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Consistent estimation of the memory parameter for nonlinear time series

  • V Dalla
  • L Giraitis
  • J Hidalgo

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.

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Handle: RePEc:yor:yorken:05/17
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  1. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, 07.
  2. Robinson, P. M., 2001. "The memory of stochastic volatility models," Journal of Econometrics, Elsevier, vol. 101(2), pages 195-218, April.
  3. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Yixiao Sun & Peter C.B. Phillips, 2002. "Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes," Cowles Foundation Discussion Papers 1366, Cowles Foundation for Research in Economics, Yale University.
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  6. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
  7. ANDREWS, DONALD W & Sun, Yixiao X, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence," University of California at San Diego, Economics Working Paper Series qt9wt048tt, Department of Economics, UC San Diego.
  8. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  9. Arteche, Josu, 2004. "Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models," Journal of Econometrics, Elsevier, vol. 119(1), pages 131-154, March.
  10. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  11. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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