I have a question about the prediction of volatility and returns of a time series. Basically it is a question about predictionpredict in the fGarchpackage.

library(fGarch)
sp5=read.table("http://faculty.chicagobooth.edu/ruey.tsay/teaching/fts/sp500.dat")% Load#Load data
plot(sp5,type="l")
m1=garchFit(formula=~arma(3,0)+garch(1,1),data=sp5,trace=F)
summary(m1)
m2=garchFit(formula=~garch(1,1),data=sp5,trace=F,cond.dist="std")
summary(m2)
stresi=residuals(m2,standardize=T)
plot(stresi,type="l")
Box.test(stresi,10,type="Ljung")
predict(m2,5)

I have a question about the prediction of volatility and returns of a time series. Basically it is a question about prediction in the fGarchpackage.

library(fGarch)
sp5=read.table("http://faculty.chicagobooth.edu/ruey.tsay/teaching/fts/sp500.dat")% Load data
plot(sp5,type="l")
m1=garchFit(formula=~arma(3,0)+garch(1,1),data=sp5,trace=F)
summary(m1)
m2=garchFit(formula=~garch(1,1),data=sp5,trace=F,cond.dist="std")
summary(m2)
stresi=residuals(m2,standardize=T)
plot(stresi,type="l")
Box.test(stresi,10,type="Ljung")
predict(m2,5)

I have a question about the prediction of volatility and returns of a time series. Basically it is a question about predict in the fGarchpackage.

library(fGarch)
sp5=read.table("http://faculty.chicagobooth.edu/ruey.tsay/teaching/fts/sp500.dat")#Load data
plot(sp5,type="l")
m1=garchFit(formula=~arma(3,0)+garch(1,1),data=sp5,trace=F)
summary(m1)
m2=garchFit(formula=~garch(1,1),data=sp5,trace=F,cond.dist="std")
summary(m2)
stresi=residuals(m2,standardize=T)
plot(stresi,type="l")
Box.test(stresi,10,type="Ljung")
predict(m2,5)
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> summary(m1)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~arma(3, 0) + garch(1, 1), data = sp5, trace = F) 

Mean and Variance Equation:
 data ~ arma(3, 0) + garch(1, 1)
<environment: 0x6ac79b0>
 [data = sp5]

Conditional Distribution:
 norm 

Coefficient(s):
         mu          ar1          ar2          ar3        omega  
 7.7077e-03   3.1968e-02  -3.0261e-02  -1.0649e-02   7.9746e-05  
     alpha1        beta1  
 1.2425e-01   8.5302e-01  

Std. Errors:
 based on Hessian 

Error Analysis:
         Estimate  Std. Error  t value Pr(>|t|)    
mu      7.708e-03   1.607e-03    4.798 1.61e-06 ***
ar1     3.197e-02   3.837e-02    0.833  0.40473    
ar2    -3.026e-02   3.841e-02   -0.788  0.43076    
ar3    -1.065e-02   3.756e-02   -0.284  0.77677    
omega   7.975e-05   2.810e-05    2.838  0.00454 ** 
alpha1  1.242e-01   2.247e-02    5.529 3.22e-08 ***
beta1   8.530e-01   2.183e-02   39.075  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1272.179    normalized:  1.606287 

Description:
 Wed Apr 23 18:07:32 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value     
 Jarque-Bera Test   R    Chi^2  73.04843  1.110223e-16
 Shapiro-Wilk Test  R    W      0.9857968 5.961505e-07
 Ljung-Box Test     R    Q(10)  11.56744  0.3150483   
 Ljung-Box Test     R    Q(15)  17.78746  0.2740041   
 Ljung-Box Test     R    Q(20)  24.11916  0.2372259   
 Ljung-Box Test     R^2  Q(10)  10.31614  0.4132084   
 Ljung-Box Test     R^2  Q(15)  14.22819  0.5082978   
 Ljung-Box Test     R^2  Q(20)  16.79404  0.6663039   
 LM Arch Test       R    TR^2   13.34305  0.3446074   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.194897 -3.153581 -3.195051 -3.179018 

> 
> summary(m2)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = sp5, cond.dist = "std", 
    trace = F) 

Mean and Variance Equation:
 data ~ garch(1, 1)
<environment: 0x6b70f70>
 [data = sp5]

