order = c(1, 0, 0))
## 
## Coefficients:
##          ar1  intercept
##       0.4254     0.0356
## s.e.  0.1176     0.0095
## 
## sigma^2 estimated as 0.001786:  log likelihood = 101.11,  aic = -196.21

calcula (y por defecto las gráficas) estimaciones de la función de autocorrelación retrasada de una serie de tiempo maximo 20.

acf(ts,lag.max = 20)

pacf(ts,lag.max = 20)

calcula (y por defecto las gráficas) estimaciones de la función de autocovarianza o autocorrelación retrasada de los retornos de la serie de tiempo maximo 20.

acf(l_ts,lag.max = 20)

pacf(l_ts,lag.max = 20)

Se genera el modelo1 con arima de la serie de tiempo, AR(1), MA(1) y primera direfencia. luego se predice a partir de los resultados de varias funciones de ajuste del modelo. y ppor ultimo se calcula el ‘Criterio de información’ de Akaike para uno o varios objetos modelo ajustados para los que se puede obtener un valor de log-verosimilitud.

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

AIC(model.1)
## [1] 427.2029

Se genera el modelo2 con autoarima de la serie de tiempo en logaritmo. luego se predice a partir de los resultados de varias funciones de ajuste del modelo.

model.2 <-auto.arima(log(ts),ic="aic",trace=T)
## 
##  ARIMA(2,1,2) with drift         : -194.4185
##  ARIMA(0,1,0) with drift         : -186.5246
##  ARIMA(1,1,0) with drift         : -196.2105
##  ARIMA(0,1,1) with drift         : -198.3388
##  ARIMA(0,1,0)                    : -162.6986
##  ARIMA(1,1,1) with drift         : -196.3404
##  ARIMA(0,1,2) with drift         : -196.3395
##  ARIMA(1,1,2) with drift         : -194.3404
##  ARIMA(0,1,1)                    : -185.6227
## 
##  Best model: ARIMA(0,1,1) with drift
summary(model.2)
## Series: log(ts) 
## ARIMA(0,1,1) with drift 
## 
## Coefficients:
##          ma1   drift
##       0.5180  0.0352
## s.e.  0.1269  0.0082
## 
## sigma^2 estimated as 0.00178:  log likelihood=102.17
## AIC=-198.34   AICc=-197.89   BIC=-192.16
## 
## Training set error measures:
##                         ME       RMSE        MAE          MPE      MAPE
## Training set 0.00002561815 0.04110477 0.03041042 -0.000660425 0.5883875
##                   MASE        ACF1
## Training set 0.6095185 0.006941875
fmodel2 <- forecast(model.2,level=c(95),h = 10)
plot(fmodel2)

#---------------------------------------------------*

Modelos de Volatilidad

options(scipen=999)
pkges<-c("pdfetch","tseries","tidyverse","forecast")
#install.packages(pkges)
lapply(pkges,"library",character.only=T)
## [[1]]
##  [1] "pdfetch"   "forecast"  "tseries"   "forcats"   "stringr"   "dplyr"    
##  [7] "purrr"     "readr"     "tidyr"     "tibble"    "ggplot2"   "tidyverse"
## [13] "WDI"       "stats"     "graphics"  "grDevices" "utils"     "datasets" 
## [19] "methods"   "base"     
## 
## [[2]]
##  [1] "pdfetch"   "forecast"  "tseries"   "forcats"   "stringr"   "dplyr"    
##  [7] "purrr"     "readr"     "tidyr"     "tibble"    "ggplot2"   "tidyverse"
## [13] "WDI"       "stats"     "graphics"  "grDevices" "utils"     "datasets" 
## [19] "methods"   "base"     
## 
## [[3]]
##  [1] "pdfetch"   "forecast"  "tseries"   "forcats"   "stringr"   "dplyr"    
##  [7] "purrr"     "readr"     "tidyr"     "tibble"    "ggplot2"   "tidyverse"
## [13] "WDI"       "stats"     "graphics"  "grDevices" "utils"     "datasets" 
## [19] "methods"   "base"     
## 
## [[4]]
##  [1] "pdfetch"   "forecast"  "tseries"   "forcats"   "stringr"   "dplyr"    
##  [7] "purrr"     "readr"     "tidyr"     "tibble"    "ggplot2"   "tidyverse"
## [13] "WDI"       "stats"     "graphics"  "grDevices" "utils"     "datasets" 
## [19] "methods"   "base"

Importa datos de yahoo finance, los datos de la serie de tiempo financiera SP500 (^GSPC) en intervalo de 1 dias de la cuarta columna.

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

Calculando retornos. Aplica un logaritmo a la serie tsSP500 y lo diferencia la serie de tiempo financiera. luego con la funcion na.omit devuelve el objeto con los casos incompletos eliminados.

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

Modelo Autorregresivo con Heterocedasticidad Condicional (ARCH)

La forma del modelo más simple ARCH(1) es la siguiente:

[ \begin{align} y_t&=x^{\prime}{t}\beta+\varepsilon_t \ \varepsilon_t& =\mu_t\sqrt{\alpha_0+\alpha\varepsilon^{2}{t-1}} \ \end{align} ] Donde (\mu_t \thicksim N(0,1))

El estimador de la varianza condicional se estima a través del siguiente modelo de regresión. [\begin{equation} \hat{\varepsilon}^{2}_t=\hat{\alpha}_0+\hat{\alpha}1\hat{\varepsilon}^{2}{t-1} \end{equation}]

La ecuación nos dice que la varianza en el periodo (t-1) afecta la varianza en el periodo (t)

###La funcion plot.ts uestra el grafico de la serie de tiemppo R1.

###La funcion hist calcula un histograma de los valores de datos dados.

###la funcion acf calcula (y por defecto las gráficas) estimaciones de la función deautocorrelación de una serie de tiempo R1.

plot.ts(R1)

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

acf(R1)

calcula la valotilidad de la serie de tiempo R1 con AR(0), y MA(1). luego aplico la función genérica summary que es utilizada para producir resúmenes de resultados de los resultados de varias funciones de ajuste del modelo.

ts.arch <- garch(R1,c(0,1))
## 
##  ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** 
## 
## 
##      I     INITIAL X(I)        D(I)
## 
##      1     1.652664e-04     1.000e+00
##      2     5.000000e-02     1.000e+00
## 
##     IT   NF      F         RELDF    PRELDF    RELDX   STPPAR   D*STEP   NPRELDF
##      0    1 -1.308e+04
##      1    7 -1.309e+04  1.01e-03  1.20e-03  1.1e-04  1.3e+11  1.1e-05  7.62e+07
##      2    8 -1.310e+04  5.25e-04  5.82e-04  1.1e-04  2.9e+00  1.1e-05  1.60e+02
##      3    9 -1.310e+04  4.10e-05  5.13e-05  1.0e-04  2.0e+00  1.1e-05  1.54e+02
##      4   10 -1.310e+04  3.78e-06  3.90e-06  1.1e-04  2.0e+00  1.1e-05  1.53e+02
##      5   17 -1.316e+04  4.98e-03  6.94e-03  3.1e-01  2.0e+00  4.6e-02  1.52e+02
##      6   19 -1.320e+04  3.16e-03  2.06e-03  2.1e-01  0.0e+00  5.0e-02  2.06e-03
##      7   20 -1.324e+04  2.53e-03  1.71e-03  2.0e-01  0.0e+00  7.1e-02  1.71e-03
##      8   22 -1.326e+04  1.63e-03  1.14e-03  1.6e-01  0.0e+00  8.3e-02  1.14e-03
##      9   23 -1.327e+04  7.78e-04  6.16e-04  1.2e-01  1.1e-01  8.3e-02  6.20e-04
##     10   24 -1.327e+04  3.62e-04  3.10e-04  9.4e-02  0.0e+00  8.0e-02  3.10e-04
##     11   25 -1.327e+04  5.93e-05  5.44e-05  4.4e-02  0.0e+00  4.3e-02  5.44e-05
##     12   26 -1.327e+04  4.06e-06  3.56e-06  1.0e-02  0.0e+00  1.0e-02  3.56e-06
##     13   27 -1.327e+04  9.44e-08  9.17e-08  2.0e-03  0.0e+00  2.0e-03  9.17e-08
##     14   28 -1.327e+04  9.34e-11  9.29e-11  6.7e-05  0.0e+00  7.0e-05  9.29e-11
## 
##  ***** RELATIVE FUNCTION CONVERGENCE *****
## 
##  FUNCTION    -1.327454e+04   RELDX        6.720e-05
##  FUNC. EVALS      28         GRAD. EVALS      15
##  PRELDF       9.289e-11      NPRELDF      9.289e-11
## 
##      I      FINAL X(I)        D(I)          G(I)
## 
##      1    9.710552e-05     1.000e+00    -4.802e-01
##      2    5.194677e-01     1.000e+00    -1.948e-04
summary(ts.arch)
## 
## Call:
## garch(x = R1, order = c(0, 1))
## 
## Model:
## GARCH(0,1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -9.08245 -0.35723  0.05855  0.49189  8.40894 
## 
## Coefficient(s):
##       Estimate  Std. Error  t value            Pr(>|t|)    
## a0 0.000097106 0.000001428    68.01 <0.0000000000000002 ***
## a1 0.519467657 0.021480441    24.18 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Diagnostic Tests:
##  Jarque Bera Test
## 
## data:  Residuals
## X-squared = 15405, df = 2, p-value < 0.00000000000000022
## 
## 
##  Box-Ljung test
## 
## data:  Squared.Residuals
## X-squared = 3.613, df = 1, p-value = 0.05733

Modelo Autorregresivo con Heterocedasticidad Condicional Generalizado (GARCH)

Por otro lado, en un modelo GARCH la distribución de los errors se define como: [ \varepsilon_t|\Psi \thicksim N(0,\sigma_t^2) ] Tomando como ejemplo un GARCH(1,1), la varianza condicionada es:

[ \sigma_t^2=\alpha_0+\delta_1\sigma_{t-1}^2+\alpha_1\varepsilon_{t-1}^2 ]

calcula la valotilidad de la serie de tiempo R1 con AR(1), y MA(1). luego aplico la función genérica summary que es utilizada para producir resúmenes de resultados de los resultados de varias funciones de ajuste del modelo. luego extrae los residuos del modelo de los objetos devueltos por las funciones de modelado. luego se crea hha para aplicar el contenido de la funcion ts que comprueban si un objeto es una serie temporal donde comienza en 2007,3 y la frecuencia es de 365.25. finanlente grafica la serie de tiempo hhat.

