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covariance function; multivariate AR(1) process; Hilbert space projections; periodic autoregressive processes; seasonal time series; interpolation
The periodic autoregressive processes are useful in statistical analysis of seasonal time series. Some procedures (e.g. extrapolation) are quite analogous to those in the clasical autoregressive models. The problem of interpolation needs, however, some special methods. They are demonstrated in the paper on the case of the process of the second order with the period of length 2.
[1] J. Anděl: On interpolation of multiple autoregressive processes. Contributions to Statistics (Jaroslav Hájek Memorial Volume), 13-17, Academia, Prague 1979. MR 0561253
[2] J. Anděl: Statistical analysis of periodic autoregression. Apl. mat. 28 (1983), 364-385. MR 0712913
[3] J. Anděl A. Rubio A. Insua: On periodic autoregression with unknown mean. Apl. mat. 30 (1985), 126-139. MR 0778983
[4] D. G. Luenberger: Optimization by Vector Space Methods. Wiley, New York 1969. MR 0238472 | Zbl 0176.12701
[5] H. Neudecker: Some theorems on matrix differentiation with special reference to Kronecker matrix products. J. Amer. Statist. Assoc. 64 (1969), 953 - 963. DOI 10.1080/01621459.1969.10501027 | Zbl 0179.33102
[6] M. Pagano: On periodic and multiple autoregression. Ann. Statist. 6 (1978), 1310-1317. DOI 10.1214/aos/1176344376 | MR 0523765
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