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Summary:
Let $X_1,\ldots,X_N$ be a finite part of the normal $p$-dimensional autoregressive series generated by $\sum^n_{k=1} A_kX_{t-k}=\zeta_t$ where random vectors $\zeta_t$ are uncorrelated and each of them has the unit covariance matrix. The Bayes approach is applied to the problem of estimating the autoregressive parameters under condition that the matrix $A_0$ is diagonal. The "vague" prior distribution is supposed. It is proved that the point estimates coincide with the least squares estimates. The posterior distribution of these parameters is given in a simple form. The results are derived without the assumption that $\{X_t\}$ is the stationary series.
References:
[1] D. G. Champernowne: Sampling theory applied to autoregressive sequences. J. Roy. Stat. Soc. ser. B, 10, 1948, 204-231. MR 0030178 | Zbl 0033.08101
[2] J. Hájek J. Anděl: Stacionární procesy. (skripta). SPN 1969.
[3] D. V. Lindley: Introduction to probability and statistics from a bayesian viewpoint. Part 2. Inference. Camb. Univ. Press, 1965. Zbl 0123.34505
[4] H. B. Mann A. Wald: On the statistical treatment of linear stochastic difference equations. Econometrica 11, 1943, 173-220. DOI 10.2307/1905674
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