ts.garch <- garch(R1,c(1,1))
## 
##  ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** 
## 
## 
##      I     INITIAL X(I)        D(I)
## 
##      1     1.565682e-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 -1.309e+04
##      1    7 -1.311e+04  1.26e-03  1.48e-03  1.2e-04  1.4e+11  1.2e-05  1.07e+08
##      2    8 -1.312e+04  6.58e-04  1.10e-03  2.3e-04  2.1e+00  2.3e-05  2.52e+02
##      3    9 -1.312e+04  1.36e-04  1.85e-04  2.1e-04  2.0e+00  2.3e-05  2.31e+02
##      4   10 -1.312e+04  1.27e-05  1.20e-05  2.3e-04  2.0e+00  2.3e-05  2.34e+02
##      5   17 -1.327e+04  1.13e-02  1.78e-02  4.8e-01  2.0e+00  9.5e-02  2.31e+02
##      6   19 -1.339e+04  8.69e-03  8.96e-03  2.9e-01  2.0e+00  9.5e-02  5.43e+01
##      7   21 -1.347e+04  6.53e-03  7.82e-03  2.2e-01  2.0e+00  9.5e-02  6.35e+01
##      8   24 -1.379e+04  2.31e-02  2.18e-02  3.3e-01  1.9e+00  2.6e-01  1.41e+00
##      9   26 -1.381e+04  1.41e-03  5.01e-03  4.8e-02  2.0e+00  5.2e-02  2.40e+00
##     10   27 -1.389e+04  5.88e-03  6.98e-03  4.3e-02  2.0e+00  5.2e-02  3.01e+00
##     11   28 -1.393e+04  2.90e-03  5.38e-03  4.0e-02  2.0e+00  5.2e-02  8.53e-01
##     12   29 -1.396e+04  1.68e-03  3.58e-03  3.7e-02  2.0e+00  5.2e-02  6.77e-01
##     13   43 -1.397e+04  7.03e-04  1.68e-03  1.5e-06  2.8e+00  2.1e-06  1.93e-02
##     14   44 -1.397e+04  6.20e-05  4.68e-05  1.5e-06  2.0e+00  2.1e-06  6.88e-04
##     15   45 -1.397e+04  5.99e-06  6.80e-06  1.5e-06  2.0e+00  2.1e-06  1.98e-03
##     16   46 -1.397e+04  9.91e-08  8.73e-08  1.5e-06  2.0e+00  2.1e-06  1.81e-03
##     17   53 -1.397e+04  1.44e-05  2.82e-05  3.6e-03  2.0e+00  5.2e-03  1.81e-03
##     18   56 -1.398e+04  4.91e-04  2.50e-04  1.3e-02  0.0e+00  2.2e-02  2.50e-04
##     19   58 -1.400e+04  1.70e-03  1.53e-03  5.1e-02  0.0e+00  8.9e-02  2.33e-03
##     20   59 -1.401e+04  7.88e-04  1.14e-03  4.5e-02  8.1e-01  8.9e-02  1.94e-03
##     21   61 -1.401e+04  1.51e-04  2.60e-04  8.0e-03  1.2e+00  1.4e-02  3.16e-04
##     22   63 -1.401e+04  1.80e-05  3.08e-05  2.0e-03  1.3e+00  3.6e-03  3.57e-05
##     23   64 -1.401e+04  2.01e-06  3.12e-06  1.2e-03  0.0e+00  1.9e-03  3.12e-06
##     24   65 -1.401e+04  4.24e-07  4.92e-07  5.9e-04  0.0e+00  1.0e-03  4.92e-07
##     25   66 -1.401e+04  4.42e-09  1.81e-08  1.2e-04  0.0e+00  2.8e-04  1.81e-08
##     26   67 -1.401e+04  3.41e-09  7.79e-10  3.3e-05  0.0e+00  6.7e-05  7.79e-10
##     27   68 -1.401e+04 -1.51e-10  3.73e-11  6.1e-06  0.0e+00  1.3e-05  3.73e-11
## 
##  ***** RELATIVE FUNCTION CONVERGENCE *****
## 
##  FUNCTION    -1.401265e+04   RELDX        6.103e-06
##  FUNC. EVALS      68         GRAD. EVALS      27
##  PRELDF       3.731e-11      NPRELDF      3.731e-11
## 
##      I      FINAL X(I)        D(I)          G(I)
## 
##      1    2.954093e-06     1.000e+00    -2.430e+03
##      2    1.440809e-01     1.000e+00    -1.175e-01
##      3    8.353693e-01     1.000e+00    -2.187e-01
summary(ts.garch)
## 
## Call:
## garch(x = R1, order = c(1, 1))
## 
## Model:
## GARCH(1,1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -6.64870 -0.45401  0.07267  0.62369  3.78183 
## 
## Coefficient(s):
##        Estimate   Std. Error  t value            Pr(>|t|)    
## a0 0.0000029541 0.0000002843    10.39 <0.0000000000000002 ***
## a1 0.1440808741 0.0099376436    14.50 <0.0000000000000002 ***
## b1 0.8353693141 0.0104132888    80.22 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Diagnostic Tests:
##  Jarque Bera Test
## 
## data:  Residuals
## X-squared = 958.32, df = 2, p-value < 0.00000000000000022
## 
## 
##  Box-Ljung test
## 
## data:  Squared.Residuals
## X-squared = 0.65726, df = 1, p-value = 0.4175
ts.garch$residuals
##    [1]            NA -0.5497281262  0.2102382842 -0.0525749043  0.2118669901
##    [6]  0.7375312816  0.5784661583  0.1015134378 -0.1182286770 -0.4171372218
##   [11]  0.4229768577 -0.8052186340  0.5387557392  1.3264023447 -1.6478171231
##   [16] -0.1547765360 -0.1492106350  0.8279226146  0.9475162524  0.7600319013
##   [21]  0.2436277586 -0.1462780056  0.1108801867  0.2320037424 -0.2041840476
##   [26] -1.2745433146 -0.5432276380  1.2848627444  1.2011026134  0.1547887825
##   [31] -0.1368668665  0.4670318982 -0.2375190809 -0.1505193432 -0.6496457175
##   [36] -0.2290432732 -6.6487032712  0.3858752304 -0.1936749671 -0.9234748219
##   [41] -0.7698839474  1.2913743923 -0.1979894774  0.6142245547  0.0613578706
##   [46]  0.2614223792 -2.1505693750  0.5627021525  0.3266693113 -0.3644902220
##   [51]  1.0968924764  0.6270097044  1.7525385590 -0.0315111621  0.1066724547
##   [56]  0.1014389779 -0.6976408029 -0.9262601064  0.4326131300 -0.1433460744
##   [61]  0.3369539488  1.2638435469  0.1437355968  0.4177195642  0.0843464194
##   [66]  0.3954103224 -1.0371919386  0.9436410680  0.5226586081  1.6397684061
##   [71]  0.2915272762  0.0992400589 -0.1818359528  1.4627738527 -0.3316538102
##   [76] -0.0528688760  1.5983418465 -0.1097167960 -0.0178534701 -1.2275883049
##   [81]  0.3898670360  0.9897172745  0.6473368998  0.3283902514  0.4081921631
##   [86] -0.1924030084  0.5530250232 -2.4564549280  1.2517441521 -0.2220677799
##   [91] -0.1713727515  1.1954338542 -0.1219581028  0.9276018055  0.2151833195
##   [96] -0.0945696106 -0.1872745804 -1.5833149584  0.7822215350  0.2274440122
##  [101]  1.2117970987  0.0367691621  0.5682241684  0.2885915700 -0.8736643336
##  [106] -1.4338678073 -2.5971527556  1.2111854582  0.0990585233 -1.1877529988
##  [111]  1.6077324156  0.4600551737  0.6591909070 -0.1276842381  0.1949344287
##  [116] -1.6471220822  0.6578551905 -1.4359773614 -0.3288248042 -0.3534647847
##  [121]  1.0369680355 -0.0476605923 -0.1911568241  1.3786264286  0.4301913755
##  [126]  0.0439775266  0.4442157380  0.1294823960 -2.1219733215  0.6807602400
##  [131]  2.3179344169  0.2956729538 -0.1961306915 -0.0105864859 -0.2422518759
##  [136]  0.5555925121 -1.5923648361  0.5625815905 -2.4145688235  0.4286207421
##  [141] -2.3090436355 -1.2339416954  0.7541798060 -0.9738351809  0.5551561294
##  [146]  0.3532620882 -2.3423470675  1.6158442376  0.3756390671  0.9181924370
##  [151] -2.0084639001  0.0211214757 -0.0300835393 -1.2094368659 -0.8983142061
##  [156]  0.2119123458  1.7153722285 -0.0168868933  0.0738538245  0.8594562561
##  [161] -0.0809075952  0.9363898889 -0.7038238728 -2.0334394010  1.5401924977
##  [166] -0.2725563456  0.7831035757  0.7547765467 -0.8680106287  0.3248427724
##  [171] -1.4014667200 -0.0981051268  1.1284325371  0.0038924762  0.7411802012
##  [176]  0.0184575988 -0.5053662935  2.9861329610  0.4290457305 -0.5094335180
##  [181]  0.3681786311 -0.4514050653 -0.0311755978  0.5294275084  0.4023050567
##  [186] -0.3311138242  1.5333088235 -0.0279421071 -0.5160905121  0.2498489913
##  [191]  1.1978005489 -0.3886617227  1.0253367655 -0.2142430966 -0.6860363398
##  [196]  0.6437480449 -1.1723655093 -0.8795693049  0.2347862735 -0.1061289924
##  [201] -3.8647283108  0.3231547150  0.8000693352 -0.2286728860 -0.0980382391
##  [206]  1.4764467539  0.3672360916 -0.6835258813  1.2991619767 -2.7655607727
##  [211]  0.0590196893 -0.3960942894  1.0200266696 -2.5302474415 -0.0366660380
##  [216] -0.9947029760 -0.6966782583  2.0755271061 -0.4232731486 -0.8499332034
##  [221]  0.3417462289 -1.2408030344  0.3045588246 -1.1763075145  1.1972680881
##  [226] -1.6347907818  0.9272870742  1.7882511006  0.0264502156  0.4676535491
##  [231] -0.3808108920 -0.4540777701  1.1126164054  1.0854126467 -0.1280923412
##  [236]  0.5831109322 -2.1000681500  0.4053423251  0.0880332141 -1.0790454957
##  [241] -1.1676183285  0.4714561866 -0.1090668257  0.4231555729  1.5227510361
##  [246]  0.6779501075  0.0709206637 -1.3619407873  0.1338840595 -0.6600151708
##  [251] -1.4513495038  0.0000000000 -2.4741058999  0.2423563951 -1.5037184796
##  [256]  1.0110428596  0.5917464064 -1.0771340254  0.8420509740 -2.0111045256
##  [261] -0.3740823711 -2.1056879219 -0.3543861142 -0.7010506248  1.3926871227
##  [266]  0.6189714255 -1.0415029271  1.1300791324  0.3927182114 -0.3274766981
##  [271]  1.2266233136  0.8678704151 -0.7663824484 -2.4495130752 -0.4399811669
##  [276]  0.4833202031 -0.2762817855  0.4154843333  0.5476370848  1.0801373597
##  [281] -1.0682683725  0.0656072702 -0.0760143908  0.7604436226 -1.2206762543
##  [286]  