On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models
25 Pages Posted: 31 Oct 2008
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On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models
On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models
Date Written: 1998
Abstract
We consider semiparametric estimation of the memory parameter in a long memorystochastic volatility model. We study the estimator based on a log periodogramregression as originally proposed by Geweke and Porter-Hudak (1983,Journal of Time Series Analysis 4, 221âÃÂÃÂ"238). Expressions for the asymptotic biasand variance of the estimator are obtained, and the asymptotic distribution is shownto be the same as that obtained in recent literature for a Gaussian long memoryseries. The theoretical result does not require omission of a block of frequenciesnear the origin. We show that this ability to use the lowest frequencies is particularlydesirable in the context of the long memory stochastic volatility model.
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