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. 10.1103/PhysRevE.79.036109Before downloading, please read NORA policies.
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):||10.1103/PhysRevE.79.036109|
|Programmes:||BAS Programmes > Global Science in the Antarctic Context (2005-2009) > Natural Complexity Programme|
|NORA Subject Terms:||Physics
|Date made live:||04 Aug 2009 15:28|
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