Abstract
In this chapter, we introduce the structure and mechanics of estimation, inference, and forecasting for Markov switching (MS) models, in which a latent state variable governs how a portion or all the parameters of a time series model change over time. Sections 9.1-9.3 introduce and compare a number of different model specifications explaining their inner mechanics also using simulations. Section 9.4 explains the nature of a Markov chain (MC) process and introduces advanced models that relax the assumption that the MC is homogenous and of first order. Section 9.5 presents the Expectation Maximization algorithm for the estimation of MS models. Section 9.6 shows how to derive forecasts from the model, while Section 9.7 explains how the MS framework can be extended to nest the ARCH and DCC models discussed in Chapters 5 and 6. Finally, Section 9.8 shortly reviews the relevant literature trying to answer the key question as to whether these models may be useful in practice.
Keywords: Markov chain; Markov switching models; expectation maximization algorithm; latent regimes; smoothed and filtered probabilities
Supplementary material: Online appendix
Essentials of Time Series for Financial Applications 