Conditional Distribution:
 std 

Coefficient(s):
        mu       omega      alpha1       beta1       shape  
0.00845504  0.00012485  0.11302582  0.84220210  7.00318063  

Std. Errors:
 based on Hessian 

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu     8.455e-03   1.515e-03    5.581 2.39e-08 ***
omega  1.248e-04   4.519e-05    2.763  0.00573 ** 
alpha1 1.130e-01   2.693e-02    4.198 2.70e-05 ***
beta1  8.422e-01   3.186e-02   26.432  < 2e-16 ***
shape  7.003e+00   1.680e+00    4.169 3.06e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1283.417    normalized:  1.620476 

Description:
 Wed Apr 23 18:09:17 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value    
 Jarque-Bera Test   R    Chi^2  99.61249  0          
 Shapiro-Wilk Test  R    W      0.9836345 9.72802e-08
 Ljung-Box Test     R    Q(10)  11.37961  0.3287173  
 Ljung-Box Test     R    Q(15)  18.2163   0.2514649  
 Ljung-Box Test     R    Q(20)  24.91842  0.2045699  
 Ljung-Box Test     R^2  Q(10)  10.52266  0.3958941  
 Ljung-Box Test     R^2  Q(15)  16.14586  0.3724248  
 Ljung-Box Test     R^2  Q(20)  18.93325  0.5261686  
 LM Arch Test       R    TR^2   14.88667  0.247693   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.228325 -3.198814 -3.228404 -3.216983 

> 
> summary(m1)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~arma(3, 0) + garch(1, 1), data = sp5, trace = F) 

Mean and Variance Equation:
 data ~ arma(3, 0) + garch(1, 1)
<environment: 0x6ac79b0>
 [data = sp5]

Conditional Distribution:
 norm 

Coefficient(s):
         mu          ar1          ar2          ar3        omega  
 7.7077e-03   3.1968e-02  -3.0261e-02  -1.0649e-02   7.9746e-05  
     alpha1        beta1  
 1.2425e-01   8.5302e-01  

Std. Errors:
 based on Hessian 

Error Analysis:
         Estimate  Std. Error  t value Pr(>|t|)    
mu      7.708e-03   1.607e-03    4.798 1.61e-06 ***
ar1     3.197e-02   3.837e-02    0.833  0.40473    
ar2    -3.026e-02   3.841e-02   -0.788  0.43076    
ar3    -1.065e-02   3.756e-02   -0.284  0.77677    
omega   7.975e-05   2.810e-05    2.838  0.00454 ** 
alpha1  1.242e-01   2.247e-02    5.529 3.22e-08 ***
beta1   8.530e-01   2.183e-02   39.075  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1272.179    normalized:  1.606287 

Description:
 Wed Apr 23 18:07:32 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value     
 Jarque-Bera Test   R    Chi^2  73.04843  1.110223e-16
 Shapiro-Wilk Test  R    W      0.9857968 5.961505e-07
 Ljung-Box Test     R    Q(10)  11.56744  0.3150483   
 Ljung-Box Test     R    Q(15)  17.78746  0.2740041   
 Ljung-Box Test     R    Q(20)  24.11916  0.2372259   
 Ljung-Box Test     R^2  Q(10)  10.31614  0.4132084   
 Ljung-Box Test     R^2  Q(15)  14.22819  0.5082978   
 Ljung-Box Test     R^2  Q(20)  16.79404  0.6663039   
 LM Arch Test       R    TR^2   13.34305  0.3446074   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.194897 -3.153581 -3.195051 -3.179018 

> 
> summary(m2)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = sp5, cond.dist = "std", 
    trace = F) 

Mean and Variance Equation:
 data ~ garch(1, 1)
<environment: 0x6b70f70>
 [data = sp5]

Conditional Distribution:
 std 

Coefficient(s):
        mu       omega      alpha1       beta1       shape  
0.00845504  0.00012485  0.11302582  0.84220210  7.00318063  

Std. Errors:
 based on Hessian 

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu     8.455e-03   1.515e-03    5.581 2.39e-08 ***
omega  1.248e-04   4.519e-05    2.763  0.00573 ** 
alpha1 1.130e-01   2.693e-02    4.198 2.70e-05 ***
beta1  8.422e-01   3.186e-02   26.432  < 2e-16 ***
shape  7.003e+00   1.680e+00    4.169 3.06e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1283.417    normalized:  1.620476 

