Anděl, Jiři; Rubio, Asunción; Insua, Antonio On periodic autoregression with unknown mean. (English) Zbl 0585.62152 Apl. Mat. 30, 126-139 (1985). Periodic autoregressive models of the form \(X_ t- \sum^{p}_{1}b_{ti}X_{t-i}=\epsilon_ t,\) where the time-varying coefficients \(b_{ti}\) are periodical functions of time, and \(\{\epsilon_ t\}\) is a Gaussian white noise (mean zero, variance \(\sigma^ 2)\), have been studied in detail in a previous paper by the first author, ibid. 28, 364-385 (1983; Zbl 0537.62073). The previous results are extended here to the more general case where \(X_ t\) has an unknown mean \(\mu_ t\), itself a periodical function of time: \[ (X_ t-\mu_ t)-\sum^{p}_{1}b_{ti}(X_{t-i}-\mu_{t- i})=\epsilon_ t; \] the innovation variance \(E(\epsilon^ 2_ t)\) can also be considered periodical. Periodical autoregressions should provide interesting models for seasonal series. A Bayesian approach is adopted, which however leads to results that are asymptotically equivalent to those of Gaussian maximum likelihood methods. Reviewer: M.Hallin Cited in 3 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F15 Bayesian inference Keywords:estimating parameters; testing hypotheses; Periodic autoregressive models; time-varying coefficients; Gaussian white noise; unknown mean; innovation; seasonal series; Gaussian maximum likelihood methods Citations:Zbl 0537.62073 × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] J. Anděl: Statistical analysis of periodic autoregression. Apl. mat. 28 (1983), 364-365. · Zbl 0537.62073 [2] 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 · doi:10.2307/2285379 [3] E. G. Gladyshev: Periodically correlated random sequences. Soviet Math. 2 (1961), 385-388. · Zbl 0212.21401 [4] E. G. Gladyshev: Periodically and almost periodically correlated random process with continuous time parameter. Theory Prob. Appl. 8 (1963), 173-177. · Zbl 0138.11003 [5] M. Pagano: On periodic and multiple autoregression. Ann. Statist. 6 (1978), 1310-1317. · Zbl 0392.62073 · doi:10.1214/aos/1176344376 [6] 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.