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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). doi:10.1103/PhysRevE.79.036109
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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 | ||||
| Official Date: | 17 March 2009 | ||||
| Dates: |
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| Volume: | Vol.79 | ||||
| Number: | No.3 | ||||
| DOI: | 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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