Description:
 Wed Apr 23 18:09:17 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value    
 Jarque-Bera Test   R    Chi^2  99.61249  0          
 Shapiro-Wilk Test  R    W      0.9836345 9.72802e-08
 Ljung-Box Test     R    Q(10)  11.37961  0.3287173  
 Ljung-Box Test     R    Q(15)  18.2163   0.2514649  
 Ljung-Box Test     R    Q(20)  24.91842  0.2045699  
 Ljung-Box Test     R^2  Q(10)  10.52266  0.3958941  
 Ljung-Box Test     R^2  Q(15)  16.14586  0.3724248  
 Ljung-Box Test     R^2  Q(20)  18.93325  0.5261686  
 LM Arch Test       R    TR^2   14.88667  0.247693   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.228325 -3.198814 -3.228404 -3.216983 

> 
> summary(m1)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~arma(3, 0) + garch(1, 1), data = sp5, trace = F) 

Mean and Variance Equation:
 data ~ arma(3, 0) + garch(1, 1)
<environment: 0x6ac79b0>
 [data = sp5]

Conditional Distribution:
 norm 

Coefficient(s):
         mu          ar1          ar2          ar3        omega  
 7.7077e-03   3.1968e-02  -3.0261e-02  -1.0649e-02   7.9746e-05  
     alpha1        beta1  
 1.2425e-01   8.5302e-01  

Std. Errors:
 based on Hessian 

Error Analysis:
         Estimate  Std. Error  t value Pr(>|t|)    
mu      7.708e-03   1.607e-03    4.798 1.61e-06 ***
ar1     3.197e-02   3.837e-02    0.833  0.40473    
ar2    -3.026e-02   3.841e-02   -0.788  0.43076    
ar3    -1.065e-02   3.756e-02   -0.284  0.77677    
omega   7.975e-05   2.810e-05    2.838  0.00454 ** 
alpha1  1.242e-01   2.247e-02    5.529 3.22e-08 ***
beta1   8.530e-01   2.183e-02   39.075  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1272.179    normalized:  1.606287 

Description:
 Wed Apr 23 18:07:32 2014 by user:  


Standardised Residuals Tests:
                                Statistic p-Value     
 Jarque-Bera Test   R    Chi^2  73.04843  1.110223e-16
 Shapiro-Wilk Test  R    W      0.9857968 5.961505e-07
 Ljung-Box Test     R    Q(10)  11.56744  0.3150483   
 Ljung-Box Test     R    Q(15)  17.78746  0.2740041   
 Ljung-Box Test     R    Q(20)  24.11916  0.2372259   
 Ljung-Box Test     R^2  Q(10)  10.31614  0.4132084   
 Ljung-Box Test     R^2  Q(15)  14.22819  0.5082978   
 Ljung-Box Test     R^2  Q(20)  16.79404  0.6663039   
 LM Arch Test       R    TR^2   13.34305  0.3446074   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.194897 -3.153581 -3.195051 -3.179018 

> 
> summary(m2)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = sp5, cond.dist = "std", 
    trace = F) 

Mean and Variance Equation:
 data ~ garch(1, 1)
<environment: 0x6b70f70>
 [data = sp5]

Conditional Distribution:
 std 

Coefficient(s):
        mu       omega      alpha1       beta1       shape  
0.00845504  0.00012485  0.11302582  0.84220210  7.00318063  

Std. Errors:
 based on Hessian 

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu     8.455e-03   1.515e-03    5.581 2.39e-08 ***
omega  1.248e-04   4.519e-05    2.763  0.00573 ** 
alpha1 1.130e-01   2.693e-02    4.198 2.70e-05 ***
beta1  8.422e-01   3.186e-02   26.432  < 2e-16 ***
shape  7.003e+00   1.680e+00    4.169 3.06e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1283.417    normalized:  1.620476 

Description:
 Wed Apr 23 18:09:17 2014 by user:  


