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Convex combinations of long memory estimates from different sampling rates

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Abstract

This paper investigates convex combinations of long memory estimates from both the original and sub-sampled data. Sub-sampling is carried out by decreasing the sampling rate, which leaves the long memory parameter unchanged. Any convex combination of these sub-sample estimates requires a preliminary correction for the bias observed at lower sampling rates, reported by Souza and Smith (2002). Through Monte Carlo simulations, we investigate the bias and the standard deviation of the combined estimates, as well as the root mean squared error (RMSE). Combining estimates can significantly lower the RMSE of a standard estimator (by about 30% on average for ARFIMA (0, d, 0) series), at the cost of inducing some bias.

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Notes

  1. 1 Note that the parameterisation of the MA polynomial differs in some works in the literature, in such a way that negative becomes positive and vice-versa.

  2. 2 Although it is calculated having the GPH in mind, for the SMGPH the phenomenon which leads to the bias is analogous and the approximation is still good.

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Acknowledgment

We are very grateful to two anonymous referees and an Associate Editor of this journal for very helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Catholic University, Rua Marquês de S. Vicente 225, CEP 22453-900, Rio de Janeiro, Brazil

    Leonardo R. Souza

  2. Department of Economics, University of Warwick, Warwick, CV4 7AL, UK

    Jeremy Smith

  3. Electrical Engineering Department, Catholic University, Rua Marquês de S. Vicente 225, CEP 22453-900, Rio de Janeiro, Brazil

    Reinaldo C. Souza

Authors
  1. Leonardo R. Souza
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  2. Jeremy Smith
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  3. Reinaldo C. Souza
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Correspondence to Leonardo R. Souza.

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Souza, L.R., Smith, J. & Souza, R.C. Convex combinations of long memory estimates from different sampling rates. Computational Statistics 21, 399–413 (2006). https://doi.org/10.1007/s00180-006-0002-3

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