Abstract
Bayestian muliperiod forecasts for AR models with random independent exogenous variables under normal-gamma and normal-inverted Wishart prior assumptions are investigated. By suitably arranging the integration order of the model's parameters, at-density mixture approximation is analytically derived to provide an estimator of the posterior predictive density for any future observation. In particular, a suitablet-density is proposed by a convenient closed form. The precision of the discussed methods is examined by using some simulated data and one set of real data up to lead-six-ahead forecasts. It is found that the numerical results of the discussed methods are rather close. In particular, when sample sizes are sufficiently large, it is encouraging to apply a convenientt-density in practical usage. In fact, thist-density estimator asymptotically converges to the true density.
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This research was supported by the National Science Council, Republic of China under contract #NSC82-0208-M-008-086.
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Liu, SI. Bayesian multiperiod forecasts for ARX models. Ann Inst Stat Math 47, 211–224 (1995). https://doi.org/10.1007/BF00773458
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DOI: https://doi.org/10.1007/BF00773458