ON THE DETERMINATION OF THE NUMBER OF REGIMES IN MARKOV‐SWITCHING AUTOREGRESSIVE MODELS

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 Markov-switching 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. Copyright 2003 Blackwell Publishing Ltd.

[1]  René Garcia,et al.  Série Scientifique Scientific Series an Analysis of the Real Interest Rate under Regime Shifts , 2022 .

[2]  Clive W. J. Granger,et al.  Comments on testing economic theories and the use of model selection criteria , 1995 .

[3]  Jing Zhang,et al.  Autocovariance Structure of Markov Regime Switching Models and Model Selection , 2001 .

[4]  René Garcia,et al.  Série Scientifique Scientific Series Nº 95s-7 Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models , 2022 .

[5]  R. Nishii.  Maximum likelihood principle and model selection when the true model is unspecified , 1988 .

[6]  James Davidson,et al.  Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes , 2002 .

[7]  George Kapetanios,et al.  Model Selection in Threshold Models , 2001 .

[8]  Bruce E. Hansen,et al.  Erratum: The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP , 1996 .

[9]  G. McLachlan.  On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture , 1987 .

[10]  J. Zakoian,et al.  Stationarity of Multivariate Markov-Switching ARMA Models , 2001 .

[11]  T. Rydén.  Estimating the Order of Hidden Markov Models , 1995 .

[12]  B. G. Quinn,et al.  The determination of the order of an autoregression , 1979 .

[13]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[14]  H. Akaike.  A new look at the statistical model identification , 1974 .

[15]  Jiří Anděl.  A TIME SERIES MODEL WITH SUDDENLY CHANGING PARAMETERS , 1993 .

[16]  H. White,et al.  Information criteria for selecting possibly misspecified parametric models , 1996 .

[17]  Jianfeng Yao,et al.  On square-integrability of an AR process with Markov switching , 2001 .

[18]  M. Puterman,et al.  Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. , 1992, Biometrics.

[19]  B. Leroux.  Consistent estimation of a mixing distribution , 1992 .

[20]  R. McCulloch,et al.  STATISTICAL ANALYSIS OF ECONOMIC TIME SERIES VIA MARKOV SWITCHING MODELS , 1994 .

[21]  J. Zakoian,et al.  Estimating linear representations of nonlinear processes , 1998 .

[22]  James D. Hamilton.  Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates , 1988 .

[23]  Frederic S. Mishkin,et al.  What Does the Term Structure Tell Us About Future Inflation? , 1988 .

[24]  ByoungSeon Choi,et al.  Two chi-square statistics for determining the orders p and q of an ARMA (p, q) process , 1993, IEEE Trans. Signal Process..

[25]  S. Chib,et al.  Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts , 1993 .

[26]  Bootstrap-based evaluation of markov-switching time series models , 1998 .

[27]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[28]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .