On the Determination of the Number of Regimes in Markov‐switching Autoregressive Models

Abstract

Dynamic models with parameters that are allowed to depend on the state of a hidden Markov chain have become a popular tool for modelling time series subject to changes in regime. An important question that arises in applications involving such models is how to determine the number of states required for the model to be an adequate characterization of the observed data. In this paper, we investigate the properties of alternative procedures that can be used to determine the state dimension of a Markovswitching autoregressive model. These include procedures that exploit the ARMA representation which Markov-switching processes admit, as well as procedures that are based on optimization of complexity-penalized likelihood measures. Our Monte Carlo analysis reveals that such procedures estimate the state dimension correctly, provided that the parameter changes are not too small and the hidden Markov chain is fairly persistent. The use of the various methods is also illustrated by means of empirical examples.

Revisiting the empirical linkages between stock returns and trading volume

“…Next, we compute the information criteria proposed by Psaradakis and Spagnolo (2003) for Markov-switching autoregressive models to determine the optimal lag length, q, of the MS-AR(q) model in equation (1) show that both bull-market and bear-market states are highly persistent. The bull-market regime persists, on average, for 1/(1 − p 11 ) = 1/(1 − 0.96) = 25 months, and it is expected that the bear-market regime will persist for 1/(1 − p 00 ) = 1/(1 − 0.91) = 11.11 months.…”

Regional and global spillovers and diversification opportunities in the GCC equity sectors

“…Sims and Zha (2006), Maheu et al (2009) andCakmakli et al (2011) select the number of regimes based on the log likelihood, marginal density, or predictive likelihoods. On the other hand, Krolzig (1997), Rydén et al (1998 and Psaradakis and Spagnolo (2003) suggest selecting the number of regimes and the type of the MS model using AIC and, using Monte Carlo experiments, Psaradakis and Spagnolo (2003) show that AIC is generally successful in selecting the correct model (see also Smith et al 2006). …”

Markov-switching generalized additive models

“…Even for the simpler parametric Markov-switching models, there is a variety of possible criteria for selecting N , including the AIC, the Bayesian Information Criterion, the Integrated Completed Likelihood criterion, the Hannan-Quinn criterion and cross-validated likelihood (see, e.g., Psaradakis and Spagnolo 2003;Celeux and Durand 2008), and it is our impression that most users pick their method of choice rather arbitrarily. For MS-GAMs, it is conceptually straightforward to choose N for example based on cross-validated likelihood or on the AIC-type statistic (8).…”