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Time Series Analysis - Bayesian Multiple Time Series Modeling

[Home] [Up] [Univariate Models] [Transfer Function] [Multiple Time Series] [Bayesian Models]

Time Series Analysis - Bayesian Multiple Time Series Modeling


The likelihood function is


On combining (V.IV-1), (V.IV-2), and Bayes' theorem, the posterior pdf is obtained as


which can be drastically simplified on using


such that the following is obtained


where the Bayesian estimator is


From (V.IV-5) it follows that


with parameter covariance


such that it can be concluded that the posterior distribution for the Bayesian estimator (V.IV-6) is normal


Since in practice the error covariance matrix is not known, it is replaced by its estimated value (on using an LS estimator). Also, it may be practical to estimate the parameters in the context of SUR (since the exogenous variables are the same in each equation). The Bayesian k-th equation parameter estimator is


Note that this LS procedure also applies in case of time series with cointegration (even with included constant).

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Univariate Models
Transfer Function
Multiple Time Series
Bayesian Models
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