0.7131634320  1.2902738861  0.6178698270 -0.0862278629 -0.9066634661
##  [291] -2.7947651669  0.0384662835 -0.2699842030  0.4394280096 -1.9911536302
##  [296] -0.6317204388 -1.2223296399  2.7658795640 -0.4903553789  0.2960354321
##  [301] -1.3126443537 -0.5374496716  2.6330795905 -1.1471508585  1.0870696549
##  [306]  0.6944359607  0.1101133412 -0.4586023818 -0.6423353997 -0.4678278152
##  [311]  0.3549230013  2.3730300221 -0.1011017650  0.0739046420  0.0491581609
##  [316]  0.1047486210 -0.3722408241 -0.6338074392  0.3647985670 -1.7990417170
##  [321] -0.2574251697  0.3754214023  1.9617011936  0.0458108327  1.4329991685
##  [326] -0.1155704971 -0.7119792585  0.2419094677  0.5770036312  0.6107176966
##  [331] -0.1037433277 -0.4129154835 -0.4321539752  2.0095971955  0.3162785237
##  [336] -0.4747585494  0.8394907977 -2.0411543981  0.3370503531 -0.6631701214
##  [341]  1.1185804858 -0.0383847478  0.4288234954  1.1932797717  0.1363748319
##  [346]  0.1048324026 -1.1617199658 -1.9456139843  0.2633911918 -1.4322205557
##  [351]  0.6807401050  0.4088499724  0.5826937289  0.1730044941 -1.2867631963
##  [356] -0.6690153425 -0.0388615377  2.4516706045 -3.0124337098  0.0517074664
##  [361] -0.1727335148 -1.3043380995  0.2392292774  1.1770082582  0.0062099610
##  [366] -0.5649940024 -0.8545956862  0.3341642892 -1.7852954828  0.0044035761
##  [371] -0.2528418488  0.5608367830 -3.0107057447 -0.2552989711  0.0936851466
##  [376]  0.3066982724 -1.5797190526  0.0852283143 -0.7101755038  1.4818621195
##  [381] -1.8602216864  0.4834556711 -0.8235854774 -0.6874345355 -0.8660396323
##  [386]  1.9942513710  0.8051322851  0.0198447682 -0.0406615641  1.0938956548
##  [391]  0.3266023338 -2.0199339642  0.2986731156 -1.4507913965  1.6593858295
##  [396]  1.0640622803 -0.8469262294 -0.3672233058 -0.6347781200  2.0941148644
##  [401]  0.2033547112 -1.1903967286  1.5140961735  0.4087998525 -0.7681126935
##  [406] -0.1915986781  0.3911425477  0.3093547629 -1.2431006094 -0.7366218887
##  [411]  0.5037613932  0.2151824616  1.0468689825 -1.8242658028  0.2925753910
##  [416]  0.6792089435  1.3095603217 -1.1682021310 -0.3378272168 -0.1797274380
##  [421] -2.8850451846  0.2924370284  1.4476449894 -2.3071752099  0.3203968817
##  [426]  0.7735409217  0.1239090706 -3.0661372621  0.7434384719 -2.1540466504
##  [431]  1.5403551734  1.3184110245 -1.2479427601 -0.4892197436 -0.0657988918
##  [436]  0.7062318823  0.1283459911 -3.8186529533  1.2742007080 -0.1062857743
##  [441] -1.0480350264 -0.3473229815 -1.0851823071 -1.6270666342 -0.2841565948
##  [446] -2.1438581362 -0.2613828834  2.6313346764 -0.0946108711 -1.8344641975
##  [451]  0.7015639099 -0.1102761621  0.9003930151 -0.6193236123 -1.3197173355
##  [456]  0.2523720238 -0.7676686072 -0.7349334074  2.4390221468 -0.2037588437
##  [461]  0.5076854161  0.3250910244 -0.0584895841  1.0099806197 -1.3767939899
##  [466] -1.2451384894  0.6669374917 -0.3145143730 -0.5965705732 -1.5130372089
##  [471]  1.7584913180 -0.9881116249 -0.6135294170  0.2433184936 -1.7054240029
##  [476] -1.6751015397  1.3270203824  1.2995013891  0.1301917519  0.7557735273
##  [481]  0.2179163814 -2.3122597368  0.7635930327  0.5183742703 -0.6461334827
##  [486]  0.8222215028  0.8938065798 -0.5687502773  0.3058564331 -0.8115455491
##  [491]  0.2033875417 -0.4035958963  1.7055670962 -0.2926683746 -0.7042438783
##  [496]  0.1012138101 -0.6954377608 -0.3855554752  0.2452313842  0.2465800293
##  [501] -0.1942185533  1.3105839744  0.7313491623  1.6873182847 -0.2265479942
##  [506]  0.4089837057 -1.7180900490  0.1696841446 -1.1707452583 -1.2158248811
##  [511]  0.0910278692 -1.9191854505  0.0638699433  0.3945638411 -3.0542370628
##  [516]  1.6196891478 -0.5267799695  0.1972502188  0.2215693829  0.4723519969
##  [521]  1.5355192761 -1.4415313183 -0.9240068293 -0.0217652201  0.6999211688
##  [526] -0.3507565002  0.8169492626  1.3783763924  0.0729246655 -2.6952021714
##  [531]  0.3083644765  0.0731979892 -0.4614435620 -2.2928295150 -0.0369619040
##  [536] -0.5130783696 -0.5193971231 -1.7031853931  1.6892495776 -0.4114118484
##  [541] -0.6569779835 -1.0367546302 -2.0799880478 -0.2314072363  0.9184080785
##  [546] -1.7341625871  0.0429712994 -0.3888091058  2.5662549410  0.0759328420
##  [551]  1.3547016269  0.2490734560 -0.1236170325  1.2105412176  0.7706127660
##  [556] -0.5070532520 -0.8276169773  2.9240610500 -0.6127733756  0.3013398181
##  [561]  0.7858422156 -0.7263907816 -1.3111307473  0.4628527547  0.6247102817
##  [566]  1.1383656673  0.3841382010 -0.3576126069 -1.1132353716  0.5347677282
##  [571]  1.8146061978  0.1071319745 -0.9350911019  0.5848894497  0.7660600254
##  [576]  0.2557593278 -2.4435530749  0.8999087129 -0.3372408170  0.4663229858
##  [581]  0.8418939447 -0.5260067173 -0.1518138952  1.2845650941 -0.0548581531
##  [586]  0.3377698786  2.2496175581 -0.2042569004  1.0063099491 -0.7784936114
##  [591]  1.4424535950 -1.2320427092 -0.0537989185 -1.6295507083  0.5553553314
##  [596] -0.6565601854  1.7982891459 -0.0911658913 -0.2935653578 -1.0414283965
##  [601] -0.0922026444  1.7351421396 -1.1304109670  0.8899116848  0.8005825573
##  [606]  1.5625812534  0.1109571365 -0.8421113643  0.7136563958 -0.1640436472
##  [611] -0.0713743551  0.2676369147 -0.2872215256  0.5390214139  0.1301487957
##  [616] -2.4134420115 -0.9838256833 -0.1066597488  0.6989979277  0.2696087969
##  [621] -2.8923343780  0.1491734176  0.4564278621  1.5874939465 -0.1003855551
##  [626]  0.6642320822 -0.6592590620  0.3500401309 -2.5471706567  0.1648435515
##  [631] -1.3858984319 -0.1096880434  0.2522955575 -0.3097107560  2.0331405948
##  [636]  0.3633551447  2.1475386304  0.5140110959 -0.0243174058  0.7845395019
##  [641]  0.2580146562 -0.0410669875  1.9154727170  0.2147853092  0.2274476009
##  [646] -0.2149789723 -0.4057409164  1.1168796216  0.0684407975  1.5182993943
##  [651]  0.2741399060 -0.2850191946 -0.5889296985  1.4551268807 -0.3368425027
##  [656] -1.3642122820  1.1504900398  0.6699223181 -0.8689070598 -2.5230507469
##  [661]  0.7764609654  0.5425404850  0.9126140695  1.5652006166 -0.0421082574
##  [666]  0.1976191194  0.0104999166  0.2695799448 -0.2066424987 -0.9009061139
##  [671] -2.4995564992 -0.2770964928  0.7658553817  1.2088265214  0.7891599587
##  [676]  0.7132136445  0.9871962915 -0.1285004389  0.6462838514  0.3326300982
##  [681]  1.7179867848 -0.3038166976  0.2787374555 -0.3851214081  0.7819089945
##  [686] -1.2287843310 -1.1081939889 -0.6907083667  2.0564551821 -0.2133931614
##  [691] -0.3419221789 -2.8478959661 -0.3450916684  1.2099042602  1.0802801897
##  [696]  0.2125637795  0.6299109308  0.4980656037  0.4098244618 -0.2777761976
##  [701]  1.8495361156  0.3780648742 -0.7896247001  0.9312228460 -0.6258601626
##  [706] -0.9264991255  1.1079303277 -1.2546047949 -1.1542596708 -0.3167570358
##  [711] -2.0089222189  1.8843387437 -2.0592188401  0.3850582077  0.1556725625
##  [716]  0.0725719112  1.4388105710  0.1760205122  1.6752409882 -0.0043474358
##  [721]  0.3700845476 -0.8146316430  0.4639694139  1.2373159064  0.0762483504
##  [726] -0.0419873997 -1.3071735336 -0.2956828391  1.3291779997 -0.0495752654
##  [731]  0.4500327140 -1.8409479521  0.3441920264  1.1653680100  0.0323288008
##  [736] -0.8575557660  0.5664468375 -0.2666610603 -1.1852083566  0.4062958526
##  [741]  0.6820218724  0.4434549420  0.8785608920 -0.7067719113  0.1466086568
##  [746] -1.6388951817  0.7091438008  1.3065945335  0.4189018269  0.2847518312
##  [751]  0.6882087482  0.1549824726 -0.1994493340  0.0292878924 -1.5940875456
##  [756]  2.2245391017  0.3430821044  0.0638181529  0.4991391640  0.3755278992
##  [761]  0.2392786200 -1.3628154537  1.1108475358  0.3144471176 -1.4888706949
##  [766]  1.5450308294 -1.1972906317 -2.0689798696 -1.9863480069  0.3406901615
##  [771] -0.3356727730  0.4158596992 -1.0814063702 -0.8860826521  1.2886879211
##  [776]  1.1185122173 -0.4675774384 -2.8591152406  0.1831737938 -0.6106893717
##  [781]  0.9352219160 -0.1632455903  0.7609863039 -0.2242461457  1.5676053266
##  [786]  0.3374970811  0.5613536698  0.1966652918 -0.1013088944 -1.2678953464
##  [791]  0.9608115556 -0.2071692703  0.1496682909  1.1533988123  0.2573353684
##  [796]  0.0505408767  0.4690895804  1.8304238497 -0.0197481188  0.2059867758
##  [801]  0.5778563976  