Bayesian forecasting in univariate autoregressive models with normal-gamma prior distribution of unknown parameters

Abstract

We consider the problem of computing the mean-square optimal Bayesian predictor in univariate autoregressive models with Gaussian innovations. The unknown coefficients of the model are ascribed a normal-gamma prior distribution providing a family of con- jugate priors. The problem is reduced to calculating the state-space realization matrices of an iterated linear discrete time-invariant system. The system theoretic solution employs a scalarization technique for computing the power moments of Gaussian random matrices developed recently by the authors. Show more