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Pseudo-nonstationarity in the scaling exponents of finite-interval time series

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Kiyani, K., Chapman, Sandra C. and Watkins, Nicholas W.. (2009) Pseudo-nonstationarity in the scaling exponents of finite-interval time series. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.79 (No.3). ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.79.036109

Abstract

The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently, a stationary stochastic process (time series) can yield anomalous time variation in the scaling exponents, suggestive of nonstationarity. The variance in the estimates of scaling exponents computed from an interval of N observations is known for finite variance processes to vary as ~1/N as N for certain statistical estimators; however, the convergence to this behavior will depend on the details of the process, and may be slow. We study the variation in the scaling of second-order moments of the time-series increments with N for a variety of synthetic and “real world” time series, and we find that in particular for heavy tailed processes, for realizable N, one is far from this ~1/N limiting behavior. We propose a semiempirical estimate for the minimum N needed to make a meaningful estimate of the scaling exponents for model stochastic processes and compare these with some “real world” time series.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Divisions:	Faculty of Science > Physics
Library of Congress Subject Headings (LCSH):	Time-series analysis, Stochastic models, Scaling laws (statistical physics)
Journal or Publication Title:	Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Publisher:	American Physical Society
ISSN:	1539-3755
Date:	17 March 2009
Volume:	Vol.79
Number:	No.3
Identification Number:	10.1103/PhysRevE.79.036109
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Science and Technology Facilities Council (Great Britain) (STFC), Engineering and Physical Sciences Research Council (EPSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/595