Abstract
This chapter discusses state space models and Kalman filtering for multivariate time series. The Kalman filter of Chap. 3 is upgraded to cover this important case. We briefly discuss how the topics of previous chapters may be extended to the multivariate case. Covariance estimation is discussed using Bayesian conjugate methods, EM algorithm and Markov chain Monte Carlo methods. In particular, the forward filtering backward sampling is discussed in detail. A data set consisting of daily values of several pollutants is used to illustrate estimation and forecasting.
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Triantafyllopoulos, K. (2021). Multivariate State Space Models. In: Bayesian Inference of State Space Models. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-76124-0_5
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DOI: https://doi.org/10.1007/978-3-030-76124-0_5
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