Fit a GARCH(1,1) model with Student-t errors

The model of daily volatility most used in finance: a day's return is mu + sigma(t) * z(t), where z follows a Student-t distribution scaled to a variance of 1 and sigma(t)^2 follows garch_variance(). The parameters are fitted by maximum likelihood with stats::optim(), in a form that keeps omega positive, alpha and beta positive with alpha + beta below 1, and nu above 2.

Usage

garch_fit(r)

Arguments

r

Numeric vector of daily returns, in percent.

Value

A list with mu, omega, alpha, beta, nu and start, the variance of the first day, or NULL when the fit fails.

Examples

set.seed(1)
golemcrypto:::garch_fit(rnorm(1000, sd = 3))[c("alpha", "beta", "nu")]
#> $alpha
#> [1] 3.165167e-05
#> 
#> $beta
#> [1] 0.4641205
#> 
#> $nu
#> [1] 4557.462
#>