在本計畫中我們假設某時間序列的生成模型(generating model)為GARCH(1,1)模型。 利用最大概似估計法我們可以估計GARCH 模型中的未知參數，並藉由所估得的參數來 預測下一期觀察值的波動率。本計畫的目的為推導最大概似估計法所估計的波動率之 漸近預測誤差。我們的研究成果不僅讓我們對於GARCH 模型的最大概似估計值的特性 有更深一層的了解，也可應用於解決最適波動率的模型選擇問題。
Assume that observations are generated from a GARCH(1,1) model. The unknown parameters of the model are estimated by the maximum likelihood estimation. Through the fitted GARCH model the volatility of the observations is predictable. The aim of this research is to derive the asymptotic expression for the least squares prediction error of the volatility. Our results not only provide a deeper understanding of the least squares predictors in GARCH processes, but also give the theoretical foundation for asymptotical efficient order selection in GARCH models.
