> summary(model.norm.hess)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = garch.norm, cond.dist = "norm", 
    algorithm = "nlminb", hessian = "rcd") 

Mean and Variance Equation:
 data ~ garch(1, 1)
attr(,"data")
[1] "data = garch.norm"

Conditional Distribution:
 norm 

Std. Errors:
 based on Hessian 

Coefficient(s):
       mu      omega     alpha1      beta1  
0.0820133  0.0137951  0.1932767  0.7488804  

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu      0.082013    0.008522    9.623  < 2e-16 ***
omega   0.013795    0.002636    5.234 1.66e-07 ***
alpha1  0.193277    0.022764    8.490  < 2e-16 ***
beta1   0.748880    0.026187   28.597  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Log Likelihood:
 -1167.435    normalized:  -0.5837177 

Standardised Residuals Tests:
                                Statistic p-Value  
 Jarque-Bera Test   R    Chi^2  0.4136367 0.8131673
 Shapiro-Wilk Test  R    W      0.998991  0.3239691
 Ljung-Box Test     R    Q(10)  4.565478  0.9182542
 Ljung-Box Test     R    Q(15)  12.96707  0.6048416
 Ljung-Box Test     R    Q(20)  19.32582  0.5007468
 Ljung-Box Test     R^2  Q(10)  7.850587  0.6434287
 Ljung-Box Test     R^2  Q(15)  16.80986  0.3303575
 Ljung-Box Test     R^2  Q(20)  21.66473  0.358977 
 LM Arch Test       R    TR^2   11.62679  0.4760989

Information Criterion Statistics:
     AIC      BIC      SIC     HQIC 
1.171435 1.182637 1.171427 1.175548 





> summary(model.norm.QMLE)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = garch.norm, cond.dist = "QMLE", 
    algorithm = "nlminb", hessian = "rcd") 

Mean and Variance Equation:
 data ~ garch(1, 1)
attr(,"data")
[1] "data = garch.norm"

Conditional Distribution:
 norm 

Std. Errors:
 robust 

Coefficient(s):
       mu      omega     alpha1      beta1  
0.0820133  0.0137951  0.1932767  0.7488804  

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu      0.082013    0.008350    9.822  < 2e-16 ***
omega   0.013795    0.002648    5.209 1.90e-07 ***
alpha1  0.193277    0.022441    8.613  < 2e-16 ***
beta1   0.748880    0.025499   29.369  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Log Likelihood:
 -1167.435    normalized:  -0.5837177 

Standardised Residuals Tests:
                                Statistic p-Value  
 Jarque-Bera Test   R    Chi^2  0.4136367 0.8131673
 Shapiro-Wilk Test  R    W      0.998991  0.3239691
 Ljung-Box Test     R    Q(10)  4.565478  0.9182542
 Ljung-Box Test     R    Q(15)  12.96707  0.6048416
 Ljung-Box Test     R    Q(20)  19.32582  0.5007468
 Ljung-Box Test     R^2  Q(10)  7.850587  0.6434287
 Ljung-Box Test     R^2  Q(15)  16.80986  0.3303575
 Ljung-Box Test     R^2  Q(20)  21.66473  0.358977 
 LM Arch Test       R    TR^2   11.62679  0.4760989

Information Criterion Statistics:
     AIC      BIC      SIC     HQIC 
1.171435 1.182637 1.171427 1.175548 





> summary(model.std.hess)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = garch.std, cond.dist = "norm", 
    algorithm = "nlminb", hessian = "rcd") 

Mean and Variance Equation:
 data ~ garch(1, 1)
attr(,"data")
[1] "data = garch.std"

Conditional Distribution:
 norm 

Std. Errors:
 based on Hessian 

Coefficient(s):
       mu      omega     alpha1      beta1  
0.1066741  0.0212663  0.1747046  0.6817867  

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu      0.106674    0.007626   13.989  < 2e-16 ***
omega   0.021266    0.004239    5.017 5.26e-07 ***
alpha1  0.174705    0.024307    7.188 6.60e-13 ***
beta1   0.681787    0.043675   15.610  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Log Likelihood:
 -830.0553    normalized:  -0.4150277 

Standardised Residuals Tests:
                                Statistic p-Value     
 Jarque-Bera Test   R    Chi^2  21.01067  2.738996e-05
 Shapiro-Wilk Test  R    W      0.9970963 0.000828843 
 Ljung-Box Test     R    Q(10)  18.41096  0.04841452  
 Ljung-Box Test     R    Q(15)  22.05674  0.1063247   
 Ljung-Box Test     R    Q(20)  24.64892  0.2151941   
 Ljung-Box Test     R^2  Q(10)  7.265089  0.7002043   
 Ljung-Box Test     R^2  Q(15)  11.75582  0.6974099   
 Ljung-Box Test     R^2  Q(20)  20.24481  0.4427123   
 LM Arch Test       R    TR^2   8.543588  0.7413401   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
0.8340553 0.8452571 0.8340473 0.8381684 





> summary(model.std.QMLE)

Title:
 GARCH Modelling 

Call:
 garchFit(formula = ~garch(1, 1), data = garch.std, cond.dist = "QMLE", 
    algorithm = "nlminb", hessian = "rcd") 

Mean and Variance Equation:
 data ~ garch(1, 1)
attr(,"data")
[1] "data = garch.std"

Conditional Distribution:
 norm 

Std. Errors:
 robust 

Coefficient(s):
       mu      omega     alpha1      beta1  
0.1066741  0.0212663  0.1747046  0.6817867  

Error Analysis:
        Estimate  Std. Error  t value Pr(>|t|)    
mu      0.106674    0.007883   13.533  < 2e-16 ***
omega   0.021266    0.004570    4.653 3.27e-06 ***
alpha1  0.174705    0.026125    6.687 2.27e-11 ***
beta1   0.681787    0.046325   14.718  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Log Likelihood:
 -830.0553    normalized:  -0.4150277 

Standardised Residuals Tests:
                                Statistic p-Value     
 Jarque-Bera Test   R    Chi^2  21.01067  2.738996e-05
 Shapiro-Wilk Test  R    W      0.9970963 0.000828843 
 Ljung-Box Test     R    Q(10)  18.41096  0.04841452  
 Ljung-Box Test     R    Q(15)  22.05674  0.1063247   
 Ljung-Box Test     R    Q(20)  24.64892  0.2151941   
 Ljung-Box Test     R^2  Q(10)  7.265089  0.7002043   
 Ljung-Box Test     R^2  Q(15)  11.75582  0.6974099   
 Ljung-Box Test     R^2  Q(20)  20.24481  0.4427123   
 LM Arch Test       R    TR^2   8.543588  0.7413401   

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
0.8340553 0.8452571 0.8340473 0.8381684