GARCH summary methods
methods-summary.RdSummary methods for GARCH modelling.
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
Examples
## garchSim -
x = garchSim(n = 200)
## garchFit -
fit = garchFit(formula = x ~ garch(1, 1), data = x, trace = FALSE)
summary(fit)
#>
#> Title:
#> GARCH Modelling
#>
#> Call:
#> garchFit(formula = x ~ garch(1, 1), data = x, trace = FALSE)
#>
#> Mean and Variance Equation:
#> data ~ garch(1, 1)
#> <environment: 0x579d2b819af0>
#> [data = x]
#>
#> Conditional Distribution:
#> norm
#>
#> Coefficient(s):
#> mu omega alpha1 beta1
#> 2.5896e-04 4.1606e-07 1.1732e-01 8.2562e-01
#>
#> Std. Errors:
#> based on Hessian
#>
#> Error Analysis:
#> Estimate Std. Error t value Pr(>|t|)
#> mu 2.590e-04 1.723e-04 1.503 0.1328
#> omega 4.161e-07 3.378e-07 1.232 0.2181
#> alpha1 1.173e-01 5.679e-02 2.066 0.0388 *
#> beta1 8.256e-01 7.644e-02 10.801 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Log Likelihood:
#> 904.4709 normalized: 4.522355
#>
#> Description:
#> Tue Mar 26 17:45:27 2024 by user: georgi
#>
#>
#> Standardised Residuals Tests:
#> Statistic p-Value
#> Jarque-Bera Test R Chi^2 0.2185727 0.8964737
#> Shapiro-Wilk Test R W 0.9979898 0.9972060
#> Ljung-Box Test R Q(10) 2.0947412 0.9955611
#> Ljung-Box Test R Q(15) 7.7722072 0.9325900
#> Ljung-Box Test R Q(20) 18.3001001 0.5676465
#> Ljung-Box Test R^2 Q(10) 9.3682085 0.4975518
#> Ljung-Box Test R^2 Q(15) 15.0351706 0.4488868
#> Ljung-Box Test R^2 Q(20) 18.6478352 0.5448116
#> LM Arch Test R TR^2 13.1763335 0.3563554
#>
#> Information Criterion Statistics:
#> AIC BIC SIC HQIC
#> -9.004709 -8.938743 -9.005489 -8.978014
#>