Data Analysis and Applications 1

6On GARCH Models with Temporary Structural Changes

When an economic shock like the Lehman Crisis occurred, it is expected to investigate its influence based on economic time series. The intervention analysis by Box and Tiao is a method for such purpose. Most of the intervention analyses are based on ARIMA models, but some are based on GARCH models. The GARCH models have been developed for analyzing time series of stock returns. Usually, the expected value function of a GARCH model is assumed to be constant. However, this assumption is not appropriate when a time series includes a varying trend. Our first purpose is to propose a trend model, which can be easily taken in intervention analysis. Based on this trend model, we generalize a GARCH model for an intervention analysis for both trend and volatility. An identification method is also provided and evaluated by simulation studies. Usability of the proposed model is demonstrated by applying to real stock returns.

6.1. Introduction

The events such as the Lehman crash and the enforcement of large-scale monetary policy have a strong influence on society, and are strongly reflected in the economic time series. It is important to analyze the magnitude of the influence of such an event using changes that occurred in time series. The intervention analysis by Box and Tiao (1975) is a method for such a purpose. Most of the intervention analyses are based on ARIMA models. In recent years, a model based on the GARCH model was also proposed. ...