Smoothness priors multichannel autoregressive time series modeling

A smoothness priors approach to the multichannel autoregressive (MVAR) modeling of stationary time series is presented. Data channels are modeled individually as in multi-input scalar-output transfer function modeling under smoothness priors constraints. The models are combined algebraically to yield a smoothness priors (SPMVAR) model. In each transfer function model, smoothness hyperparameters balance the tradeoff between the infidelity of the models to the data and the infidelity of the model to the smoothness constraints. The likelihood of the hyperparameters is maximized by a BFGS-least squares procedure. The fitted SPMVAR model yields an estimate of the power spectral density matrix of the process and the coherence, phase and transfer function. The SPMVAR method tends to be less sensitive than other MVAR methods to overparameterization and to spectral line feedthrough. Several examples are worked.<<ETX>>

[1]  I. Good,et al.  Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data , 1980 .

[2]  G. Kitagawa,et al.  A smoothness priors time-varying AR coefficient modeling of nonstationary covariance time series , 1985, IEEE Transactions on Automatic Control.

[3]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

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

[5]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[6]  Edmund Taylor Whittaker.  On a New Method of Graduation , 1922, Proceedings of the Edinburgh Mathematical Society.

[7]  W. Gersch,et al.  A smoothness priors long AR model method for spectral estimation , 1985, IEEE Transactions on Automatic Control.

[8]  Will Gersch,et al.  A data analytic approach to the smoothing problem and some of its variations , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[9]  Genshiro Kitagawa,et al.  A NONSTATIONARY TIME SERIES MODEL AND ITS FITTING BY A RECURSIVE FILTER , 1981 .

[10]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[11]  Genshiro Kitagawa,et al.  An approach to the prediction of time series with trends and seasonalities , 1982, 1982 21st IEEE Conference on Decision and Control.

[12]  Hirotugu Akaike,et al.  Likelihood and the Bayes procedure , 1980 .

[13]  Richard H. Jones.  Identification and autoregressive spectrum estimation , 1974 .

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

[15]  B. Yandell,et al.  Automatic Smoothing of Regression Functions in Generalized Linear Models , 1986 .

[16]  R. Shiller.  A DISTRIBUTED LAG ESTIMATOR DERIVED FROM SMOOTHNESS PRIORS , 1973 .

[17]  Genshiro Kitagawa,et al.  Smoothness Priors ansfer Function Estimation * WILL GERSCHt and GENSHIRO KITAGAWA ¢ , 2002 .