BL-GARCH model with elliptical distributed innovations

We are interested in the parametric class of Bilinear GARCH (BL-GARCH) models which are capable of simultaneously capturing the well known properties of financial retrun series, volatility clustering and leverage effects. Specifically, as it is often observed that the distribution of many financial time series data has heavy tails, heavier than the Normal distribution, we examine, in this paper, the BL-GARCH model in a general setting under some non-normal distributions. We also propose and implement a maximum likelihood estimation (MLE) methodology for parameter estimation. To evaluate the small-sample performance of this method for various models, a Monte Carlo study is conducted. Finally, the capability of within-sample estimation, using the S&P 500 daily returns, is also studied.