0.5348253160 -0.0299120257  0.0658914998  1.1913226119
##  [806]  0.8471715888 -0.0475225425 -0.7844703555  0.7842226921  1.1056997117
##  [811] -0.8193628854 -0.2540282941  0.1151239234  0.9277904940  0.0068528993
##  [816] -0.5515739106  1.2665536193  1.2608212995  0.2516868560 -0.9237700852
##  [821]  0.5199992454  1.0579788780  0.2708480402  0.1098843231  1.8610166488
##  [826]  0.1187175171 -2.4210067306  0.5084773656  0.9482649551 -0.1200848082
##  [831]  0.2841856409  0.9436388924 -0.5679076404 -3.2303339225  0.5684620218
##  [836]  1.1929509388 -1.5084277308  1.0750157333 -1.9682633039 -0.4534881146
##  [841] -2.4073773929 -0.8695932641  2.4840227059 -0.1491603063  0.6509553633
##  [846] -0.6133675918 -1.0058646522  0.0590753256 -0.8290824405 -0.3069201636
##  [851] -2.5589205965  0.7172252123 -0.6527627229  0.0186978047 -0.3265730175
##  [856]  2.0059282606 -0.6465179224 -0.9457443475  1.4128138208  0.2104246626
##  [861] -1.9770197448 -0.6482668879  0.5467126297 -0.3171090727  1.6703156795
##  [866]  0.2247758807 -0.1007435517  1.4081413693 -0.0316937891  0.0794921285
##  [871]  0.0886363657 -0.2822645489 -1.2741667104 -0.2254835809 -1.3784948346
##  [876]  0.2186197306 -0.1681429218 -2.8065767462 -0.6412176391 -0.2150700024
##  [881] -0.3348933283  0.4114118845  2.5353778376  0.5768624055  0.4673136906
##  [886]  0.0508634672  1.1492673958 -0.0114426501  0.0955475555 -2.5270075453
##  [891]  0.3865666398  0.7891540947 -0.9254555774  1.6180795525  0.5368608304
##  [896]  0.7744150511 -0.0754518711 -0.5409745261 -0.3429828646  0.0055954778
##  [901]  2.0719704248 -0.3758244245  0.5044940089 -0.1123449426 -0.3541017456
##  [906]  0.5561076104 -0.6379291882 -3.1632276919 -0.3924276948 -0.3139341673
##  [911]  0.0100700912  1.0950279379  0.1317764497 -1.6368946044 -0.3147422753
##  [916] -0.3719712149 -1.4316135890  0.2987238456 -0.7511986233  1.6481249297
##  [921] -1.3253905197  0.0331162115  2.6626314021  0.6034570389  0.9235618185
##  [926] -0.8226303150  0.4700219273  0.3756896360  0.4045157050  0.9841358208
##  [931] -0.0634797672  0.3393209635 -0.0373067309  0.0908982101  1.7775256409
##  [936] -0.2619821350 -0.5273845418 -0.9558994323  2.3896313527 -0.4971860562
##  [941]  0.4477697371 -0.2542315999 -0.3243035849  0.4923993312 -0.9464272926
##  [946]  2.4160425371 -0.0600349639 -0.1587451173  0.6316843325  0.0156962270
##  [951]  0.4399325738  0.8620694496 -0.4463253976  0.2600149484  0.9800692507
##  [956] -2.1431971040  1.1259992461  0.1858329697  0.2678294756  0.2561621120
##  [961]  0.0021414870 -0.3636470657  0.1592203557 -0.0656579035  0.1488611584
##  [966]  1.2737019266  0.5643173581  3.0103639450  0.4146751554 -0.2379388540
##  [971] -0.9654971667  0.5183993221 -0.5274134100 -1.5356985490 -0.1423176926
##  [976] -2.0363572001  0.0217435340  1.6781518442  0.2472236175 -0.1644952198
##  [981] -1.6079981294  1.4838723708 -0.6906671111 -0.1318790107 -0.6257617216
##  [986]  2.2878461192  1.0694288370  0.2160341748 -0.1162339063  0.0496554037
##  [991]  0.3834910115  0.4223367474  0.6957461794  0.0057793073  0.1162508543
##  [996] -0.6967906825  0.8539803104  0.1160144508  0.3733143350  0.9198719143
## [1001]  0.5095279910 -0.2563233435  0.0996525724  0.1311402854  0.1785370192
## [1006] -0.2766667046 -0.0359661728  2.1868470479 -0.1996613854  0.7959228916
## [1011] -0.3383813270 -0.3053982019 -0.2362593593  0.6612731793  1.6013734812
## [1016] -0.2682724720  1.2029873020  0.2122381661 -1.6425938084 -0.1835236591
## [1021]  0.3599907018  0.9060585534  0.0405068176  0.6806502586  0.3660824342
## [1026] -3.0446877491  0.8590923782  1.8830237399 -0.2635285629  0.2432741562
## [1031]  0.3184495472  0.7306951259  0.5024525697 -0.3509851120  0.0993689273
## [1036]  0.7726901693  0.3385546482 -0.4823316421  0.9606525066  0.4641085778
## [1041]  0.3007116207 -3.3807131491 -0.6244470905 -0.1055210659  1.1933113864
## [1046]  0.6070992668 -1.8069013334  0.1585472614  1.8007081823 -0.6759062199
## [1051] -0.7945610099  0.8632176506 -0.1344018037 -2.0184306093  0.6196006823
## [1056] -0.5575170780 -1.0878344140 -1.8704147761  1.0818368089  0.3455602148
## [1061]  1.2800829475 -0.2927406686  0.2570846727  0.8817286834  0.3032931115
## [1066] -0.2825304270  0.7709122699  0.7464926130 -0.2102001133  0.6055723452
## [1071]  0.0437223892 -0.0242743618  0.3118414743 -0.2279986290 -0.6307168539
## [1076] -0.4474482092 -1.2881818338  0.0292057699  0.0135036291  0.6619410815
## [1081] -1.8881895331  0.8130964651  1.9192229038  0.6299785889 -0.1973304758
## [1086]  1.1755912515  0.7863718950  0.4544702996  0.3078708503 -0.2474521343
## [1091] -0.5024874753 -1.0549924505 -1.3539009966  0.5249626948  0.6469603213
## [1096]  1.1737143476 -1.5572366867  0.6106652752 -1.0473376727 -0.7880399439
## [1101] -0.0473378844  1.1969018138  0.2836556976 -1.0623837385 -1.6086001882
## [1106] -0.0988192639  0.4047258252  0.5275936048  0.5652568076  1.5097884744
## [1111] -2.9844645738 -0.1077754661 -0.9275991285 -1.0332478726 -0.0906591561
## [1116] -0.4278958040  0.7935069930 -1.5507523852  0.0667327195  1.3447707283
## [1121] -1.7751109306  0.1540285159  0.2878364387  0.5449449537  1.4168662634
## [1126] -0.6408007023 -0.2910225153 -1.2929988719  0.9505185520  1.3388361012
## [1131]  0.8093276358  1.0092005871  1.4256631111 -0.1238390017  0.0998105323
## [1136]  1.1141177754 -0.7309801304 -1.9654968819 -0.4005731303  0.2975900425
## [1141] -0.6912057624  0.5874751129 -0.9034652584  1.8002131648 -0.0645372515
## [1146]  1.3927197431  0.0877212059 -0.5885024069 -0.4466587722 -2.3498237980
## [1151] -0.2870964275 -0.6147760160 -0.4109082997 -2.7250181990  0.3782871360
## [1156] -3.9656372459 -0.0263460388 -3.4435095062  1.4480568164 -1.3220268026
## [1161]  1.2690656692  0.1422998270  0.6374183795 -0.3057076829  0.0320525684
## [1166] -1.6858833943 -0.5000930235  0.0091230445  1.3012730735  0.4833284381
## [1171] -0.6225573750  0.6292561829  1.2341208156  0.1007352093  0.2298880231
## [1176] -0.6066878800 -1.3742648388 -0.3791905596  1.5439062253 -0.5351497216
## [1181] -1.4440401404  0.3461917173  0.4882458307  0.7683781275  1.0139552377
## [1186]  0.3396151755 -0.6330450485 -0.1122768564 -2.1844783105 -1.9128151005
## [1191]  0.3055029863  1.2559696490  0.5592327912 -1.1666861116  0.4420478008
## [1196] -1.4811543700 -1.5683899516  1.1038350418  0.8710305188  0.9144912649
## [1201] -0.4210502419  1.8493446262  0.0259210221  0.5062210578 -0.1648547279
## [1206]  1.0355873322 -1.1752327496  1.1880179657 -0.7305341915  0.2715676008
## [1211]  1.2033361228  0.8036730941 -1.3121571114  0.6488463667  2.1911797744
## [1216]  0.0203821033 -1.4284359780 -1.5143386336  0.7878193703  0.9504657998
## [1221] -0.3261855238  0.3506872309  0.7020611435 -2.3491005635  0.4210664454
## [1226]  1.0154058949 -0.5070463725  0.2705821916 -1.0201446714 -1.0334545446
## [1231] -0.0240761201 -1.2479104048 -0.2655848662 -1.5442013048 -0.1701546713
## [1236]  1.9764476820  0.1276065590  2.6580380953 -0.0876937682 -0.0120513805
## [1241]  0.5574432352  0.0638446350  0.1266571031 -1.4564779442  1.0619560379
## [1246] -0.9485012756 -0.5571885407 -0.7717542685  0.2264605756  0.2425665074
## [1251] -0.9610097194  2.4075270550  0.1227156825  0.5628068600  0.6501078583
## [1256]  0.0059880943 -1.0295709112  0.8698068262 -0.3577138664  1.3660193070
## [1261]  0.0157418625  0.2661343498 -0.2466046571  0.2348599930  0.9830868435
## [1266]  0.0342099138  0.2762730383 -0.6231762866  0.4600876363  1.4976316699
## [1271]  0.6064744638  0.0852867329  0.0638578104 -0.1474101723  1.3087225278
## [1276] -0.8149544694 -0.2262739109 -0.3773583251 -0.0711335445  1.4474201487
## [1281]  0.1621461956  2.2591806656 -0.0515433685  0.2620511217  0.2957223237
## [1286]  0.2123805769 -1.0482861721  0.9977809794 -0.1355182912 -0.8205736292
## [1291]  1.6664250812  0.3122724620  0.1008694328 -0.4957201331  0.6529859645
## [1296]  0.2603864463  0.2203080648  0.5683626392 -0.8190837649  1.0486176797
## [1301] -0.5343438160 -0.6516550272 -2.6298034590  0.8432816842  1.2088280101
## [1306]  0.4293365151  0.0199953766  2.3853879729 -0.1216097795  0.6487872852
## [1311]  0.1264320219  0.4790289935 -0.3801680899 -0.2492847133 -1.0166078367
## [1316]  0.4272841091  