單一方程式共整合-GARCH模型：臺灣股市之實證研究

Abstract

共整合與GARCH模型可謂當代總體計量理論中最成功的二個應用，但是將二者結合在一起的研究卻不多見。就此，本文建構一個單一方程式共整合-GARCH(1,1)模型。該模型參數的最大概似估計式及其漸近分配被導出，其中共整合參數估計式的漸近分配是混合常態。在實證應用上，本文以台灣股市之股價指數與其指數期貨之日資料進行模型配適。實證結果顯示股價指數與指數期貨確實是共整合的，並且二者之干擾項都呈現頗強的GARCH效果。

The cointegration and GARCH models are the two most successful applications in macroeconomic econometrics, but only few researchers attempt to integrate these two popular models. This paper introduces a single equation cointegration model with GARCH(1,1) disturbances. Maximum likelihood estimators and their asymptotic distributions are derived for the parameters in the equation, in which the estimator of the cointegrating coefficient is asymptotically mixed and normally distributed. Empirically, we employ the model to examine Taiwan stock indexes and the associated futures prices of daily stock market data. The resulting estimates show that index futures and spot indexes are indeed cointegrated, and that the disturbances also exhibit a strong GARCH effect.