Observable or latent Markov chains for score-driven regime-switching volatility?

Abstract

We study the statistical and forecasting performances of two regime-switching Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) models, i.e. observable-switching (OS) Beta-t-EGARCH and Markov-switching (MS) Beta-t-EGARCH. Both are non-path-dependent score-driven regime-switching volatility models, and their regime-switching specifications can be related to corresponding non-path-dependent Markov-switching GARCH (MS-GARCH) specifications. We present the estimation procedures for OS-Beta-t-EGARCH and MS-Beta-t-EGARCH. We use data on the weekly log-returns of the Standard & Poor’s 500 (S&P 500) index and a random sample of 50 stocks from the S&P 500 from March 1986 to July 2024 ($T = 2,000$T=2,000). The out-of-sample forecasting window is from May 2005 to July 2024 (${T_f} = 1,000$Tf=1,000). We compare the in-sample statistical and out-of-sample density forecasting performances of Beta-t-EGARCH, OS-Beta-t-EGARCH, and MS-Beta-t-EGARCH. We find that the statistical and density forecasting performances of OS-Beta-t-EGARCH are superior to MS-Beta-t-EGARCH, motivating its practical use by investors and risk managers.