Abstract:
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This paper proposes the possibility of using Laplace periodogram and quantile periodogram in analyzing long-memory process. Laplace periodogram, based on the LAD estimator, is a robust alternative to the ordinary periodogram and provide robust estimator in the presence of outliers or heavy-tailed distributed data. We extend the Laplace periodogram to the quantile periodogram and provide asymptotic distribution of the quantile periodogram for long-memory process. Through the simulation, we demonstrate that the usefulness of the proposed quantile periodogram under long-memory process. We also provide an application of the proposed robust periodogram under long-memory process, that is estimation of the long-memory parameter based on a log periodogram regression approach.
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