$$\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2.$$
Examples
morie_garch_fit(x = rnorm(50))
#> Warning:
#> ugarchfit-->waring: using less than 100 data
#> points for estimation
#> $omega
#> [1] 0.001971441
#>
#> $alpha
#> [1] 4.841863e-11
#>
#> $beta
#> [1] 0.9989997
#>
#> $persistence
#> [1] 0.9989997
#>
#> $loglik
#> [1] -67.90172
#>
#> $conditional_variance
#> [1] 0.8858606 0.8869459 0.8880301 0.8891133 0.8901953 0.8912763 0.8923562
#> [8] 0.8934351 0.8945128 0.8955895 0.8966651 0.8977396 0.8988130 0.8998854
#> [15] 0.9009567 0.9020269 0.9030961 0.9041641 0.9052312 0.9062971 0.9073620
#> [22] 0.9084258 0.9094885 0.9105502 0.9116109 0.9126704 0.9137289 0.9147864
#> [29] 0.9158428 0.9168981 0.9179524 0.9190056 0.9200578 0.9211089 0.9221590
#> [36] 0.9232080 0.9242559 0.9253028 0.9263487 0.9273935 0.9284373 0.9294801
#> [43] 0.9305217 0.9315624 0.9326020 0.9336406 0.9346781 0.9357146 0.9367500
#> [50] 0.9377845
#>
#> $n
#> [1] 50
#>
#> $method
#> [1] "GARCH(1,1) via rugarch"
#>
