GARCH, Outliers, and Forecasting Volatility

Abstract

High-frequency time series of financial asset returns typically exhibit excess kurtosis and volatility clustering. That is, large observations occur (much) more often than might be expected for a normally distributed variable, and these large returns tend to occur in clusters, resembling sequences of outliers. The generalized autoregressive conditional heteroskedasticity (GARCH) model often is applied to describe these two stylized facts (see Bollerslev et al. 1992). In applications of the GARCH model to stock and exchange-rate returns, it is typically found that the model cannot capture all excess kurtosis in case a conditional normal distribution is assumed for the returns. In response to this failure of the standard GARCH model, conditional distributions with fatter tails than the normal have been used, such as the student t distribution (see Bollerslev 1987; and Baillie and Bollerslev 1989). However, when the properties of returns series are examined more closely, it appears that the excess kurtosis often is caused almost entirely by only a few extreme observations. Following Friedman and Laibson (1989), we consider the possibility that these large returns are caused by extraordinary events that occur only occasionally and, consequently, assume that the observed time series can be described as a GARCH process which is contaminated with outliers.