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Variance-type estimation of long memory

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  • Giraitis, Liudas
  • Robinson, Peter M.

Abstract

The aggregation procedure when a sample of length N is divided into blocks of length m = o(N), m ® ¥ and observations in each block are replaced by their sample mean, is widely used in statistical inference. Taqqu, Teverovsky and Willinger (1995), Teverovsky and Taqqu (1997) introduced an aggregate variance estimator of the long memory parameter of a stationary sequence with long range dependence and studied its empirial performance. With respect to autovariance 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 derivation 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., 1998. "Variance-type estimation of long memory," LSE Research Online Documents on Economics 2327, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2327
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    File URL: http://eprints.lse.ac.uk/2327/
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    References listed on IDEAS

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    1. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, October.
    2. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, October.
    3. 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.
    4. 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. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.

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    More about this item

    Keywords

    Long memory; aggregation; semiparametric model;
    All these keywords.

    JEL classification:

    • 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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