Consistent estimation of the memory parameter for nonlinear time series
AbstractFor linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties are well established. 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 ξt 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 small Monte-Carlo study
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Bibliographic InfoPaper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 6813.
Length: 36 pages
Date of creation: Jan 2006
Date of revision:
Long memory; semiparametric estimation; local Whittle estimator;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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