Testing for a change of the long-memory parameter

Beran, Jan; Terrin, Norma

Testing for a change of the long-memory parameter

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Date

1996

Authors

Beran, Jan

Terrin, Norma

Publication type

Journal article

Published in

Biometrika ; 83 (1996), 3. - pp. 627-638

Abstract

Long-range dependence is often observed in long time series. Correlations decay approximately like |k|2H-2, with H ε (0.5, 1), as the lag k tends to infinity. The long-term features of the data are essentially characterised by the parameter H. Small changes of H have strong implications for the long-term behaviour of the process. In particular, rates of convergence of estimators for the mean, and for many other parameters of interest, differ for different values of H. For some data sets, H appears to change with time. In this paper we consider a simple test of the null hypothesis that H is constant. The test is based on a functional central limit theorem for quadratic forms. Critical values for the test statistic are given. Simulations confirm the validity of the test. A data example illustrates its practical application.

Subject (DDC)

510 Mathematics

Keywords

Change point,fractional ARIMA,Fractional Gaussian Noise,Long-range dependence,quadratic forms,stationarity

Cite This

ISO 690

BERAN, Jan, Norma TERRIN, 1996. Testing for a change of the long-memory parameter. In: Biometrika. 83(3), pp. 627-638. Available under: doi: 10.1093/biomet/83.3.627

BibTex

@article{Beran1996Testi-18829,
  year={1996},
  doi={10.1093/biomet/83.3.627},
  title={Testing for a change of the long-memory parameter},
  number={3},
  volume={83},
  journal={Biometrika},
  pages={627--638},
  author={Beran, Jan and Terrin, Norma}
}

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