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A power-law model and other models for long-range dependence

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

R. J. Martin  and
A. M. Walker
R. J. Martin*
Affiliation:
University of Sheffield
A. M. Walker*
Affiliation:
University of Sheffield
*
∗Postal address: School of Mathematics and Statistics, The University of Sheffield, Sheffield S3 7RH, UK.
∗Postal address: School of Mathematics and Statistics, The University of Sheffield, Sheffield S3 7RH, UK.
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Abstract

It is becoming increasingly recognized that some long series of data can be adequately and parsimoniously modelled by stationary processes with long-range dependence. Some new discrete-time models for long-range dependence or slow decay, defined by their correlation structures, are discussed. The exact power-law correlation structure is examined in detail.

Keywords

LONG MEMORYPERSISTENCESLOW DECAY

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60G10: Stationary processes 60G18: Self-similar processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 657 - 670
Copyright
Copyright © Applied Probability Trust 1997 

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References

Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Bartlett, M. S. (1975) The Statistical Analysis of Spatial Pattern. Chapman and Hall, London.Google Scholar
Beran, J. (1992) Statistical methods for data with long-range dependence (with discussion). Statist. Sci. 4, 404–427.Google Scholar
Beran, J. (1993) Fitting long-memory models by generalized linear regression. Biometrika 80, 817–822.CrossRefGoogle Scholar
Beran, J. (1994) Statistics for Long-Memory Processes. Chapman and Hall, London.Google Scholar
Besag, J. (1981) On a system of two-dimensional recurrence equations. J. R. Statist. Soc. B 43, 302–309.Google Scholar
Brockwell, P. J. and Davis, R. A. (1987) Time Series: Theory and Methods. Springer, New York.CrossRefGoogle Scholar
Cox, D. R. (1984) Long-range dependence: a review. In: Statistics: an Appraisal. ed. David, H. A. and David, H. T. Iowa State University Press, Iowa. pp. 55–74.Google Scholar
Edwards, H. M. (1974) Riemann's Zeta Function. Academic Press, New York.Google Scholar
Gradshteyn, I. S. and Ryzhik, I. M. (1980) Tables of Integrals, Series and Products. 2nd edn. Academic Press, New York.Google Scholar
Hosking, J. R.M. (1981) Fractional differencing. Biometrika 68, 165–176.Google Scholar
Martin, R.J. and Eccleston, J. A. (1992) A new model for slowly-decaying correlations. Statist. Prob. Lett. 13, 139–145.Google Scholar
Matérn, B. (1986) Spatial Variation. 2nd edn. Springer, Berlin.Google Scholar
Newbold, P. and Agiakloglou, C. (1993) Bias in the sample autocorrelations of fractional noise. Biometrika 80, 698–702.Google Scholar
Smith, R. L. (1993) Long-range dependence and global warming. In: Statistics for the Environment. ed. Barnett, V. and Turkman, K. F. Wiley, Chichester. pp. 144–161.Google Scholar
Spolia, S. K. Chander, S. and O'Connor, K. M. (1980) An autocorrelation approach for parameter estimation of fractional order equal-root autoregressive models using hypergeometric functions. J. Hydrol. 47, 1–17.CrossRefGoogle Scholar
Titchmarsh, E. C. and Heath-Brown, D. R. (1986) The Theory of the Riemann Zeta Function. 2nd edn. Clarendon Press, Oxford.Google Scholar
Yajima, Y. (1988) On estimation of a regression model with long-memory stationary errors. Ann. Statist. 16, 791–807.CrossRefGoogle Scholar
Yajima, Y. (1991) Asymptotic properties of the LSE in a regression model with long-memory stationary errors. Ann. Statist. 19, 158–177.Google Scholar
Zygmund, A. (1959) Trigonometric Series. Vol. I. Cambridge University Press, Cambridge.Google Scholar