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Estimating seasonal long-memory processes: a Monte Carlo study. (English) Zbl 1157.62495

Summary: This paper discusses extensions of the popular methods proposed by J. Geweke and S. Porter-Hudak [J. Time Ser. Anal. 4, 221–238 (1983; Zbl 0534.62062)] and R. Fox and M.S. Taqqu [Ann. Stat. 14, 517–532 (1986; Zbl 0606.62096)] for estimating the long-memory parameter of autoregressive fractionally integrated moving average models to the estimation of long-range dependent models with seasonal components. The proposed estimates are obtained from a selection of harmonic frequencies chosen between the seasonal frequencies. The maximum likelihood method given by J. Beran [Statistics for long-memory processes. New York: Chapman & Hall (1994; Zbl 0869.60045)] and the semi-parametric approaches introduced by J. Arteche and P. M. Robinson [J. Time Ser. Anal. 21, No. 1, 1–25 (2000; Zbl 0974.62079)] are also considered in the study. Our finite sample Monte Carlo investigations indicate that the proposed methods perform well and can be used as alternative estimating procedures when the data display both long-memory and cyclical behavior.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F10 Point estimation
62F35 Robustness and adaptive procedures (parametric inference)

Software:

longmemo; FinTS
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References:

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