Pseudononstationarity in the scaling exponents of finiteinterval time series
Kiyani, K.H.; Chapman, S.C.; Watkins, N.W.. 2009 Pseudononstationarity in the scaling exponents of finiteinterval time series. Physical Review E, 79, 036109. 11, pp. 10.1103/PhysRevE.79.036109
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Abstract/Summary
The accurate estimation of scaling exponents is central in the observational study of scaleinvariant 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 secondorder moments of the timeseries 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):  10.1103/PhysRevE.79.036109 
Programmes:  BAS Programmes > Global Science in the Antarctic Context (20052009) > Natural Complexity Programme 
NORA Subject Terms:  Physics Mathematics Space Sciences 
Related URLs:  
Date made live:  04 Aug 2009 15:28 
URI:  http://nora.nerc.ac.uk/id/eprint/7609 
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