Dynamic linear models with switching

Abstract The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and nonlinear optimization. We relate the models to those considered previously in the literature and give an application involving the tracking of multiple targets.

[1]  R. Quandt.  A New Approach to Estimating Switching Regressions , 1972 .

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

[3]  Y. Bar-Shalom,et al.  Tracking in a cluttered environment with probabilistic data association , 1975, Autom..

[4]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[5]  Yaakov Bar-Shalom,et al.  Tracking methods in a multitarget environment , 1978 .

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

[7]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[8]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[9]  A F Smith,et al.  Monitoring renal transplants: an application of the multiprocess Kalman filter. , 1983, Biometrics.

[10]  A. Harvey,et al.  Forecasting Economic Time Series With Structural and Box-Jenkins Models: A Case Study , 1983 .

[11]  G. Kitagawa,et al.  A Smoothness Priors–State Space Modeling of Time Series with Trend and Seasonality , 1984 .

[12]  Biing-Hwang Juang,et al.  Mixture autoregressive hidden Markov models for speech signals , 1985, IEEE Trans. Acoust. Speech Signal Process..

[13]  L. Rabiner,et al.  An introduction to hidden Markov models , 1986, IEEE ASSP Magazine.

[14]  G. Kitagawa.  Non-Gaussian State—Space Modeling of Nonstationary Time Series , 1987 .

[15]  R. Shumway.  Applied Statistical Time Series Analysis , 1988 .

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

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

[18]  K. Gordon,et al.  Modeling and Monitoring Biomedical Time Series , 1990 .

[19]  Nicholas G. Polson,et al.  A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling , 1992 .