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Rate Optimal Semiparametric Estimation of the Memory Parameter of the Gaussian Time Serieswith Long-Range Dependence - (Now published in 'Journal of Time Series Analysis', 18 (1997), pp.49-60.)

Author

Listed:
  • Liudas Giraitis
  • Peter M Robinson
  • Alexander Samarov

Abstract

There exist several estimators of the memory parameter in long-memory time series models with mean µ and the spectrum specified only locally near zero frequency. In this paper we give a lower bound for the rate of convergence of any estimator of the memory parameter as a function of the degree of local smoothness of the spectral density at zero. The lower bound allows one to evaluate and compare different estimators by their asymptotic behaviour, and to claim the rate optimality for any estimator attaining the bound. The log-periodogram regression estimator, analysed by Robinson (1992), is then shown to attain the lower bound, and is thus rate optimal.

Suggested Citation

  • Liudas Giraitis & Peter M Robinson & Alexander Samarov, 1997. "Rate Optimal Semiparametric Estimation of the Memory Parameter of the Gaussian Time Serieswith Long-Range Dependence - (Now published in 'Journal of Time Series Analysis', 18 (1997), pp.49-60.)," STICERD - Econometrics Paper Series 323, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:323
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    Cited by:

    1. Michelacci, Claudio, 2004. "Cross-sectional heterogeneity and the persistence of aggregate fluctuations," Journal of Monetary Economics, Elsevier, vol. 51(7), pages 1321-1352, October.
    2. 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.
    3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    4. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    5. Claudio Michelacci, 1999. "Cross-Sectional Heterogeneity and the Persistence of Aggregate Fluctuations," Working Papers wp1999_9906, CEMFI.
    6. Robinson, Peter M., 2014. "The estimation of misspecified long memory models," LSE Research Online Documents on Economics 53692, London School of Economics and Political Science, LSE Library.
    7. Hidalgo, Javier, 2005. "Semiparametric estimation for stationary processes whose spectra have an unknown pole," LSE Research Online Documents on Economics 6842, London School of Economics and Political Science, LSE Library.
    8. Javier Hidalgo, 2005. "Semiparametric Estimation for Stationary Processes whose Spectra have an Unknown Pole," STICERD - Econometrics Paper Series 481, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Robinson, Peter M., 2014. "The estimation of misspecified long memory models," Journal of Econometrics, Elsevier, vol. 178(P2), pages 225-230.
    10. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2012. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 8/12, Monash University, Department of Econometrics and Business Statistics.

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