methods-summary function

GARCH summary methods

Summary methods for GARCH modelling. methods

Methods

Methods for summary defined in package fGarch:

• 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:

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:

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:

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 -port

Examples

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

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