Adaptive quasi-maximum likelihood estimation of GARCH models with Student’stlikelihood

This paper proposes an adaptive quasi-maximum likelihood estimation (QMLE) when forecasting the volatility of financial data with the generalized autoregressive conditional heteroscedasticity (GARCH) model. When the distribution of volatility data is unspecified or heavy-tailed, we worked out adaptive QMLE based on data by using the scale parameter ηf to identify the discrepancy between wrongly specified innovation density and the true innovation density. With only a few assumptions, this adaptive approach is consistent and asymptotically normal. Moreover, it gains better efficiency under the condition that innovation error is heavy-tailed. Finally, simulation studies and an application show its advantage.