Anděl, Jiří Statistical analysis of periodic autoregression. (English) Zbl 0537.62073 Apl. Mat. 28, 364-385 (1983). This article describes methods for estimating parameters and testing hypotheses in a periodic autoregression. The statistical analysis is based on the Bayes approach. The parameters of the model are supposed to be random variables with a vague prior density. The innovation process can have either constant or periodically changing variances. Theoretical results are demonstrated on two simulated series and on two sets of real data. Reviewer: H.Hietikko Cited in 1 ReviewCited in 6 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F15 Bayesian inference Keywords:periodic autoregression; vague prior density; innovation process; changing variances; simulated series; real data PDF BibTeX XML Cite \textit{J. Anděl}, Apl. Mat. 28, 364--385 (1983; Zbl 0537.62073) Full Text: EuDML OpenURL References: [1] J. Anděl: The Statistical Analysis of Time Series. SNTL, Prague 1976 [2] J. Anděl: Mathematical Statistics. SNTL, Prague, 1978 [3] G. E. P. Box G. M. Jenkins: Time Series Analysis, Forecasting and Control. Holden Day, San Francisco, 1970. · Zbl 0249.62009 [4] G. E. P. Box G. C. Tiao: Intervention analysis with applications to economic and environmental problems. J. Amer. Statist. Assoc. 70 (1975), 70-79. · Zbl 0316.62045 [5] W. P. Cleveland G. C. Tiao: Modeling seasonal time series. Rev. Economic Appliquée 32 (1979), 107-129. [6] E. G. Gladyshev: Periodically correlated random sequences. Soviet Math. 2 (1961), 385-388. · Zbl 0212.21401 [7] E. G. Gladyshev: Periodically and almost periodically correlated random processes with continuous time parameter. Theory Prob. Appl. 8 (1983), 173-177. · Zbl 0138.11003 [8] J. Janko: Statistical Tables. NČSAV, Prague, 1958 [9] N. L. Johnson S. Kotz: Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York, 1972. · Zbl 0248.62021 [10] R. H. Jones W. M. Brelsford: Time series with periodic structure. Biometrika 54 (1967), 403-408. · Zbl 0153.47706 [11] H. J. Newton: Using periodic autoregression for multiple spectral estimation. Technometrics 24 (1982), 109-116. · Zbl 0485.62109 [12] M. Pagano: On periodic and multiple autoregression. Ann. Statist. 6 (1978), 1310-1317. · Zbl 0392.62073 [13] C. G. Tiao M. R. Grupe: Hidden periodic autoregressive-moving average models in time series data. Biometrika 67 (1980), 365-373. · Zbl 0436.62076 [14] A. Zellner: An Introduction to Bayesian Inference in Econometrics. Wiley, New York, 1971. · Zbl 0246.62098 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.