| 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 |
| . |
