Two Parameter Estimation Methods for Quantile-GARCH Models

In this article, we consider the parameter estimation problems in Quantile-GARCH model, a new GARCH type model proposed by Deng and Jiang (2004), which have been applied successfully in the empirical analysis in stock market, foreign exchange rate market and electricity market. In practice study, we found that only parameter estimation problem is effectively solved, the Quantile-GARCH model can be widely applied to other financial markets. The first parameter estimation method named two steps estimation is based on Hull and Yao (2003), while the second one named Quantile-Quantile estimation just explores a nice property of Quantile type GARCH models. By comparison, the two step method is more effective for Quantile-GARCH model.