GARCH(1,1) Model Fitting Function

Fits a GARCH(1,1) model to a time series using maximum likelihood estimation. This function estimates the parameters of the GARCH(1,1) model: \(\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2\)

garch11Fit(x, return_model = TRUE)

Arguments

x

A numeric vector or time series of data to fit the GARCH model to

return_model

Logical. If TRUE (default), returns a complete model object suitable for forecasting. If FALSE, returns coefficient table with statistics.

Value

If return_model = TRUE, returns an object of class "garch11" containing:

  • coefficients: Estimated parameters (mu, omega, alpha, beta)

  • data: Original time series data

  • residuals: Model residuals

  • sigma_squared: Conditional variances

  • fitted_mean: Fitted mean values

  • loglik: Log-likelihood value

  • convergence: Optimization convergence code

  • last_residual: Last residual for forecasting

  • last_variance: Last conditional variance for forecasting

  • stationarity: Alpha + beta stationarity measure

If return_model = FALSE, returns a coefficient matrix with estimates, standard errors, t-values, and p-values.

See also

garch11f for forecasting with the fitted model

Examples

# \donttest{
# Generate sample GARCH(1,1) data
set.seed(123)
n <- 500
omega <- 0.1; alpha <- 0.1; beta <- 0.8; mu <- 0.05

y <- numeric(n)
sigma2 <- numeric(n)
sigma2[1] <- omega / (1 - alpha - beta)
y[1] <- mu + sqrt(sigma2[1]) * rnorm(1)

for (t in 2:n) {
  sigma2[t] <- omega + alpha * (y[t-1] - mu)^2 + beta * sigma2[t-1]
  y[t] <- mu + sqrt(sigma2[t]) * rnorm(1)
}

# Fit GARCH(1,1) model
model <- garch11Fit(y, return_model = TRUE)
#> Error in garch11Fit(y, return_model = TRUE): could not find function "garch11Fit"
print(model$coefficients)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'print': object 'model' not found
# }