1.9816411900 -0.3352110524 -0.6228670602 -0.2089211633
## [1321]  0.5076141957  1.0670071947 -0.5541004644 -1.4692678944 -0.0820584623
## [1326] -1.5821410894 -2.1319968822  0.7411033138  1.4066198155 -1.2023331094
## [1331] -0.0466243154  1.5329722129 -0.3695086827 -0.5771373116  0.1187076198
## [1336] -0.9206430801  0.4019961161  1.5686819604  0.6950201908  0.2600290295
## [1341] -0.4474143297  0.6826525968 -0.3109927630 -1.0110201156 -2.1054811527
## [1346]  0.0367294037 -0.4822609417 -0.7945109862  0.3019875097 -0.4317246596
## [1351] -1.4904916786 -0.6992762378 -0.5496985274 -1.9642411047 -0.8001053661
## [1356]  1.7501339017  0.0466906456  0.1749368349  0.1527234600 -0.2566715651
## [1361]  1.3856217777 -1.6868520768 -0.2348446690 -2.7488804990  0.0086207827
## [1366]  0.4863731776  2.0562983446 -0.0079278249  0.6520110435 -1.0707135405
## [1371]  0.9661895581 -0.5907226130  0.9469585236  0.9111476109  0.1293201617
## [1376]  0.9426781602 -0.1636296073 -2.3440963741  0.5778936204 -1.3683289460
## [1381]  0.3816565300  0.7663428852 -0.1864678972  2.3387994108  0.1816828659
## [1386]  0.4966032864 -0.3981078095 -0.8563994738 -0.1508609112 -0.8075383703
## [1391] -0.0015089101 -0.5433247648  1.8612191340 -0.2249454977  0.7681778630
## [1396]  0.7099440723  0.2981614034 -1.1819801289 -1.0078789859 -1.0131856292
## [1401] -0.0346739058  1.9410441311  1.8769119041 -0.0409874571 -0.3962132003
## [1406] -0.2830920257 -0.7848922129  2.0100014398  0.2058271696  0.4846419532
## [1411]  0.0623842765  0.0446804066  0.2531654542 -0.1542784081 -0.0167906112
## [1416]  0.1585287313  1.0402393536  0.2677060138 -0.0031837043 -0.5546201350
## [1421]  0.0366941780 -1.3747982551  0.9993160558 -0.0741224204 -0.1288611487
## [1426]  0.1407950937 -1.3626067850  0.8058767676 -0.1854293177 -0.1775038966
## [1431]  3.5017619636  0.4265265058 -0.6880926316  0.3601552293  0.2545203561
## [1436]  2.0896513777  0.4147931253 -0.3477278814 -0.1508864830  0.1488487056
## [1441] -0.0722212955 -0.0106681346 -0.3346926776 -1.6501931813 -0.7887467137
## [1446]  1.3295009571 -0.5802423249  0.3543978543  0.1225712336  0.5373247067
## [1451]  1.0938667289 -0.0474249033 -0.5382105578 -1.5864140364 -0.8779496802
## [1456]  0.0275570369 -0.4430782603  1.2448004311  1.4875868235  0.5422701197
## [1461] -0.3350051714 -2.4024979454  0.0480670169 -1.7049972604 -0.3182473840
## [1466]  0.3281333112 -0.0849720653  0.0193988881  1.4408082849 -1.1470833814
## [1471]  0.2545014150  0.9787101712 -2.9725367723 -1.0367638266  0.1424921548
## [1476]  0.0118184072 -0.3901262446 -1.4481411199 -0.1531114790  0.4981228603
## [1481]  2.1357600302  0.0582704528  0.2197516639  1.3165575638 -0.1956635560
## [1486] -0.5416101172  0.8482158758  0.4680026367  0.0187880064 -0.5879612197
## [1491] -0.2193129001  0.2150290309  0.4734112422  0.4341005708  0.0523001766
## [1496]  1.0593931637  0.0701519884 -1.0415106980 -0.6575445492  1.8992090967
## [1501]  1.5362719959 -0.9243864129  0.6634506566 -1.1767673457 -0.2934755541
## [1506] -0.6108762940 -0.1603265332 -1.5487200403  2.1042249348  2.5488317119
## [1511] -0.1580269777  0.3970736128 -0.2731419546 -0.3042763554  0.2657148369
## [1516]  0.8105050413 -0.0051826231 -0.1088502144  0.1407802318  0.0261421435
## [1521]  0.7927429135  0.4823820957  0.6510472679  0.2264701007  0.0010426906
## [1526]  0.8980584748 -0.3013133562  0.8610683038 -0.6519672161 -0.4328637620
## [1531]  1.7340756014 -1.7269504959  1.3368103288  0.0662754046 -0.2326607224
## [1536]  0.7690840169 -0.0836796138  0.2328516628  0.0908573059  0.1113019255
## [1541] -0.1763206632  1.2824043308 -2.0303212920 -0.8377042546  1.1639657810
## [1546] -2.3663551074  0.5998641626  1.3013662796 -0.0844125376  0.2437652976
## [1551]  0.5160098233  1.1189586716  0.1239370286  0.2216860947  0.5800562555
## [1556]  0.4355486733 -0.3375700071  0.1931367220  0.8639818743 -0.2487878104
## [1561] -0.8877364529 -0.3848627020  1.0976816505 -1.3106659027  1.0476798667
## [1566] -0.4769270736  1.1474652317 -0.0834178846  0.6063165210 -0.6872711926
## [1571]  0.8017519983 -1.6482309476  0.5512744813 -0.6076233841  0.9112474414
## [1576]  0.5087982316  1.8030231870  0.4509870808 -0.3782374946 -3.2458148024
## [1581]  1.2781135364 -1.2409975782 -0.5565847614  0.7685593927  0.4178608572
## [1586]  0.9903042551  0.0006046576  0.4135473967 -0.2005956681  0.8322471803
## [1591]  0.2921267996 -1.1676965434  1.1262251092  1.2237132274  0.2130379779
## [1596]  0.6219921846  0.5098414040 -0.4759209894  0.5801854063  0.0059600346
## [1601]  1.4844191496  0.6802653675 -0.6855095630  1.4289410362 -0.0905996298
## [1606]  0.2341384421 -1.1928610498 -0.4006160011 -0.0789361571  0.9553371704
## [1611] -1.0510906137  0.5288616474 -2.1487712732  0.7051444991 -0.6758730492
## [1616] -1.7454141975  0.9252816907  1.3995197918 -0.0354565628 -1.1206928577
## [1621] -0.8998921171  1.5825408556 -0.5737498563  0.7679090962  0.8106489530
## [1626] -1.4852079834 -2.4757507267  0.1971894517 -0.9761423893  0.7583343076
## [1631]  0.7909648144  0.5266583748 -0.3868073049  0.5166818445 -0.0550530675
## [1636]  0.0894063281  1.1802480338  0.5871452828  0.8409037977  0.0214383791
## [1641]  1.6977641957  0.3411498858  0.1613717662 -0.4652502748  0.3630432301
## [1646]  0.6915639509  0.2261403838  0.3007469373 -0.2872434006 -0.6175151201
## [1651]  0.4197594376  0.1403510656 -0.6604066539  0.0662690935 -0.0250974015
## [1656]  2.3705746611  0.2355568259 -0.2237934304 -0.9091865062 -0.5955787806
## [1661]  0.6186583869 -0.5805916677 -0.1909590934  0.4780266775 -0.9152510144
## [1666] -2.4779816218 -0.4241009902 -0.7949198737  0.5175891933 -0.8164107661
## [1671]  1.2149105543  0.5299406638 -0.5648861628 -2.3045990616  0.3065476164
## [1676]  0.2328377212 -0.4012238439  0.5510701635  1.1110162269  0.1607187134
## [1681]  0.0076633923  1.4806801643  0.9880457124  0.4054170448 -0.4718534518
## [1686]  0.3928305843  0.8578051524  0.6331759716  1.8584849557 -0.2391465742
## [1691] -0.9935323270 -0.6384162744 -0.3604576590 -0.3984123624  0.5266808675
## [1696] -0.6363143445 -0.9593724720  1.2379154065 -0.0975911330 -1.3913561465
## [1701]  0.9961192360 -1.1885527117 -1.6490201878  0.0674096934  2.7096971551
## [1706]  0.5645595532  0.3850383966 -0.7142139756  1.4279625202  0.6485995852
## [1711]  0.6554611447  0.0095669647  0.6406124314 -0.5494190853  0.3937391839
## [1716]  0.5592129874  0.1758605217  0.7805084000 -0.6916257874 -0.5545466748
## [1721]  0.4308354949  0.5500110362 -0.4449805189  0.6960729349 -2.1875256994
## [1726]  1.7354559087  0.0818617071 -0.2875149425  1.0350413289  0.6079131335
## [1731]  0.5487515269 -0.5007096744 -0.2872907110 -0.5376827495  1.2317574536
## [1736]  0.7107860337 -0.1844241781  0.0229951822  0.4005034314 -0.1311377235
## [1741] -0.4735844577 -0.5685872611 -0.2348225794 -0.8079646732  2.0443061108
## [1746]  0.2679340366 -0.4926981558 -1.8150914615 -0.5118883047 -0.0142701412
## [1751]  0.9376349406 -0.4560077294  2.5151160803 -0.0655855296  0.5814361708
## [1756]  0.6662094582  0.3760057950  0.6426979012 -0.0469041177 -0.0264311989
## [1761]  0.6142783010 -1.4113537262 -0.0482689204 -0.3847163686  0.9639705145
## [1766] -0.0330238536  0.0568972194  0.3935977791 -2.2253428190  1.4772664489
## [1771]  0.6443499838 -0.1737349384 -0.5335357900  0.3923220193  0.0850116586
## [1776] -1.3914947431 -3.0186573752 -0.4706322665  0.6231389365 -1.0878585721
## [1781]  1.1652079430 -0.6542904568 -2.4196751205  0.6095922877 -0.1706421247
## [1786]  1.1202040412  1.1738348107  0.1354670148  1.0248684921 -0.0249339676
## [1791]  0.5781358791  0.5010947019  0.1272016820 -0.7695359216  0.7209398019
## [1796] -0.2359014025  0.8039176046 -0.1776910746  0.0030286620  0.7290479330
## [1801]  0.4153738088 -1.1502535200  2.2466821540 -0.0062007786  0.2132908929
## [1806]  0.0709364023 -0.0648588493 -0.7543540677  0.0455846537 -1.8518863384
## [1811] -0.3754053502  1.3340573817  0.9356536750 -0.7954218374  0.7883869113
## [1816] -0.3892700081 -0.6778917553  0.6238763880 -1.0227399656 -0.2703863427
## [1821]  0.6916105208  1.1970966447  1.0099057566  0.4015582456 -0.1658525400
## [1826] -1.9533949263 -1.3868603067  0.4457760494  1.3585900474 -2.4649984965
## [1831] -0.8412767225  