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The Bayes approach in multiple autoregressive series
Applications of Mathematics, Tome 16 (1971) no. 3, pp. 220-228
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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.
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.
DOI : 10.21136/AM.1971.103348
Classification : 62H10 
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Anděl, Jiří. The Bayes approach in multiple autoregressive series. Applications of Mathematics, Tome 16 (1971) no. 3, pp. 220-228. doi: 10.21136/AM.1971.103348

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[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

[4] H. B. Mann A. Wald: On the statistical treatment of linear stochastic difference equations. Econometrica 11, 1943, 173-220. | DOI

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