Copyright © 2005 John Wiley & Sons, Ltd. The Multi-chain Markov Switching Model EDOARDO OTRANTO* Università di Sassari, Italy ABSTRACT In many real phenomena the behaviour of a certain variable, subject to differ- ent regimes, depends on the state of other variables or the same variable observed in other subjects, so the knowledge of the state of the latter could be important to forecast the state of the former. In this paper a particular multi- variate Markov switching model is developed to represent this case. The tran- sition probabilities of this model are characterized by the dependence on the regime of the other variables. The estimation of the transition probabilities provides useful information for the researcher to forecast the regime of the variables analysed. Theoretical background and an application are shown. Copyright © 2005 John Wiley & Sons, Ltd. key words regime switching; multivariate time series; transition probabilities INTRODUCTION The Markov switching (MS hereafter) model, introduced in econometrics by Hamilton (1989), has been largely used for the study of phenomena with two or more unobservable regimes, represented by states of a Markov chain. For example, it was used for the representation of business cycles (Hamilton, 1989), for the study of segmented trends in exchange rates (Engel and Hamilton, 1990; Engel, 1994), and for the evaluation of monetary effects on output (Garcia and Schaller, 2002). Generally, univariate approaches are used for the applications in these fields and the extensions to multivariate cases look for common states for the same variable observed in different subjects (coun- tries, markets, firms, etc.) or for several different variables. For example, Kim and Nelson (1998) extract a common component subject to two different regimes from four economic variables and interpret it as the common cycle; Krolzig (1997) extends the MS model to the VAR case, consider- ing a common state for all the variables studied. The multivariate MS model has not received much attention, essentially because it does not provide easily interpretable results in terms of inference on the regimes (see, for example, the results in Engel and Hamilton, 1990). Maybe this fact is due to the common practice of econometricians in attributing to each regime an economic interpretation; for example, in the analysis of the business cycle, two states are considered representing respectively the recession and the growth regimes. Anyway, the correspondence between regimes and economic periods is subjective (see, for example, Journal of Forecasting J. Forecast. 24, 523–537 (2005) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/for.965 *Correspondence to: Edoardo Otranto, Dipartimento di Economia, Impresa e Regolamentazione (DEIR), Università di Sassari, Via Torre Tonda 34, I-07100 Sassari, Italy. E-mail: eotranto@uniss.it Italian MIUR ‘Metodi e modelli statistici per la previsione di serie temporali non stazionarie e non lineari’.