M-estimation of the long-memory parameter by Laplace periodogram

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.