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Posterior mode estimation by extended Kalman filtering for multivariate dynamic generalized linear models. (English) Zbl 0781.62147

A family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family. Besides common conditionally Gaussian models, this article deals with univariate models for counted and binary data and, as the most interesting multivariate case, models for nonstationary multicategorical time series. To avoid a full Bayesian analysis based on numerical integration, which becomes computationally critical for higher dimensions, we propose to estimate time-varying parameters by posterior modes. A generalization of the extended Kalman filter and smoother for conditionally Gaussian observations is suggested for approximate posterior mode estimation.

MSC:

62M20 Inference from stochastic processes and prediction
62J12 Generalized linear models (logistic models)
65C99 Probabilistic methods, stochastic differential equations
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