The conditional distribution of the series Y for time t is written where denotes all available information at time t -1 . Therefore, if and . However, this condition is not sufficient for weak stationarity in the presence of autocorrelation. Note that if .
Large innovations increase the conditional variance if and decrease the conditional variance if .
Suppose that . The log-likelihood function is computed from the product of all conditional densities of the prediction errors. Under the conditional t distribution, the additional parameter is estimated. The likelihood function is maximized via either the dual quasi-Newton or trust region algorithm. The default is the dual quasi-Newton algorithm.