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Pseudononstationarity in the scaling exponents of finiteinterval time series
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Kiyani, K., Chapman, Sandra C. and Watkins, Nicholas W.. (2009) Pseudononstationarity in the scaling exponents of finiteinterval time series. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol.79 (No.3). ISSN 15393755

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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 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 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:  Journal Article 

Subjects:  Q Science > QC Physics 
Divisions:  Faculty of Science > Physics 
Library of Congress Subject Headings (LCSH):  Timeseries 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:  15393755 
Official 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) 
References:  [1] U. Frisch, Turbulence (Cambridge University Press, 
URI:  http://wrap.warwick.ac.uk/id/eprint/595 
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