GARCH Summary Methods

Description

Summary methods for GARCH Modelling.

Methods

object = "ANY"

Generic function

object = "fGARCH"

Summary function for objects of class "fGARCH".

How to read a diagnostic summary report?

The first five sections return the title, the call, the mean and variance formula, the conditional distribution and the type of standard errors:

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        Title:
         GARCH Modelling 
        
        Call:
         garchFit(~ garch(1, 1), data = garchSim(), trace = FALSE) 
        
        Mean and Variance Equation:
         ~arch(0)
        
        Conditional Distribution:
         norm 
        
        Std. Errors:
         based on Hessian
        

The next three sections return the estimated coefficients, and an error analysis including standard errors, t values, and probabilities, as well as the log Likelihood values from optimization:

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        Coefficient(s):
                  mu         omega        alpha1         beta1  
        -5.79788e-05   7.93017e-06   1.59456e-01   2.30772e-01  
        
        Error Analysis:
                 Estimate  Std. Error  t value Pr(>|t|)
        mu     -5.798e-05   2.582e-04   -0.225    0.822
        omega   7.930e-06   5.309e-06    1.494    0.135
        alpha1  1.595e-01   1.026e-01    1.554    0.120
        beta1   2.308e-01   4.203e-01    0.549    0.583
        
        Log Likelihood:
         -843.3991    normalized:  -Inf 
        

The next section provides results on standardized residuals tests, including statistic and p values, and on information criterion statistic including AIC, BIC, SIC, and HQIC:

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        Standardized Residuals Tests:
                                        Statistic p-Value    
         Jarque-Bera Test   R    Chi^2  0.4172129 0.8117146  
         Shapiro-Wilk Test  R    W      0.9957817 0.8566985  
         Ljung-Box Test     R    Q(10)  13.05581  0.2205680  
         Ljung-Box Test     R    Q(15)  14.40879  0.4947788  
         Ljung-Box Test     R    Q(20)  38.15456  0.008478302
         Ljung-Box Test     R^2  Q(10)  7.619134  0.6659837  
         Ljung-Box Test     R^2  Q(15)  13.89721  0.5333388  
         Ljung-Box Test     R^2  Q(20)  15.61716  0.7400728  
         LM Arch Test       R    TR^2   7.049963  0.8542942  
         
        Information Criterion Statistics:
                 AIC      BIC      SIC     HQIC 
            8.473991 8.539957 8.473212 8.500687  
        

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

Examples

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## garchSim -
   x = garchSim(n = 200)

## garchFit - 
   fit = garchFit(formula = x ~ garch(1, 1), data = x, trace = FALSE)
   summary(fit)

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