For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined. However, except for some specific cases, little is known about the estimation of the memory parameter for nonlinear processes. The purpose of this paper is to provide general conditions under which the local Whittle estimator of the memory parameter of a stationary process is consistent and to examine its rate of convergence. We show that these conditions are satisfied for linear processes and a wide class of nonlinear models, among others, signal plus noise processes, nonlinear transforms of a Gaussian process, and EGARCH models. Special cases where the estimator satisfies the central limit theorem are discussed. The finite sample performance of the estimator is investigated in a Monte-Carlo study.
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Paper provided by Department of Economics, University of York in its series Discussion Papers with number
05/17.
Length: Date of creation: Date of revision: Handle: RePEc:yor:yorken:05/17
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Ghysels, E. & Harvey, A. & Renault, E., 1995.
"Stochastic Volatility,"
Papers
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Other versions:
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Universite de Montreal, Departement de sciences economiques.
[Downloadable!]
Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005.
"Estimating Long Memory in Volatility,"
Econometrica,
Econometric Society, vol. 73(4), pages 1283-1328, 07.
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