Factor Garch, Regime-Switching and the Term Structure of Interest Rates

Abstract

The presence of time-changing variance (heteroskedasticity) in financial timeseries is often cited as the cause of fat-tailedness in the unconditional distribution of the series. However, many researchers have found that, after allowing for heteroskedastic behaviour, the conditional distributions remain fat-tailed. Consequently, one approach adopted by applied econometricians has been to postulate a fat-tailed conditional distribution. In the multivariate context, few such distributions offer tractable solutions which accurately capture multivariate deviations from normality. The approach taken in this paper is to model the multivariate dynamics of the conditional covariance matrix with a parsimonious regime-switching factor GARCH model. The factor loading matrix switches within a finite state-space according to the value of an unobserved Markov state variable. The conditional distribution of the process is then a mixture of multivariate normals. Fat-tails are explicitly generated by the presence of structural breaks or changes of regime. We develop some theoretical properties of such models, and filters for inference about the unobserved factor process and Markov chain, as well as maximum likelihood estimation via the EM algorithm. We fit our model to daily changes in the term structure of US interest rates and apply one-step ahead distributional forecasts in a simple portfolio risk management context.

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