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Correlation models with long-range dependence

Part of: Stochastic processes Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Chunsheng Ma
Chunsheng Ma*
Affiliation:
Wichita State University
*
∗ Postal address: Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260-0033, USA. Email address: cma@math.twsu.edu
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Abstract

This paper is concerned with the correlation structure of a stationary discrete time-series with long memory or long-range dependence. Given a sequence of bounded variation, we obtain necessary and sufficient conditions for a function generated from the sequence to be a proper correlation function. These conditions are applied to derive various slowly decaying correlation models. To obtain correlation models with short-range dependence from an absolutely summable sequence, a simple method is introduced.

Keywords

Correlationlong memoryshort memoryslow decayspectral density

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 39 , Issue 2 , June 2002 , pp. 370 - 382
Copyright
Copyright © Applied Probability Trust 2002 

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References

Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics. J. Econometrics 73, 5–59.CrossRefGoogle Scholar
Beran, J. (1992). Statistical methods for data with long-range dependence (with discussion). Statist. Sci. 4, 404–427.Google Scholar
Beran, J. (1994). Statistics for Long-Memory Processes. Chapman and Hall, New York.Google Scholar
Cox, D. R. (1984). Long-range dependence: a review. In Statistics: an Appraisal, eds David, H. A. and David, H. T., Iowa State University Press, Iowa, pp. 55–74.Google Scholar
Gneiting, T. (2000). Power-law correlations, related models for long-range dependence and their simulation. J. Appl. Prob. 37, 1104–1109.CrossRefGoogle Scholar
Hardy, G. H. (1949). Divergent Series. Oxford University Press.Google Scholar
McLeod, A. I., and Hipel, K. W. (1978). Preservation of the rescaled adjusted range, 1: A reassessment of the Hurst phenomenon. Water Resources Res. 14, 491–508.CrossRefGoogle Scholar
Martin, R. J., and Eccleston, J. A. (1992). A new model for slowly-decaying correlations. Statist. Prob. Lett. 13, 139–145.CrossRefGoogle Scholar
Martin, R. J., and Walker, A. M. (1997). A power-law model and other models for long-range dependence. J. Appl. Prob. 34, 657–670.CrossRefGoogle Scholar
Varga, R. S. (2000). Matrix Iterative Analysis, 2nd edn. Springer, Berlin.CrossRefGoogle Scholar
Wold, H. (1954). A Study in the Analysis of Stationary Time Series, 2nd edn. Almqvist and Wiksell, Stockholm.Google Scholar
Zygmund, A. (1959). Trigonometric Series, Vol. I, 2nd edn. Cambridge University Press.Google Scholar