On a class of M-estimators for Gaussian long-memory models

Beran, Jan

On a class of M-estimators for Gaussian long-memory models

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Date

1994

Publication type

Journal article

Published in

Biometrika ; 81 (1994), 4. - pp. 755-766. - ISSN 0006-3444

Abstract

We consider estimation for parametric stationary Gaussian models with long memory. The spectral density f(x; θ) is assumed to be characterised by a vector θ = (θ1, θ2, θ3,…, θm) such that θ2 = H ε (½, 1) and f(x; θ) is proportional to x1−2H as x tends to zero. An approximate maximum likelihood estimator based on the autoregressive representation of the process is proposed. Its asymptotic distribution is derived. More generally, the approach leads to a class of M-estimators for which a central limit theorem holds. By choosing an appropriate ψ-function, robustness against additive outliers can be achieved, while keeping high efficiency under the ideal model. This is illustrated by a small simulation study. A simple algorithm and an explicit formula for the efficiency, and thus for choosing an appropriate tuning parameter, are given for Hampel's redescending ψ-function.

Subject (DDC)

510 Mathematics

Keywords

Autoregressive,Fractional ARIMA,Influence function,Long-range dependence,Maximum likelihood estimation,Redescending function,Robustness

Cite This

ISO 690

BERAN, Jan, 1994. On a class of M-estimators for Gaussian long-memory models. In: Biometrika. 81(4), pp. 755-766. ISSN 0006-3444. Available under: doi: 10.1093/biomet/81.4.755

BibTex

@article{Beran1994class-18822,
  year={1994},
  doi={10.1093/biomet/81.4.755},
  title={On a class of M-estimators for Gaussian long-memory models},
  number={4},
  volume={81},
  issn={0006-3444},
  journal={Biometrika},
  pages={755--766},
  author={Beran, Jan}
}

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