# Periodic moving average process

Aplikace matematiky (1985)

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

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topCipra, 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

top- J. Anděl, Statistical analysis of periodic autoregression, Aplikace matematiky 28 (1983). 364-385. (1983) MR0712913
- T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York 1958. (1958) Zbl0083.14601MR0091588
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- H. Cramér, Mathematical Methods of Statistics, Princeton University Press, Princeton 1946. (1946) MR0016588
- J. Durbin, 10.1093/biomet/46.3-4.306, Biometrika 46 (1959), 306-316. (1959) Zbl0097.34602MR0114283DOI10.1093/biomet/46.3-4.306
- 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
- H. J. Newton, 10.1080/00401706.1982.10487731, Technometrics 24 (1982), 109-116. (1982) Zbl0485.62109MR0655574DOI10.1080/00401706.1982.10487731
- M. Pagano, 10.1214/aos/1176344376, Ann. Statist. 6 (1978), 1310-1317. (1978) Zbl0392.62073MR0523765DOI10.1214/aos/1176344376
- 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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