Composite quantile regression estimation for P-GARCH processes

We consider the periodic generalized autoregressive conditional heteroskedasticity (P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator. The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions. The proposed methodology is also illustrated by VaR on stock price data.