Estimating seasonal long-memory processes: a Monte Carlo study

Abstract

This paper discusses extensions of the popular methods proposed by Geweke and Porter-Hudak [Geweke, J. and Porter-Hudak, S., 1983, The estimation and application of long memory times series models. Journal of Time Series Analysis, 4(4), 221–238.] and Fox and Taqqu [Fox, R. and Taqqu, M.S., 1986, Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics, 14, 517–532.] 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 in Beran [Beran, J., 1994, Statistic for Long-Memory Processes (New York: Chapman & Hall).] and the semi-parametric approaches introduced by Arteche and Robinson [Arteche, J. and Robinson, P.M., 2000, Semiparametric inference in seasonal and cyclical long memory processes. Journal of Time Series Analysis, 21(1), 1–25.] 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.

Keywords:

• Fractional differencing
• Long-memory
• Periodogram regression
• Seasonality
• Whittle maximum likelihood procedure

Acknowledgements

The first two authors gratefully acknowledge partial financial support from PIBIC-UFES and CNPq/Brazil. The third author was partially supported by Fondecyt grant number 1040934. We also would like to thank Ricardo Olea for carrying out part of the Monte Carlo experiments, and the referee of the JSCS for his contribution to the improvement of the paper.