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BAYESIAN MULTIPERIOD FORECASTS FOR ARX MODELS

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SHU-ING LIU

*Graduate Institute of Statistics, National Central University,
Chung-Li, Taiwan 320, R.O.C.*
(Received February 21, 1994; revised January 9, 1995)

**Abstract.**
Bayesian multiperiod 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, a
*t*-density mixture approximation is analytically derived to provide
an estimator of the posterior predictive density for any future
observation. In particular, a suitable *t*-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 convenient
*t*-density in practical usage. In fact, this *t*-density estimator
asymptotically converges to the true density.

*Key words and phrases*:
ARX model, Bayesian forecast,
*t*-density mixture, posterior predictive density, random regression.

**Source**
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