Pseudononstationarity in the scaling exponents of finite-interval time series

Kiyani, K.H.; Chapman, S.C.; Watkins, N.W.. 2009 Pseudononstationarity in the scaling exponents of finite-interval time series. Physical Review E, 79, 036109. 11, pp. https://doi.org/10.1103/PhysRevE.79.036109

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Abstract/Summary

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→ infinity 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:	Publication - Article
Digital Object Identifier (DOI):	https://doi.org/10.1103/PhysRevE.79.036109
Programmes:	BAS Programmes > Global Science in the Antarctic Context (2005-2009) > Natural Complexity Programme
NORA Subject Terms:	Physics Mathematics Space Sciences
Related URLs:	Author's Homepage
Date made live:	04 Aug 2009 15:28 +0 (UTC)
URI:	https://nora.nerc.ac.uk/id/eprint/7609

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