0.7370328876  0.6263817151  1.0131680286  0.1316150043
## [1836]  0.3911422900  0.4495465528 -0.2570666145  0.2116035355 -1.0648440912
## [1841]  0.4131102166  0.6372271914  0.4118872536 -0.0206387824 -0.2052669605
## [1846]  0.2981517902 -1.4985993322  0.8346860277 -0.2047140801  0.2374425349
## [1851]  1.5731354172  0.0611275424 -0.7208478218 -1.4539760588  0.5254510007
## [1856]  0.5580273807 -0.9764512092  1.1877102423  0.3301876208  0.6222850513
## [1861]  0.8968036077 -0.1659691293  0.8378513396  0.2870465013  0.1182725338
## [1866] -0.0644416951  0.3345365992  1.1849408874  0.7893009483  0.1594982779
## [1871] -0.0434943235 -0.6502989195 -1.3083976648  0.5294391915  0.1443800732
## [1876]  0.3892400671  1.4132810519  0.2121863456  0.2989630812 -0.0236744111
## [1881] -1.1965435566  0.8468870881 -0.2017220188  0.3389660754 -0.0680040382
## [1886]  1.2574405899  0.1151019896  0.9916516757 -0.6882781168 -1.2420911545
## [1891]  0.7591076303 -0.6789809422  0.2433736806  0.8319011195 -0.3292628025
## [1896]  0.7375031082 -2.0888671822  1.4370350676 -0.2994619406  0.6809210371
## [1901]  0.2438606222  0.0715232861 -0.7511079745  0.0448069252 -0.7410097532
## [1906]  0.0099797301 -3.4608401889 -0.3014405660  0.8033840122 -1.1108640904
## [1911]  0.0017405290 -0.6641457805  1.4088480299  0.3135839007 -0.1978276882
## [1916]  0.8586453854  0.5597132154 -0.0082157955  1.2066037665  0.6740503225
## [1921]  0.3422395773  0.4273118366 -0.3010433765  0.7533441833  0.1664753108
## [1926]  0.0082874852 -0.2928998265  0.5932664385 -0.0983511291 -0.1458132205
## [1931] -0.2960103041  0.9894282716 -0.5804010463 -1.2451706743  0.6393948398
## [1936]  0.1560080741 -1.0966771943 -0.1237612065  1.3490261229  0.2143571385
## [1941]  0.8408089113 -0.0812567484 -1.4262867196 -0.9293038562  1.2297009880
## [1946] -2.4205623576  0.9599861020 -0.2858944090 -0.3326123042 -1.6823862799
## [1951]  0.0005712057  1.3206694999 -0.1753817357 -1.8224592447  1.7774356599
## [1956] -1.8646254698 -0.8820606148 -1.2947264104  0.1175607720 -0.6559306416
## [1961]  0.0122117552  1.1653399453  0.8063882033  1.7601429448 -0.5820474154
## [1966]  1.0224672912  0.5857579474 -0.1316174793  1.1206000534 -0.1281905798
## [1971]  0.6182112273  1.2105428312 -0.0118871164 -0.3045673802  0.6501877169
## [1976]  0.4457888718  0.0434554118  0.4125783173  0.0965975527 -0.1029105778
## [1981]  0.0819049507  0.0390057929  0.1248752027  0.9055427704 -0.2597623928
## [1986]  0.3517102919  0.9602010685  0.5087278921 -0.2082433647  0.5234825122
## [1991] -0.4809138480 -1.3116781102  1.1159797991  0.6266515369 -0.1964373072
## [1996]  0.2922668838 -1.3203491399 -0.0396346116 -2.8678323127  0.5419761493
## [2001] -2.0409638128 -0.6526705785 -0.9078639215  2.1589913950  2.0485901111
## [2006]  0.3255228071  0.2918238207  0.1439488559 -0.0124040386  0.3174665059
## [2011]  0.0883710183 -0.5397541527 -1.1945723006 -0.0377068155 -2.1908382034
## [2016] -0.8470994952  1.1159618756  1.6761040784 -0.7089023008 -0.7083853428
## [2021] -0.2333608812 -0.5658026343 -0.9455714577  1.3606925866  0.1484767237
## [2026]  0.4863830213  1.6451732308 -0.5325392415  0.2609331606 -1.4650722513
## [2031] -1.3599057557  0.8928987200 -1.2452508032  1.1770731271  1.2728164227
## [2036] -0.3538252071  0.9300730317 -0.3134897564 -0.4167580531  1.1029577836
## [2041] -0.0029535531  1.0492643104  0.4381638814  0.1815761630 -0.0381538041
## [2046] -0.1375540847  0.8392179820 -0.0418399822  0.4023267208 -0.1165217646
## [2051] -0.2361004624 -0.4936800971  1.0431999212 -0.7483590172 -0.7250110751
## [2056]  0.1979040327 -2.4613833963  0.5064727162 -2.2930544125 -0.2005477630
## [2061]  1.3999547068 -0.6339211568  1.4539600432 -0.3319043308  1.2852135611
## [2066] -0.4937598698  0.9556931385 -0.1860642789 -0.7015364328 -1.7189704349
## [2071] -0.2445357342  0.2597955115  1.4231836275 -0.9567039603 -0.4298567963
## [2076]  0.4025817632  0.7945343412 -0.2528753654  0.3481135817  0.6082845380
## [2081]  0.7305111082 -0.6560410872  0.2377424693  0.7874047446 -0.1197640356
## [2086] -1.8366724479  1.2551075034 -0.1913775127  0.6947889222  0.3290253743
## [2091]  0.3298290608 -0.6360629517  0.4319100875 -0.6054996930 -1.6742702528
## [2096]  1.5555632608  0.3768907913 -1.6070522534 -0.5366280551  0.4720280919
## [2101]  1.7524120752 -0.5803046182 -0.3498563139 -0.0381949277  1.4297246356
## [2106]  0.0941966502  0.3976011779 -0.0882115932 -0.1351041612  0.3571768035
## [2111] -0.3560795023 -1.7077412289  1.3037753877 -0.1696520682 -0.8980257335
## [2116]  0.2899095844 -0.1493808459  0.3296724547 -1.4042857578 -0.2129873353
## [2121] -1.0108742424  0.0633989417  1.9085393961  0.2311796995 -0.9871479435
## [2126] -0.6407687053  0.8046077841  0.2821511084  1.4761878025 -0.7225106622
## [2131]  0.8403906382  0.0881968421 -1.0834148408 -0.4229809701 -0.0577516902
## [2136] -3.2891254133  0.2637131404  0.7341667607 -0.0336362551 -0.4527267764
## [2141]  0.7455224246 -2.1075060858  0.2298778841  1.3347726787  1.1283330511
## [2146]  0.4446053794 -0.0778360296  0.9063513755  0.1260427409  0.0939039461
## [2151] -0.5543925267 -0.3218848324 -0.8061787597 -1.5330875921 -0.7427992523
## [2156]  1.6084441973  0.8493071344  0.0033385051 -0.2859059466 -0.3671143615
## [2161] -0.3144761897  0.4558865905 -1.1839037116 -0.4164772885  1.9171629377
## [2166] -1.2088729301  0.1143550104 -0.1637976799  0.5318757409  0.7338840384
## [2171] -0.3765189034 -1.2401340490 -3.0106694070 -3.0807374903 -2.5630623487
## [2176] -0.6478978497  1.9181365401  1.0263696855  0.0261145511 -0.3943559221
## [2181] -1.5112691084  0.8429168283  0.0557087852 -0.8053828813  1.3343660202
## [2186] -0.7185683457  0.2821635215  0.2594777602 -0.2568664710  0.8635182538
## [2191]  0.6002996222 -0.1870533280 -1.2847146234  0.3437374160 -1.0031870991
## [2196] -0.1660006973 -0.2942625113 -0.0436231297 -2.6228777999  0.0912147969
## [2201]  1.5148720905  0.1452255564  1.1324559273  1.4167492730 -0.2628670127
## [2206]  0.6307007776  0.7248704307  0.0620154635  0.1177658940 -0.6813012459
## [2211] -0.4872608490  1.6009786306  0.4447651270  0.0279361069 -0.1577277153
## [2216] -0.6926212348  2.0100044240  1.1060640590 -0.1891754368 -0.2709622161
## [2221]  1.3301029112 -0.0478662433 -0.5502652732  1.4064344539  0.3010908316
## [2226] -0.4173632648 -0.1402187900 -0.0457872512 -1.3803775598  0.1953365860
## [2231] -0.4434379785 -2.0153507823 -1.3247498389  1.6364247968 -0.1322200909
## [2236]  1.6990459759 -0.1050722938  0.3828174700 -0.1321105314  0.1398568672
## [2241] -0.0157928554  0.0773812837 -0.6442429315  1.5081147128 -1.4194776635
## [2246] -1.7151737475  2.1105505217 -0.5931105510 -0.5780591556 -0.7243285305
## [2251]  0.2166412643 -2.0262655640  0.4058423017  0.9628041318  1.3178694327
## [2256] -1.3152740317 -1.4813702170  0.5905074557  0.7040943336  1.0288275194
## [2261] -0.1328160612 -0.1954271492  1.0189711604 -0.6937484208 -0.9382643543
## [2266] -1.5368688190  0.1824895225 -1.2890122399 -2.2299382075 -0.8066794043
## [2271]  0.0649362016  0.6406869928 -2.1791670549  1.1494951749 -1.4864574433
## [2276]  0.0334982409 -0.8051434835  0.3653372829  1.5184354955 -1.0951043743
## [2281]  0.9650977083 -0.7568159911  0.3956774890  1.8785200345 -0.0291842663
## [2286] -1.3523447020  0.3372138111  0.1110599371 -1.4705413146 -1.0410018343
## [2291] -0.0483031056 -0.0149020992 -1.0563755206  1.6353687507  1.2436817965
## [2296]  1.1967642471 -0.3329463152 -0.0019912893  1.1887515992 -1.0086937939
## [2301]  0.3563521762  0.9716372178 -0.1617195218 -0.7591312152  2.2602186771
## [2306]  0.3096586819  0.2844109449  0.2887037794  0.0829628442 -1.1415846164
## [2311]  0.4959276718  0.0161652907  1.8120189079 -0.1212196538 -0.1899513022
## [2316]  0.6178273984  0.7555092960  0.5165589365  0.1210390515 -0.1148357678
## [2321] -0.8895113647 -0.0523379923  0.0798684331  1.3559357182  0.6197080101
## [2326] -0.2989250090  0.9677053165 -0.4832350959 -1.5850028908  1.4425721050
## [2331] -1.5232857863  0.3189334479 -0.3335309092  1.2356117626  1.2216841862
## [2336]  0.0202111239 -0.1229985021  0.8662802404  0.4101003610  0.1061483312
## [2341] -0.7677937564  0.0071114571 -0.2839839063  0.3055266798  0.2794168703
## [2346] -1.6290945873 -0.7793953074  1.1990138764 -1.2732822540 -0.8177217055
## [2351] -0.0330344527  0.4638093311  0.1143138815  1.9789307058 -1.2619276691
## [2356] -0.0210742166 -1.1279115255  1.2481983898 -1.1500122974  0.0241254504
## [2361] -0.4665032896  0.7888607601 -0.2777522876  1.9070100241  0.8192741839
## [2366] -0.0251483488  0.5456070436 -0.1332871431  0.1593702490  0.4183317350
## [2371] -0.4495303831  0.7789740450  0.2056875743  0.5508296344 -0.2923447883
## [2376] -1.6225962067 -1.2550172804 -0.2606033546 -0.2800000832  0.4970114154
## [2381] -0.5332152197  0.9682366481  0.4412591609 -0.2774909952  2.3113827065
## [2386] -4.8924841938 -1.1728335301  1.1061929302  1.0485108069  0.8343314520
## [2391]  0.1238721622 -0.4743542545  0.3924763612 -0.0685860763  1.2882584661
## [2396]  0.2766217843  0.6101915518  0.0123302973  0.5175080112 -0.0965062295
## [2401]  0.2651186448 -0.1703734177  0.5385177007 -0.4757183798  0.6230078394
## [2406] -0.4249993854  0.0474122635 -0.1857690751  0.2604356655  0.2753243416
## [2411] -0.2224811936 -1.1568611581  0.5347027144  0.0370157575  1.5510713306
## [2416] -0.1453092009  0.0652610464 -0.5011736052  0.8414358926 -0.1397076143
## [2421]  0.5076087949 -1.0151124025  0.3311856266  0.4011563680 -0.2689917141
## [2426] -0.1079691331  0.3842309405 -1.0504954649 -0.2589755103 -0.3071135141
## [2431]  1.0341139378 -0.3688369544 -0.4578744791 -0.0080676526  0.8395064183
## [2436]  0.5803478867 -0.0285918311 -0.4463710373 -5.0228401642  1.3756764071
## [2441] -1.3245502789 -0.0494316315  0.9138634714 -0.3468503164 -0.0018224732
## [2446]  0.0315277082  1.2282617127  0.7017988686 -0.6424570235 -0.9978075475
## [2451]  0.7364047817  0.6205797354 -1.1398418730  0.9354252977 -0.3844740018
## [2456] -0.6172717018  0.5506795258  0.0641972618 -0.4609998258  0.6758736565
## [2461] -1.8751159599  0.1445755556 -0.4161959817  0.0282802059 -0.4515403778
## [2466]  0.9452085112  0.3313886932 -0.2173622086 -0.0138828438  0.8169508141
## [2471] -0.6497372422 -0.3001156483 -0.5326689743 -0.5629124025 -0.0223629536
## [2476] -1.2884840055 -1.1401581592 -0.7320572417 -0.2763078732  3.7818297035
## [2481]  0.3750233734  1.1664817580  0.2000072574 -0.1537248124 -0.0135737448
## [2486]  0.9356463431 -0.1979988520  0.6193323795 -0.3267217731  1.0678037487
## [2491]  0.3017062655  0.1183601713  0.6031863478 -0.8309667761  0.2095979584
## [2496] -0.4363843948 -0.5958053277  0.0681452941  1.0371874513  0.5842155966
## [2501]  2.2763706355  0.2904187176  0.8398803107 -0.1617115215  0.9769834487
## [2506] -1.1982658595  0.5417933277 -0.2532555427  0.2995772539  0.5758618221
## [2511] -0.3987918691 -0.3124221916  0.2170565420  0.4038515454 -1.5446315436
## [2516] -0.0477406665 -0.7912211886  1.4306377831  0.8763704538 -0.1174923145
## [2521]  0.5621111365 -0.5819358839  0.0000000000  0.4919989593 -0.3816013120
## [2526]  0.3370571625 -0.5560913971  0.3325142454 -0.6976313247  0.6434293342
## [2531] -0.5149031390  1.2624337761  1.4229081322 -0.1185177085 -0.1460694080
## [2536] -1.0576164647 -0.1497978574  0.0522672269  0.1037827843  1.3627836437
## [2541] -0.3627849664  0.0400545727  0.1270794427  1.0865072258  0.6395710554
## [2546]  0.9449498094  0.7014326300  0.8746677014 -0.1491253367  0.3005696517
## [2551]  1.1126615402 -0.1892746703  0.0758982715  0.2798865481  0.1957339739
## [2556] -0.5094983075  2.6967132720 -0.8252496678  0.0710292830 -0.4892980432
## [2561] -0.4496355843 -0.3645342065  0.1321968089  0.5629261947  0.0642384143
## [2566] -0.6161740923  1.5274411676 -0.2645220974 -0.2223716686 -0.3533271000
## [2571] -2.2562304568  0.2643960320 -0.1562944260 -0.1309102757 -0.1659013492
## [2576]  1.2267755339  0.1726959795  0.4879148059 -0.3852903610 -0.2888655933
## [2581]  0.1014789453 -0.5743064342  0.3642187186 -0.1595749429  0.1360949960
## [2586] -0.2908659201 -0.7757458380 -1.3759548902  1.5574893548 -0.4662911846
## [2591] -0.2837402569  1.2912154142 -0.4835119838  1.7653361699  0.8514230744
## [2596] -0.0681918299  0.0820485211 -0.2993835922  0.2820331172  0.2013090210
## [2601] -0.2239569796  0.1059949895  0.7686103831  0.0069659338 -0.1970708452
## [2606]  0.2227269767 -0.4361894827 -0.3006816565  0.9830629600 -0.1351396368
## [2611] -3.6973630054  0.4336620917  0.8361817054  0.6440683837  0.2368205023
## [2616]  0.3393782906  0.6353017134  0.0455627199 -0.1865143322 -0.0745831117
## [2621]  1.2791061254  0.5837141822 -0.1963437553 -0.4681533595  0.2703830915
## [2626]  0.0477034103 -0.1537460036 -0.1870099209  0.8828362079 -0.1896793080
## [2631] -0.4384878083  0.0561393598  1.6868478165 -1.1661966868 -0.0955691437
## [2636] -0.0781030334  0.2781393960  0.0580627401 -1.5408386291  1.4710663785
## [2641] -1.3062523818  0.2161772089  0.3431306567  0.2253693420 -1.5281126263
## [2646]  0.9269054558  0.1332469839 -0.1186628710  1.1594479911  0.2839147948
## [2651]  0.7389908815 -0.0084361939  0.0998640311  0.9337738219 -0.0261257258
## [2656] -0.0651864704 -0.1956622430  0.5532625192  0.0539595671 -0.1912847217
## [2661] -0.2699618216 -0.1491301087  0.5104929064  0.1027068623 -0.4639657070
## [2666]  0.4006745899  0.3508788855 -0.5186421628 -0.0776349388 -3.1588588140
## [2671]  0.1778400555  1.4717304819 -0.0667546816  0.2013848568 -2.3262667781
## [2676] -0.2118591387  0.1427589782  1.2933690966 -0.4261207134 -0.2686700014
## [2681]  0.2285585792  0.0702612377  0.1283052432  0.7366322045  0.9176210216
## [2686]  0.3134356228 -1.2481713521  0.4818172907 -0.0284027161 -0.2485514773
## [2691]  1.8684539171  0.4872102913  0.1137493175 -0.1740955128  0.3052205757
## [2696]  0.2495627331  0.1972328579  0.1166176321 -0.5794708913  0.1236103065
## [2701] -0.4367500515  0.0143361288  0.8300741580  0.2384087048  0.7477063281
## [2706]  0.7677732686  0.4205532851  0.2463013281  1.1363508188 -0.2028816191
## [2711] -0.3505792468  0.4585250036  0.3595849553 -0.3417742087  0.1801191415
## [2716]  0.3655181537  0.1416608848  0.1587963266  0.0710983380  1.1206304058
## [2721] -0.8119048168  0.3213032526 -0.9447080507  0.2465024140  1.5964979725
## [2726] -0.5527990718  0.1659037610  0.2898213074  0.0355879390  0.5978029873
## [2731]  0.2459398005 -0.0374678222  0.2929952657 -0.7773912245 -0.1809294192
## [2736]  0.2021605311 -0.4837175127 -1.1601005918  1.5875977628 -0.4467744906
## [2741]  0.2223138679  1.1774833038 -0.1274292047  0.3630127221 -0.0698137438
## [2746]  1.8425005123 -0.0580813402  1.3457407856 -0.3081994416 -0.1671485781
## [2751] -0.6222493642 -0.0192178012  0.5143360066  0.9820915951  0.5530341169
## [2756]  0.2721584095 -0.0859198283 -0.7666471931  1.6590171548  0.8599564216
## [2761] -0.5155272865 -0.1354907793  0.3388654755 -0.0808254299 -0.1938607963
## [2766]  0.1493008920  0.3561416277 -1.0280751885  1.5574656272  1.0578821733
## [2771]  0.6422801784  1.1367777502  0.2569328543  0.2105003841 -0.1876725942
## [2776]  1.2293617668  1.1031259136 -0.5545360304  1.5080310377 -0.2338256963
## [2781]  0.6648463987  1.2412515651  0.3159662846 -0.0853118696  0.0964541455
## [2786]  1.9730746068 -0.9308742686 -1.4980405653  0.0606546050 -0.0856779328
## [2791] -3.0063490654 -3.9601724068  0.9262484829 -0.2730852037 -2.2536388090
## [2796]  0.6953351404  0.6788305656  0.1344621477  0.7459178828  0.6989443090
## [2801]  0.0227327872 -0.3876861328 -0.3910438389  0.0739203978  1.3077431037
## [2806]  0.9158076088 -1.0150897780 -0.8845859057 -1.0816265282  0.4032729270
## [2811]  0.9336446643  0.2262665834 -0.0446916746  0.4431933678  1.8146433000
## [2816] -0.1158743651 -0.6251040119 -0.5860819780 -0.0834539606  0.1946746416
## [2821] -1.7448471876  0.1573096398 -0.2099508970 -3.0903918702 -1.7111906069
## [2826]  1.9151845728 -1.0607506667 -0.1770433692  0.8986988950 -1.5116164963
## [2831]  0.7729132141  0.7341930517  0.4539828756 -1.5700102732  0.2149175613
## [2836]  1.1579688487 -0.3787186681  0.6022022779 -0.2228904911  0.6714539381
## [2841]  0.9188513926  0.0727628313 -0.5425805620 -0.8518767801  0.0056756986
## [2846] -1.4615769194  0.1834805336  1.1126882062  0.1165600292 -0.9232005652
## [2851]  0.2865381685 -0.8654349592 -0.2719647043  1.6274776816  0.3923452019
## [2856] -0.0319058053  1.2348669867  1.1378284006  0.2016030764  0.1110815072
## [2861] -0.9185773342  0.5395318412 -0.1182334173 -0.3849791855  1.1208997702
## [2866] -0.4592386034  0.4920297511 -0.3172110069 -0.3848882097 -1.9615003153
## [2871]  1.7525033548 -0.8300006711  1.3123586988  0.5119933820  0.0842507259
## [2876]  1.0915596771 -0.0889837544  0.4138314145  0.1483063668  0.2555748059
## [2881] -0.6210596368  0.3876607817 -0.1657263637 -0.3618367009 -0.7070589822
## [2886]  0.3002862038 -1.1528968548  0.3178068214 -2.4402278143  0.2910087554
## [2891] -1.2042992790  0.8178353426  0.1014814192  0.4347026029 -0.7329458785
## [2896]  1.2831990385  1.1831690821  1.1760107800  0.4451016226 -0.9567167635
## [2901]  1.1587136403  0.1379944985 -0.1397728537  0.5703266053  0.3195556264
## [2906] -0.6131545505 -0.1498970247  0.3037087658  0.8181970734  1.5399154744
## [2911] -0.4593945135 -1.0308745795 -0.8772498942  0.7354291826 -0.1586435823
## [2916]  0.7861967069  0.7412436234  0.5678441121  0.4631975913 -0.0443133817
## [2921] -0.2540149008 -1.2990955224 -0.6734413229  1.0772524298 -1.2379771680
## [2926]  1.2017249016  0.4792897409  0.3632689500  0.3226008168 -0.0647344465
## [2931] -0.2878046541  1.0879654013  1.2841270203  0.0420766914  0.9325215797
## [2936] -0.7141081857  0.0217876764 -0.2807606884 -0.4931481399 -0.6555307114
## [2941] -0.3985509539  0.3491913899  0.7041798559  0.0668736887  1.0190564289
## [2946]  0.0509032700 -1.0665322790  0.9718302579  0.2198840815  1.4191958102
## [2951] -0.0605639386 -0.6047389760 -0.2270812455 -0.5933843929  0.5015430849
## [2956] -0.0012683857  0.6935343461 -0.0752524788  0.1389589426 -1.6434630312
## [2961] -0.9582971628 -0.0664838376 -0.2489188756 -6.0618868705 -1.5111627202
## [2966]  0.9440095864 -0.4009796590  1.5419290080 -0.0167700166 -1.0444685597
## [2971] -0.0259249010 -0.3352738525 -0.4612289186 -2.7784817678  1.1649681915
## [2976] -1.0806232922 -0.4038742000  1.0227784791  0.7104986322  0.7204623730
## [2981] -0.4522031148  0.4248714890  0.5064809106  1.8039038587 -0.1875055707
## [2986] -0.7451876923 -1.6596726532 -0.1105138290 -0.6127106518  0.8916901901
## [2991]  0.1906968877 -1.5518463755 -1.5413113575  0.2335417249 -0.5448166569
## [2996]  1.3471313725  0.2690077396  2.0163965473 -0.1614277051  0.6499466494
## [3001]  0.9085813421 -2.7821008470 -0.0917413347 -1.5437664413  0.1055289708
## [3006] -0.0232042633  0.3821320780 -0.0151459747 -1.5811562244 -1.5622627799
## [3011]  0.0058612581 -1.1423804010 -1.1481247347 -1.4727089831 -1.8046017138
## [3016]  2.7687891041  0.3493024653 -0.0549502781  0.4077303435  0.0656725059
## [3021] -1.4136590677  1.7887787267  0.3240682901  0.4835249201  0.2189142799
## [3026]  0.2616343688 -0.0091818117 -0.3594498217  0.7806710299  0.1676668130
## [3031]  0.6173895760  1.1208168727 -1.1976765605  0.1792843873  0.1208107417
## [3036]  0.8008576628 -0.7640351049 -0.1452197354  1.6505699562  0.8152797425
## [3041]  0.0873995364  0.7067843171  0.5071376041 -0.2524673716 -1.1345449384
## [3046]  0.0790910175  0.0885778619  1.7035594725  0.3514574399 -0.3270143213
## [3051]  1.4081504336  0.1801053668  0.2272638794 -0.4789771275  0.9020252519
## [3056]  0.1727810628 -0.1171244431 -0.0848621292 -0.4629856922  1.1564385193
## [3061] -0.6205851035 -0.1838491087 -1.1092665504 -1.3198509472 -0.3200117852
## [3066]  2.2805867651  0.3588211210  0.8894208006 -0.1116329319  0.6791048948
## [3071]  0.5164391080 -0.0188887968 -0.4503350378  1.7062137301 -2.6270775049
## [3076] -0.0838327378  0.7681954688 -0.5114450836  0.4129575837  0.8157585648
## [3081]  1.4158974340  0.0019873868  0.2614084873  0.2690240969  0.6316220687
## [3086]  0.1468252194 -0.9014184145  0.5098493911  0.0057849490  1.0517382123
## [3091] -0.0971679944  0.0825213565 -0.3858749784  0.2756164091  0.1825853936
## [3096]  1.6419478284 -0.3553537022 -0.0619413471  0.8183419634  0.1854264261
## [3101]  0.1708391129 -1.3991294817 -0.3577490988  1.6668980308 -0.6765132927
## [3106] -2.5539892021 -0.1814655316 -0.3647767361  0.4725194431 -3.2487083869
## [3111]  0.6842541098  0.5189310603  0.8331491412 -0.5616835334 -0.6818566360
## [3116]  0.8821629240 -0.2979839250 -1.3453652830  0.1426176911 -0.9501473812
## [3121] -0.7822913180  0.2411699105 -1.6264285695 -0.3019567568  2.4599813985
## [3126]  0.7134228043  0.5562501871  0.9986012947  0.4432369286 -0.0353531337
## [3131] -0.2214657525  0.4740262925 -0.1962717986  0.1204982088  1.3285911226
## [3136]  0.3826264883  1.2720305605 -0.1604802615 -0.2344118468 -1.3622016001
## [3141] -0.1634537937  0.5351725471  0.8327906387  1.1101209973  0.4095483224
## [3146]  1.1176807035 -0.2545184334 -0.7181436433  0.1854697864  0.7092859259
## [3151]  0.3631656548  0.7608265347  0.0290364001 -0.5882176800 -1.1459514000
## [3156]  0.5922075337 -1.0435908351  0.4586427860  1.1406857979  0.7436130318
## [3161] -0.8432120575  1.1685759317 -0.2441063917 -0.4082184871 -1.7913094384
## [3166] -1.2608219207 -0.9625333201 -3.9414667613  0.9540434763  0.0570481033
## [3171]  1.4984963543 -0.4930572204 -0.9775517547  1.1896675816 -2.2897953769
## [3176]  0.1494727856  0.9437717312  0.8023593864 -0.5461277284  0.5975581552
## [3181] -0.0387696117 -2.1801483054  0.7298409500 -0.2228524050  0.4895863928
## [3186]  1.0048111859  0.0512235612 -0.5970022768  0.9755335210  1.1712802107
## [3191]  0.0802112024 -0.0089380132  0.0329965052  0.7923952613  0.3225042739
## [3196] -0.0862876589 -0.3990042386  0.3441670036  0.0480732442  0.0029642834
## [3201] -0.7675111505 -0.0152179733 -1.3922551881  0.9252448946 -0.3618423475
## [3206] -0.8270695014  0.7792389964 -1.9150407842 -2.3414991394  0.7952145418
## [3211]  1.4458689882 -0.4254412124 -1.5775466027  0.8240905194  0.5942122338
## [3216]  1.0586745366 -0.1334259711  1.0237116503 -0.2050078183  0.3025509659
## [3221] -0.4579976610  0.8391868358 -0.4422742365  0.3689579391  0.2617637008
## [3226]  0.5844491856  0.8230137897 -0.1232892357  0.5062437376 -0.4856330691
## [3231]  1.5864448989  0.5394841608 -0.1785346800  0.1109718151  0.4514069515
## [3236]  0.4354142353 -0.3434438985  0.2815304987  0.1319263093  0.1601057149
## [3241]  1.5072421131  0.0875240355 -0.1071863310 -0.7042605123 -0.2949195841
## [3246]  0.4149442451  1.4519443669  0.3807423729  0.7438234692 -0.7143703516
## [3251] -1.5389932127 -1.0493621957  0.9613333996  0.2244825947  1.4284346157
## [3256] -0.4537965095 -0.1634148875  0.4545758057  1.3804373796  0.0107693191
## [3261]  1.1137187220  0.0502949894 -0.0682960181  0.7368123865  0.8190471396
## [3266]  0.1428002201 -0.0336372377  0.9162056825  0.0059374490 -1.0528595509
## [3271]  0.5111011224  1.4779172306 -1.1256996147  0.5361618117 -0.4389498969
## [3276]  0.7906913608  1.0710292853 -0.4447237530  1.1180546395 -0.2332777088
## [3281]  0.3009311515  1.3952109814  0.5895841286 -0.4157162837  0.0468529273
## [3286]  0.1934226302 -1.6013046339 -2.4547659983  1.1626413090 -0.0974416565
## [3291]  0.3761023528 -2.2651002432  0.7196206987  1.5274180679  1.0479373533
## [3296]  0.3080018870 -0.5372332753  0.7607802100  0.1803128487  0.7365528529
## [3301] -0.1912053547  0.2299078581 -0.3871307643  0.6519908845 -0.5436652091
## [3306] -1.5529117074 -4.4839867898 -2.0793927448 -0.2110243439 -2.7293745873
## [3311] -0.3608058088  2.1172451040 -1.0994838908  1.5831093557 -1.2061400979
## [3316] -0.5870753698 -2.8609137728  1.2288152556 -1.2432879863 -2.4089966672
## [3321]  1.6548272812 -2.1439073701  0.7988703486 -0.7580628954  0.0697923503
## [3326] -0.7201000720 -0.5060683071  1.6336737648  0.1890783490  1.0881908518
## [3331] -0.6137910218  0.6257010826 -0.3242436002 -0.9826138128  0.4973291058
## [3336] -0.3597864364  1.7331971914 -0.0363009739  0.8282239152  0.3676752774
## [3341] -0.2804736202  0.9026109477 -0.6830954963  0.1869092671  0.9278049968
## [3346] -0.6451549371 -1.1748445513  0.8389517215 -0.0205850638  0.5754533464
## [3351]  0.6452644552 -0.2446006573  1.3240037247 -0.4462354175 -1.4703751816
## [3356]  0.2038894299  0.4698271843 -0.3908210059  0.6856817500  1.0491681852
## [3361]  0.0083214095 -1.4074921774 -1.1239234002  0.7205383892  0.2566386076
## [3366]  2.1934762756 -0.6000036704  0.9927156640 -0.4719569891  0.1517107292
## [3371]  0.8544373453
hhat <- ts(ts.garch$fitted.values[-1,1]^2,start = c(2007,3),frequency = 365.25)
plot.ts(hhat)