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Consistent estimation of the memory parameter for nonlinear time series

Author

Listed:
  • V Dalla
  • L Giraitis
  • J Hidalgo

Abstract

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.

Suggested Citation

  • V Dalla & L Giraitis & J Hidalgo, "undated". "Consistent estimation of the memory parameter for nonlinear time series," Discussion Papers 05/17, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:05/17
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    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; Diffusion Processes

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