Estimation of the long-memory parameter, based on a multivariate central limit theorem

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1994
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Terrin, Norma
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Zusammenfassung

Long memory is known to occur in many fields of statistical application. Stationary processes whose correlations decay asymptotically like ‖k‖2H-2, where k is the lag and Hε (0.5, 1), provide useful parsimonious models with long memory. The parameter H characterizes the long-memory features of the data. For long time series, maximum likelihood estimation of H can be costly in terms of CPU time. In this paper, we show that, for disjoint stretches of the data, estimates of H and other parameters that characterize the dependence structure are asymptotically independent. Averaging these estimates leads to a fast and efficient approximate maximum likelihood method.

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510 Mathematik
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Long-range dependence, fractional Gaussian noise, fractional ARIMA, self-similar, quadratic forms, maximum likelihood estimator
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ISO 690BERAN, Jan, Norma TERRIN, 1994. Estimation of the long-memory parameter, based on a multivariate central limit theorem. In: Journal of Time Series Analysis. 1994, 15(3), pp. 269-278. ISSN 0143-9782. Available under: doi: 10.1111/j.1467-9892.1994.tb00192.x
BibTex
@article{Beran1994Estim-18821,
  year={1994},
  doi={10.1111/j.1467-9892.1994.tb00192.x},
  title={Estimation of the long-memory parameter, based on a multivariate central limit theorem},
  number={3},
  volume={15},
  issn={0143-9782},
  journal={Journal of Time Series Analysis},
  pages={269--278},
  author={Beran, Jan and Terrin, Norma}
}
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