Estimation Methods of the Long Memory Parameter: Monte Carlo Analysis and Application
Since the seminal paper of Granger & Joyeux (1980), the concept of a long memory has focused the attention of many statisticians and econometricians trying to model and measure the persistence of stationary processes. Many methods for estimating d, the long-range dependence parameter,
have been suggested since the work of Hurst (1951). They can be summarized in three classes: the heuristic methods, the semi-parametric methods and the maximum likelihood methods. In this paper, we try by simulation, to verify the two main properties of dˆ: the consistency
and the asymptotic normality. Hence, it is very important for practitioners to compare the performance of the various classes of estimators. The results indicate that only the semi-parametric and the maximum likelihood methods can give good estimators. They also suggest that the AR component
of the ARFIMA (1, d, 0) process has an important impact on the properties of the different estimators and that the Whittle method is the best one, since it has the small mean squared error. We finally carry out an empirical application using the monthly seasonally adjusted US Inflation series,
in order to illustrate the usefulness of the different estimation methods in the context of using real data.
Keywords: ARFIMA (p d q) process; Long memory; Monte Carlo study; fractional Gaussian noise
Document Type: Research Article
Affiliations: GREQAM, Université de la Méditerranée, Marseille, France
Publication date: 01 April 2007
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