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Class "fGARCH" - fitted ARMA-GARCH/APARCH models

class-fGARCH.Rd

Class 'fGARCH' represents models fitted to heteroskedastic time series, including ARCH, GARCH, APARCH, ARMA-GARCH and ARMA-APARCH models.

Objects from the Class

Objects from class "fGARCH" can be created by calls of the function garchFit.

Slots

call:

Object of class "call", the call used to fit the model and create the object.

formula:

Object of class "formula", a formula object representing the mean and variance equations.

method:

Object of class "character", a string denoting the optimization method, by default "Max Log-Likelihood Estimation".

data:

Object of class "list", a list with one entry, x, containing the data of the time series to which the model is fitted.

fit:

Object of class "list", a list with the results from the parameter estimation. The entries of the list depend on the selected algorithm, see below.

residuals:

Object of class "numeric", the raw, unstandardized residuals.

fitted:

Object of class "numeric", the fitted values.

h.t:

Object of class "numeric", the conditional variances (\(h_t = \sigma_t^\delta\)).

sigma.t:

Object of class "numeric", the conditional standard deviations.

title:

Object of class "character", a title string.

description:

Object of class "character", a string with a brief description.

Methods

Besides the S4 methods described below, the are "fGARCH" methods (S3) for tsdiag (tsdiag), VaR (VaR), expected shortfall (ES), volatility (volatility), and maybe others.

plot

signature(x = "fGARCH", y = "missing"): plots an object of class "fGARCH", see the help page of the method for details and options.

show

signature(object = "fGARCH"): prints the object.

summary

signature(object = "fGARCH"): summarizes the object. The help page of the "fGARCH" method gives details on the output, as well as interpretation of the results.

predict

signature(object = "fGARCH"): Computes forecasts of the mean and some measures of risk (such as volatility, value-at-risk and expected shortfall), see the method's help page for full details.

fitted

signature(object = "fGARCH"): extracts fitted values from the object (help page).

residuals

signature(object = "fGARCH"): returns residuals from the fitted model (help page).

coef

signature(object = "fGARCH"): extracts the estimated coefficients (help page).

formula

signature(x = "fGARCH"): extracts the formula expression, see the method's help page.

update

signature(object = "fGARCH"): ...

Author

Diethelm Wuertz and Rmetrics Core Team

See also

garchFit, garchSpec, garchFitControl

Examples

## simulate a time series, fit a GARCH(1,1) model, and show it:
x <- garchSim( garchSpec(), n = 500)
fit <- garchFit(~ garch(1, 1), data = x, trace = FALSE)
coef(fit)
#>            mu         omega        alpha1         beta1 
#> -1.311144e-04  1.288087e-06  8.792572e-02  7.803781e-01 
summary(fit)
#> 
#> Title:
#>  GARCH Modelling 
#> 
#> Call:
#>  garchFit(formula = ~garch(1, 1), data = x, trace = FALSE) 
#> 
#> Mean and Variance Equation:
#>  data ~ garch(1, 1)
#> <environment: 0x5c825a8a7d58>
#>  [data = x]
#> 
#> Conditional Distribution:
#>  norm 
#> 
#> Coefficient(s):
#>          mu        omega       alpha1        beta1  
#> -1.3111e-04   1.2881e-06   8.7926e-02   7.8038e-01  
#> 
#> Std. Errors:
#>  based on Hessian 
#> 
#> Error Analysis:
#>          Estimate  Std. Error  t value Pr(>|t|)    
#> mu     -1.311e-04   1.338e-04   -0.980   0.3272    
#> omega   1.288e-06   8.186e-07    1.573   0.1156    
#> alpha1  8.793e-02   3.955e-02    2.223   0.0262 *  
#> beta1   7.804e-01   1.038e-01    7.518 5.57e-14 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Log Likelihood:
#>  2183.772    normalized:  4.367544 
#> 
#> Description:
#>  Thu Nov 13 09:34:07 2025 by user: georgi 
#> 
#> 
#> 
#> Standardised Residuals Tests:
#>                                  Statistic    p-Value
#>  Jarque-Bera Test   R    Chi^2   0.8749564 0.64566259
#>  Shapiro-Wilk Test  R    W       0.9978536 0.78316127
#>  Ljung-Box Test     R    Q(10)  17.8536807 0.05748257
#>  Ljung-Box Test     R    Q(15)  24.2180027 0.06148270
#>  Ljung-Box Test     R    Q(20)  25.8442849 0.17101649
#>  Ljung-Box Test     R^2  Q(10)  13.1441777 0.21572205
#>  Ljung-Box Test     R^2  Q(15)  14.9334373 0.45622242
#>  Ljung-Box Test     R^2  Q(20)  19.3320156 0.50034833
#>  LM Arch Test       R    TR^2   13.9249937 0.30552369
#> 
#> Information Criterion Statistics:
#>       AIC       BIC       SIC      HQIC 
#> -8.719089 -8.685372 -8.719216 -8.705859 
#> 
fit # == print(fit) and also == show(fit)
#> 
#> Title:
#>  GARCH Modelling 
#> 
#> Call:
#>  garchFit(formula = ~garch(1, 1), data = x, trace = FALSE) 
#> 
#> Mean and Variance Equation:
#>  data ~ garch(1, 1)
#> <environment: 0x5c825a8a7d58>
#>  [data = x]
#> 
#> Conditional Distribution:
#>  norm 
#> 
#> Coefficient(s):
#>          mu        omega       alpha1        beta1  
#> -1.3111e-04   1.2881e-06   8.7926e-02   7.8038e-01  
#> 
#> Std. Errors:
#>  based on Hessian 
#> 
#> Error Analysis:
#>          Estimate  Std. Error  t value Pr(>|t|)    
#> mu     -1.311e-04   1.338e-04   -0.980   0.3272    
#> omega   1.288e-06   8.186e-07    1.573   0.1156    
#> alpha1  8.793e-02   3.955e-02    2.223   0.0262 *  
#> beta1   7.804e-01   1.038e-01    7.518 5.57e-14 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Log Likelihood:
#>  2183.772    normalized:  4.367544 
#> 
#> Description:
#>  Thu Nov 13 09:34:07 2025 by user: georgi 
#>