A time varying hidden Markov model with latent information

The time varying hidden Markov models are based on the use of some observable variables, which we suppose to drive the transition probabilities. The estimation of the model is conditional on the availability of this information, which is not obvious. In this paper we propose a time varying hidden Markov model with the transition probabilities driven by a latent variable subject to the same Markovian changes of the dependent variable. The model has a state-space form and the latent variable is estimated using a modified Kim filter, so that this information is always available; furthermore, the estimation of this latent variable is useful to forecast the changes in the state. We show the practical characteristics of this model through an example in which the latent variable is the business cycle.

[1]  Shigeo Abe DrEng.  Pattern Classification , 2001, Springer London.

[2]  Chang‐Jin Kim,et al.  Dynamic linear models with Markov-switching , 1994 .

[3]  Chang-Jin Kim,et al.  Estimation of Markov regime-switching regression models with endogenous switching , 2003 .

[4]  Giampiero M. Gallo,et al.  Volatility transmission across markets: a Multichain Markov Switching model , 2007 .

[5]  Edoardo Otranto,et al.  The multi‐chain Markov switching model , 2005 .

[6]  James D. Hamilton.  Analysis of time series subject to changes in regime , 1990 .

[7]  Ben J. A. Kröse,et al.  Online multicamera tracking with a switching state-space model , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[8]  Choosing information variables for transition probabilities in a time-varying transition probability Markov switching model , 1998 .

[9]  Chang-Jin Kim,et al.  Business Cycle Turning Points, A New Coincident Index, and Tests of Duration Dependence Based on a Dynamic Factor Model With Regime Switching , 1998, Review of Economics and Statistics.

[10]  Stephen Gordon,et al.  Business cycle durations , 1998 .

[11]  Giampiero M. Gallo,et al.  Volatility spillovers, interdependence and comovements: A Markov Switching approach , 2008, Comput. Stat. Data Anal..

[12]  Patrick Lam,et al.  The Hamilton model with a general autoregressive component , 1990 .

[13]  Michael J. Dueker,et al.  Non-Markovian Regime Switching with Endogenous States and Time-Varying State Strengths , 2004 .

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

[15]  E. Otranto,et al.  Modelling the discrete and infrequent official interest rate change in the UK , 2006 .

[16]  Kjersti Aas,et al.  Applications of hidden Markov chains in image analysis , 1999, Pattern Recognit..

[17]  Chang‐Jin Kim,et al.  State Space Models with Regime Switching , 1999 .

[18]  Andrew J. Filardo.  Business-Cycle Phases and Their Transitional Dynamics , 1994 .

[19]  Darren J. Wilkinson,et al.  Detecting homogeneous segments in DNA sequences by using hidden Markov models , 2000 .

[20]  Michael J. Dueker.  Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility , 1997 .

[21]  Thomas H. McCurdy,et al.  Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth , 1994 .

[22]  P. Guttorp,et al.  A non‐homogeneous hidden Markov model for precipitation occurrence , 1999 .

[23]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[24]  Andrew Harvey,et al.  10 Structural time series models , 1993 .

[25]  William J. J. Roberts,et al.  Revisiting autoregressive hidden Markov modeling of speech signals , 2005, IEEE Signal Processing Letters.

[26]  F. Diebold,et al.  Regime Switching with Time-Varying Transition Probabilities , 2020, Business Cycles.

[27]  Eric Ghysels,et al.  On the Periodic Structure of the Business Cycle , 1992 .

[28]  S. Goldfeld,et al.  A Markov model for switching regressions , 1973 .

[29]  G. Lindgren.  Markov regime models for mixed distributions and switching regressions , 1978 .

[30]  J. Stock,et al.  A Probability Model of the Coincident Economic Indicators , 1988 .

[31]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[32]  Alex Bateman,et al.  An introduction to hidden Markov models. , 2007, Current protocols in bioinformatics.

[33]  Beveridge-Nelson-Stock-Watson Decomposition,et al.  Structural Time Series Models , 2004 .

[34]  Pok-sang Lam.  A Markov-Switching Model of Gnp Growth with Duration Dependence , 2004 .