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M-estimation of the long-memory parameter by Laplace periodogram
Journal of the Korean Data & Information Science Society 2018;29:523-32
Published online March 31, 2018
© 2018 Korean Data and Information Science Society.

Yaeji Lim1

1Department of Statistics, Pukyong National University
Correspondence to: Assistant professor, Department of Statistics, Pukyong National University, 1 Yongsoro, Nam-gu, Busan 48513, Korea. E-mail:
Received January 16, 2018; Revised January 31, 2018; Accepted February 12, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The estimation of the long-memory parameter is a crucial issue in the long-range dependent process. The log-regression method proposed by Geweke and Porter-Hudak (1983) is one of the popular semi-parametric approach to estimate the long-memory parameter. However, the conventional method is highly in uenced by the presence of outliers or heavy-tailed distributed errors. This paper investigates the possibility of using Laplace periodogram to analyze long-memory processes. Laplace periodogram derived by the least absolute deviations in the harmonic regression procedure is a robust alternative to the ordinary periodogram for spectral analysis. Numerical studies including simulation study and real data analysis are presented for the comparison.
Keywords : ARFIMA, Laplace periodogram, log periodogram regression, long-memory process, robustness.