# Article

 Title: The Bayes approach in multiple autoregressive series (English) Author: Anděl, Jiří Language: English Journal: Aplikace matematiky ISSN: 0373-6725 Volume: 16 Issue: 3 Year: 1971 Pages: 220-228 Summary lang: English Summary lang: Czech . Category: math . 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. () MSC: 62H10 idZBL: Zbl 0231.62069 idMR: MR0290498 DOI: 10.21136/AM.1971.103348 . Date available: 2008-05-20T17:50:44Z Last updated: 2020-07-28 Stable URL: http://hdl.handle.net/10338.dmlcz/103348 . Reference: [1] D. G. Champernowne: Sampling theory applied to autoregressive sequences.J. Roy. Stat. Soc. ser. B, 10, 1948, 204-231. Zbl 0033.08101, MR 0030178 Reference: [2] J. Hájek J. Anděl: Stacionární procesy.(skripta). SPN 1969. Reference: [3] D. V. Lindley: Introduction to probability and statistics from a bayesian viewpoint.Part 2. Inference. Camb. Univ. Press, 1965. Zbl 0123.34505 Reference: [4] H. B. Mann A. Wald: On the statistical treatment of linear stochastic difference equations.Econometrica 11, 1943, 173-220. 10.2307/1905674 .

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