Regularization in Regime-Switching Gaussian Autoregressive Models

Abstract

Regime-switching Gaussian autoregressive models form an effective platform for analyzing financial and economic time series. They explain the heterogeneous behaviour in volatility over time and multi-modality of the conditional or marginal distributions. One important task is to infer the number of regimes and regime-specific parsimonious autoregressive models. Information-theoretic criteria such as aic or bic are commonly used for such inference, and they typically evaluate each regime/autoregressive combination separately in order to choose the optimal model accordingly. However, the number of combinations can be so large that such an approach is computationally infeasible. In this paper, we first use a computationally efficient regularization method for simultaneous autoregressive-order and parameter estimation when the number of autoregressive regimes is pre-detertermined. We then use a regularized Bayesian information criterion (rbic) to select the most suitable number of regimes. Finite sample performance of the proposed methods are investigated via extensive simulations. We also analyze the U.S. gross domestic product growth and the unemployment rate data to demonstrate this method.