| Title:
|
On multiple periodic autoregression (English) |
| Author:
|
Anděl, Jiří |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1987 |
| Pages:
|
63-80 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The model of periodic autoregression is generalized to the multivariate case. The autoregressive matrices are periodic functions of time. The mean value of the process can be a non-vanishing periodic sequence of vectors. Estimators of parameters and tests of statistical hypotheses are based on the Bayes approach. Two main versions of the model are investigated, one with constant variance matrices and the other with periodic variance matrices of the innovation process. (English) |
| Keyword:
|
estimating autoregressive matrices |
| Keyword:
|
matrixvariate$t$-distribution |
| Keyword:
|
multivariate processes |
| Keyword:
|
periodic autoregression |
| Keyword:
|
test of periodicity |
| Keyword:
|
test of fit |
| Keyword:
|
vector autoregression |
| Keyword:
|
asymptotic posterior chi-square distribution |
| Keyword:
|
confidence regions |
| Keyword:
|
Bayes approach |
| MSC:
|
62F15 |
| MSC:
|
62M07 |
| MSC:
|
62M09 |
| MSC:
|
62M10 |
| idZBL:
|
Zbl 0634.62086 |
| idMR:
|
MR0879331 |
| DOI:
|
10.21136/AM.1987.104237 |
| . |
| Date available:
|
2008-05-20T18:31:42Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104237 |
| . |
| Reference:
|
[1] J. Anděl: The Statistical Analysis of Time Series.SNTL Prague 1976 (in Czech). |
| Reference:
|
[2] J. Anděl: Mathematical Statistics.SNTL Prague 1978 (in Czech). |
| Reference:
|
[3] J. Anděl: Statistical analysis of periodic autoregression.Apl. mat. 28 (1983), 164-185. MR 0712913 |
| Reference:
|
[4] J. Anděl A. Rubio A. Insua: On periodic autoregression with unknown mean.Apl. mat. 30(1985), 126-139. MR 0778983 |
| Reference:
|
[5] T. W. Anderson: An Introduction to Multivariate Statistical Analysis.Wiley, New York 1958. Zbl 0083.14601, MR 0091588 |
| Reference:
|
[6] W. P. Cleveland G. C. Tiao: Modeling seasonal time series.Rev. Economic Appliquée 32 (1979), 107-129. |
| Reference:
|
[7] H. Cramér: Mathematical Methods of Statistics.Princeton Univ. Press, Princeton 1946. MR 0016588 |
| Reference:
|
[8] E. G. Gladyshev: Periodically correlated random sequences.Soviet Math. 2 (1961), 385-388. Zbl 0212.21401 |
| Reference:
|
[9] R. H. Jones W. M. Brelsford: Time series with periodic structure.Biometrika 54 (1967), 403-408. MR 0223041, 10.1093/biomet/54.3-4.403 |
| Reference:
|
[10] H. Neudecker: Some theorems on matrix differentiation with special reference to Kronecker matrix products.J. Amer. Statist. Assoc. 64 (1969), 953-963. Zbl 0179.33102, 10.1080/01621459.1969.10501027 |
| Reference:
|
[11] M. Pagano: On periodic and multiple autoregression.Ann. Statist. 6 (1978), 1310-1317. MR 0523765, 10.1214/aos/1176344376 |
| Reference:
|
[12] C. R. Rao: Linear Statistical Inference and Its Application.Wiley, New York 1965. MR 0221616 |
| Reference:
|
[13] C. G. Tiao M. R. Grupe: Hidden periodic autoregressive - moving average models in time series data.Biometrika 67 (1980), 365-373. MR 0581732 |
| . |
