Cipra, Tomáš Periodic moving average process. (English) Zbl 0586.62146 Apl. Mat. 30, 218-229 (1985). 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 being lately concentrated mainly on the 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 M. Pagano’s [Ann. Stat. 6, 1310-1317 (1978; Zbl 0392.62073)] results for the periodic autoregressions) and the test of the periodic structure. The results are demonstrated by means of numerical simulations. Cited in 1 ReviewCited in 3 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M09 Non-Markovian processes: estimation Keywords:Periodic moving average processes; seasonal time series; multivariate moving average models; estimation procedure; Durbin’s construction; test of the periodic structure; numerical simulations Citations:Zbl 0392.62073 PDF BibTeX XML Cite \textit{T. Cipra}, Apl. Mat. 30, 218--229 (1985; Zbl 0586.62146) Full Text: EuDML References: [1] J. Anděl: Statistical analysis of periodic autoregression. Aplikace matematiky 28 (1983). 364-385. · Zbl 0537.62073 [2] T. W. Anderson: An Introduction to Multivariate Statistical Analysis. Wiley, New York 1958. · Zbl 0083.14601 [3] W. P. Cleveland G. C. Tiao: Modeling seasonal time series. Revue Economic Appliquée 32, (1979), 107-129. [4] H. Cramér: Mathematical Methods of Statistics. Princeton University Press, Princeton 1946. · Zbl 0063.01014 [5] J. Durbin: Efficient estimation of parameters in moving average models. Biometrika 46 (1959), 306-316. · Zbl 0097.34602 [6] R. H. Jones W. M. Brelsford: Time series with periodic structure. Biometrika 54 (1967), 403-408. · Zbl 0153.47706 [7] H. J. Newton: Using periodic autoregressions for multiple spectral estimation. Technometrics 24 (1982), 109-116. · Zbl 0485.62109 [8] M. Pagano: On periodic and multiple autoregressions. Ann. Statist. 6 (1978), 1310-1317. · Zbl 0392.62073 [9] G. C. Tiao M. R. Grupe: Hidden periodic autoregressive-moving average models in time series data. Biometrika 67 (1980), 365-373. · Zbl 0436.62076 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.