Standardised Residuals Tests:
                                Statistic p-Value    
 Jarque-Bera Test   R    Chi^2  99.61249  0          
 Shapiro-Wilk Test  R    W      0.9836345 9.72802e-08
 Ljung-Box Test     R    Q(10)  11.37961  0.3287173  
 Ljung-Box Test     R    Q(15)  18.2163   0.2514649  
 Ljung-Box Test     R    Q(20)  24.91842  0.2045699  
 Ljung-Box Test     R^2  Q(10)  10.52266  0.3958941  
 Ljung-Box Test     R^2  Q(15)  16.14586  0.3724248  
 Ljung-Box Test     R^2  Q(20)  18.93325  0.5261686  
 LM Arch Test       R    TR^2   14.88667  0.247693   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.228325 -3.198814 -3.228404 -3.216983 

> 
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Edit: as asked by user12348 here are my outputs of summary(m1) and summary(m2).

> summary(m1)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~arma(3, 0) + garch(1, 1), data = sp5, trace = F) 

Mean and Variance Equation:
 data ~ arma(3, 0) + garch(1, 1)
<environment: 0x6ac79b0>
 [data = sp5]

Conditional Distribution:
 norm 

Coefficient(s):
         mu          ar1          ar2          ar3        omega  
 7.7077e-03   3.1968e-02  -3.0261e-02  -1.0649e-02   7.9746e-05  
     alpha1        beta1  
 1.2425e-01   8.5302e-01  

Std. Errors:
 based on Hessian 

Error Analysis:
         Estimate  Std. Error  t value Pr(>|t|)    
mu      7.708e-03   1.607e-03    4.798 1.61e-06 ***
ar1     3.197e-02   3.837e-02    0.833  0.40473    
ar2    -3.026e-02   3.841e-02   -0.788  0.43076    
ar3    -1.065e-02   3.756e-02   -0.284  0.77677    
omega   7.975e-05   2.810e-05    2.838  0.00454 ** 
alpha1  1.242e-01   2.247e-02    5.529 3.22e-08 ***
beta1   8.530e-01   2.183e-02   39.075  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1272.179    normalized:  1.606287 

Description:
 Wed Apr 23 18:07:32 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value     
 Jarque-Bera Test   R    Chi^2  73.04843  1.110223e-16
 Shapiro-Wilk Test  R    W      0.9857968 5.961505e-07
 Ljung-Box Test     R    Q(10)  11.56744  0.3150483   
 Ljung-Box Test     R    Q(15)  17.78746  0.2740041   
 Ljung-Box Test     R    Q(20)  24.11916  0.2372259   
 Ljung-Box Test     R^2  Q(10)  10.31614  0.4132084   
 Ljung-Box Test     R^2  Q(15)  14.22819  0.5082978   
 Ljung-Box Test     R^2  Q(20)  16.79404  0.6663039   
 LM Arch Test       R    TR^2   13.34305  0.3446074   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.194897 -3.153581 -3.195051 -3.179018 

> 

and for summary(m2):

> summary(m2)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = sp5, cond.dist = "std", 
    trace = F) 

Mean and Variance Equation:
 data ~ garch(1, 1)
<environment: 0x6b70f70>
 [data = sp5]

Conditional Distribution:
 std 

Coefficient(s):
        mu       omega      alpha1       beta1       shape  
0.00845504  0.00012485  0.11302582  0.84220210  7.00318063  

Std. Errors:
 based on Hessian 

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu     8.455e-03   1.515e-03    5.581 2.39e-08 ***
omega  1.248e-04   4.519e-05    2.763  0.00573 ** 
alpha1 1.130e-01   2.693e-02    4.198 2.70e-05 ***
beta1  8.422e-01   3.186e-02   26.432  < 2e-16 ***
shape  7.003e+00   1.680e+00    4.169 3.06e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1283.417    normalized:  1.620476 

Description:
 Wed Apr 23 18:09:17 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value    
 Jarque-Bera Test   R    Chi^2  99.61249  0          
 Shapiro-Wilk Test  R    W      0.9836345 9.72802e-08
 Ljung-Box Test     R    Q(10)  11.37961  0.3287173  
 Ljung-Box Test     R    Q(15)  18.2163   0.2514649  
 Ljung-Box Test     R    Q(20)  24.91842  0.2045699  
 Ljung-Box Test     R^2  Q(10)  10.52266  0.3958941  
 Ljung-Box Test     R^2  Q(15)  16.14586  0.3724248  
 Ljung-Box Test     R^2  Q(20)  18.93325  0.5261686  
 LM Arch Test       R    TR^2   14.88667  0.247693   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.228325 -3.198814 -3.228404 -3.216983 

> 

Edit: as asked by user12348 here are my outputs of summary(m1) and summary(m2).

