methods-summary: GARCH Summary Methods

Description Methods How to read a diagnostic summary report? Author(s) Examples

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)

Example output

Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fBasics


Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org

Title:
 GARCH Modelling 

Call:
 garchFit(formula = x ~ garch(1, 1), data = x, trace = FALSE) 

Mean and Variance Equation:
 data ~ garch(1, 1)
<environment: 0x1c5e458>
 [data = x]

Conditional Distribution:
 norm 

Coefficient(s):
         mu        omega       alpha1        beta1  
-6.4040e-05   1.2383e-11   8.8709e-04   1.0000e+00  

Std. Errors:
 based on Hessian 

Error Analysis:
         Estimate  Std. Error  t value Pr(>|t|)    
mu     -6.404e-05   2.473e-04   -0.259    0.796    
omega   1.238e-11   1.389e-07    0.000    1.000    
alpha1  8.871e-04   1.394e-02    0.064    0.949    
beta1   1.000e+00   6.466e-03  154.655   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Log Likelihood:
 847.0734    normalized:  4.235367 

Description:
 Tue Jul  4 05:44:55 2017 by user: anon 


Standardised Residuals Tests:
                                Statistic p-Value  
 Jarque-Bera Test   R    Chi^2  1.712507  0.4247504
 Shapiro-Wilk Test  R    W      0.9917929 0.320692 
 Ljung-Box Test     R    Q(10)  7.711915  0.6569533
 Ljung-Box Test     R    Q(15)  17.65768  0.2810895
 Ljung-Box Test     R    Q(20)  24.6037   0.2170152
 Ljung-Box Test     R^2  Q(10)  4.991155  0.8917681
 Ljung-Box Test     R^2  Q(15)  10.18916  0.8076755
 Ljung-Box Test     R^2  Q(20)  11.26092  0.9391733
 LM Arch Test       R    TR^2   6.153837  0.9081293

Information Criterion Statistics:
      AIC       BIC       SIC      HQIC 
-8.430734 -8.364768 -8.431514 -8.404039 

fGarch documentation built on May 31, 2017, 4:02 a.m.