On multiple periodic autoregression

Jiří Anděl

Aplikace matematiky (1987)

  • Volume: 32, Issue: 1, page 63-80
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Anděl, Jiří. "On multiple periodic autoregression." Aplikace matematiky 32.1 (1987): 63-80. <http://eudml.org/doc/15481>.

@article{Anděl1987,
abstract = {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.},
author = {Anděl, Jiří},
journal = {Aplikace matematiky},
keywords = {estimating autoregressive matrices; matrixvariate$t$-distribution; multivariate processes; periodic autoregression; test of periodicity; test of fit; vector autoregression; asymptotic posterior chi-square distribution; confidence regions; Bayes approach; estimating autoregressive matrices; matrixvariate t-distribution; multivariate processes; periodic autoregression; test of periodicity; test of fit; vector autoregression; asymptotic posterior chi-square distribution; confidence regions},
language = {eng},
number = {1},
pages = {63-80},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On multiple periodic autoregression},
url = {http://eudml.org/doc/15481},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Anděl, Jiří
TI - On multiple periodic autoregression
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 1
SP - 63
EP - 80
AB - 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.
LA - eng
KW - estimating autoregressive matrices; matrixvariate$t$-distribution; multivariate processes; periodic autoregression; test of periodicity; test of fit; vector autoregression; asymptotic posterior chi-square distribution; confidence regions; Bayes approach; estimating autoregressive matrices; matrixvariate t-distribution; multivariate processes; periodic autoregression; test of periodicity; test of fit; vector autoregression; asymptotic posterior chi-square distribution; confidence regions
UR - http://eudml.org/doc/15481
ER -

References

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  1. J. Anděl, The Statistical Analysis of Time Series, SNTL Prague 1976 (in Czech). (1976) 
  2. J. Anděl, Mathematical Statistics, SNTL Prague 1978 (in Czech). (1978) 
  3. J. Anděl, Statistical analysis of periodic autoregression, Apl. mat. 28 (1983), 164-185. (1983) MR0712913
  4. J. Anděl A. Rubio A. Insua, On periodic autoregression with unknown mean, Apl. mat. 30(1985), 126-139. (1985) MR0778983
  5. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York 1958. (1958) Zbl0083.14601MR0091588
  6. W. P. Cleveland G. C. Tiao, Modeling seasonal time series, Rev. Economic Appliquée 32 (1979), 107-129. (1979) 
  7. H. Cramér, Mathematical Methods of Statistics, Princeton Univ. Press, Princeton 1946. (1946) MR0016588
  8. E. G. Gladyshev, Periodically correlated random sequences, Soviet Math. 2 (1961), 385-388. (1961) Zbl0212.21401
  9. R. H. Jones W. M. Brelsford, 10.1093/biomet/54.3-4.403, Biometrika 54 (1967), 403-408. (1967) MR0223041DOI10.1093/biomet/54.3-4.403
  10. H. Neudecker, 10.1080/01621459.1969.10501027, J. Amer. Statist. Assoc. 64 (1969), 953-963. (1969) Zbl0179.33102DOI10.1080/01621459.1969.10501027
  11. M. Pagano, 10.1214/aos/1176344376, Ann. Statist. 6 (1978), 1310-1317. (1978) MR0523765DOI10.1214/aos/1176344376
  12. C. R. Rao, Linear Statistical Inference and Its Application, Wiley, New York 1965. (1965) MR0221616
  13. C. G. Tiao M. R. Grupe, Hidden periodic autoregressive - moving average models in time series data, Biometrika 67 (1980), 365-373. (1980) MR0581732

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