> summary(m1)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~arma(3, 0) + garch(1, 1), data = sp5, trace = F) 

Mean and Variance Equation:
 data ~ arma(3, 0) + garch(1, 1)
<environment: 0x6ac79b0>
 [data = sp5]

Conditional Distribution:
 norm 

Coefficient(s):
         mu          ar1          ar2          ar3        omega  
 7.7077e-03   3.1968e-02  -3.0261e-02  -1.0649e-02   7.9746e-05  
     alpha1        beta1  
 1.2425e-01   8.5302e-01  

Std. Errors:
 based on Hessian 

Error Analysis:
         Estimate  Std. Error  t value Pr(>|t|)    
mu      7.708e-03   1.607e-03    4.798 1.61e-06 ***
ar1     3.197e-02   3.837e-02    0.833  0.40473    
ar2    -3.026e-02   3.841e-02   -0.788  0.43076    
ar3    -1.065e-02   3.756e-02   -0.284  0.77677    
omega   7.975e-05   2.810e-05    2.838  0.00454 ** 
alpha1  1.242e-01   2.247e-02    5.529 3.22e-08 ***
beta1   8.530e-01   2.183e-02   39.075  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1272.179    normalized:  1.606287 

Description:
 Wed Apr 23 18:07:32 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value     
 Jarque-Bera Test   R    Chi^2  73.04843  1.110223e-16
 Shapiro-Wilk Test  R    W      0.9857968 5.961505e-07
 Ljung-Box Test     R    Q(10)  11.56744  0.3150483   
 Ljung-Box Test     R    Q(15)  17.78746  0.2740041   
 Ljung-Box Test     R    Q(20)  24.11916  0.2372259   
 Ljung-Box Test     R^2  Q(10)  10.31614  0.4132084   
 Ljung-Box Test     R^2  Q(15)  14.22819  0.5082978   
 Ljung-Box Test     R^2  Q(20)  16.79404  0.6663039   
 LM Arch Test       R    TR^2   13.34305  0.3446074   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.194897 -3.153581 -3.195051 -3.179018 

> 

and for summary(m2):

> summary(m2)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = sp5, cond.dist = "std", 
    trace = F) 

Mean and Variance Equation:
 data ~ garch(1, 1)
<environment: 0x6b70f70>
 [data = sp5]

Conditional Distribution:
 std 

Coefficient(s):
        mu       omega      alpha1       beta1       shape  
0.00845504  0.00012485  0.11302582  0.84220210  7.00318063  

Std. Errors:
 based on Hessian 

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu     8.455e-03   1.515e-03    5.581 2.39e-08 ***
omega  1.248e-04   4.519e-05    2.763  0.00573 ** 
alpha1 1.130e-01   2.693e-02    4.198 2.70e-05 ***
beta1  8.422e-01   3.186e-02   26.432  < 2e-16 ***
shape  7.003e+00   1.680e+00    4.169 3.06e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Log Likelihood:
 1283.417    normalized:  1.620476 

Description:
 Wed Apr 23 18:09:17 2014 by user: nicolas 


Standardised Residuals Tests:
                                Statistic p-Value    
 Jarque-Bera Test   R    Chi^2  99.61249  0          
 Shapiro-Wilk Test  R    W      0.9836345 9.72802e-08
 Ljung-Box Test     R    Q(10)  11.37961  0.3287173  
 Ljung-Box Test     R    Q(15)  18.2163   0.2514649  
 Ljung-Box Test     R    Q(20)  24.91842  0.2045699  
 Ljung-Box Test     R^2  Q(10)  10.52266  0.3958941  
 Ljung-Box Test     R^2  Q(15)  16.14586  0.3724248  
 Ljung-Box Test     R^2  Q(20)  18.93325  0.5261686  
 LM Arch Test       R    TR^2   14.88667  0.247693   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-3.228325 -3.198814 -3.228404 -3.216983 

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