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Variance-type estimation of long memory

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  • Giraitis, Liudas
  • Robinson, Peter M.
  • Surgailis, Donatas

Abstract

The aggregation procedure when a sample of length N is divided into blocks of length m=o(N), m-->[infinity] and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu et al. (1995, Fractals, 3, 785-798), and Teverovsky and Taqqu (1997, J. Time Ser. Anal., 18, 279-304) introduced an aggregated variance estimator of the long-memory parameter of a stationary sequence with long range dependence and studied its empirical performance. With respect to autocovariance structure and marginal distribution, the aggregated series is closer to Gaussian fractional noise than the initial series. However, the variance type estimator based on aggregated data is seriously biased. A refined estimator, which employs least-squares regression across varying levels of aggregation, has much smaller bias, permitting deriviation of limiting distributional properties of suitably centered estimates, as well as of a minimum-mean squared error choice of bandwidth m. The results vary considerably with the actual value of the memory parameter.

Suggested Citation

  • Giraitis, Liudas & Robinson, Peter M. & Surgailis, Donatas, 1999. "Variance-type estimation of long memory," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 1-24, March.
    • Handle: RePEc:eee:spapps:v:80:y:1999:i:1:p:1-24
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    References listed on IDEAS

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    1. Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Lobato, I. & Robinson, P. M., 1996. "Averaged periodogram estimation of long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 303-324, July.
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    Cited by:

    1. Rea, William & Oxley, Les & Reale, Marco & Brown, Jennifer, 2013. "Not all estimators are born equal: The empirical properties of some estimators of long memory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 29-42.
    2. Ting Zhang & Hwai-Chung Ho & Martin Wendler & Wei Biao Wu, 2013. "Block Sampling under Strong Dependence," Papers 1312.5807, arXiv.org.
    3. Kang, Taegyu & Kim, Young Min & Im, Jongho, 2021. "A note on stationary bootstrap variance estimator under long-range dependence," Statistics & Probability Letters, Elsevier, vol. 169(C).
    4. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Mutual information and persistence in the stochastic volatility of market returns: An emergent market example," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 36-59.
    5. Jennifer Brown & Les Oxley & William Rea & Marco Reale, 2008. "The Empirical Properties of Some Popular Estimators of Long Memory Processes," Working Papers in Economics 08/13, University of Canterbury, Department of Economics and Finance.
    6. Marco Dozzi & Yuliya Mishura & Georgiy Shevchenko, 2015. "Asymptotic behavior of mixed power variations and statistical estimation in mixed models," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 151-175, July.

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