Periodic moving average process

Tomáš Cipra

Aplikace matematiky (1985)

  • Volume: 30, Issue: 3, page 218-229
  • ISSN: 0862-7940

Abstract

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Periodic moving average processes are representatives of the class of periodic models suitable for the description of some seasonal time series and for the construction of multivariate moving average models. The attention having been lately concentrated mainly on periodic autoregressions, some methods of statistical analysis of the periodic moving average processes are suggested in the paper. These methods include the estimation procedure (based on Durbin's construction of the parameter estimators in the moving average processes and on Pagano's results for the periodic autoregressions) and the test of the periodic structure. The results are demonstrated by means of numerical simulations.

How to cite

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Cipra, Tomáš. "Periodic moving average process." Aplikace matematiky 30.3 (1985): 218-229. <http://eudml.org/doc/15398>.

@article{Cipra1985,
abstract = {Periodic moving average processes are representatives of the class of periodic models suitable for the description of some seasonal time series and for the construction of multivariate moving average models. The attention having been lately concentrated mainly on periodic autoregressions, some methods of statistical analysis of the periodic moving average processes are suggested in the paper. These methods include the estimation procedure (based on Durbin's construction of the parameter estimators in the moving average processes and on Pagano's results for the periodic autoregressions) and the test of the periodic structure. The results are demonstrated by means of numerical simulations.},
author = {Cipra, Tomáš},
journal = {Aplikace matematiky},
keywords = {periodic moving average processes; seasonal time series; multivariate moving average models; estimation procedure; Durbin’s construction; test of the periodic structure; numerical simulations; Periodic moving average processes; seasonal time series; multivariate moving average models; estimation procedure; Durbin's construction; test of the periodic structure; numerical simulations},
language = {eng},
number = {3},
pages = {218-229},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic moving average process},
url = {http://eudml.org/doc/15398},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Cipra, Tomáš
TI - Periodic moving average process
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 3
SP - 218
EP - 229
AB - Periodic moving average processes are representatives of the class of periodic models suitable for the description of some seasonal time series and for the construction of multivariate moving average models. The attention having been lately concentrated mainly on periodic autoregressions, some methods of statistical analysis of the periodic moving average processes are suggested in the paper. These methods include the estimation procedure (based on Durbin's construction of the parameter estimators in the moving average processes and on Pagano's results for the periodic autoregressions) and the test of the periodic structure. The results are demonstrated by means of numerical simulations.
LA - eng
KW - periodic moving average processes; seasonal time series; multivariate moving average models; estimation procedure; Durbin’s construction; test of the periodic structure; numerical simulations; Periodic moving average processes; seasonal time series; multivariate moving average models; estimation procedure; Durbin's construction; test of the periodic structure; numerical simulations
UR - http://eudml.org/doc/15398
ER -

References

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  1. J. Anděl, Statistical analysis of periodic autoregression, Aplikace matematiky 28 (1983). 364-385. (1983) MR0712913
  2. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York 1958. (1958) Zbl0083.14601MR0091588
  3. W. P. Cleveland G. C. Tiao, Modeling seasonal time series, Revue Economic Appliquée 32, (1979), 107-129. (1979) 
  4. H. Cramér, Mathematical Methods of Statistics, Princeton University Press, Princeton 1946. (1946) MR0016588
  5. J. Durbin, 10.1093/biomet/46.3-4.306, Biometrika 46 (1959), 306-316. (1959) Zbl0097.34602MR0114283DOI10.1093/biomet/46.3-4.306
  6. 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
  7. H. J. Newton, 10.1080/00401706.1982.10487731, Technometrics 24 (1982), 109-116. (1982) Zbl0485.62109MR0655574DOI10.1080/00401706.1982.10487731
  8. M. Pagano, 10.1214/aos/1176344376, Ann. Statist. 6 (1978), 1310-1317. (1978) Zbl0392.62073MR0523765DOI10.1214/aos/1176344376
  9. G. C. 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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