Pseudononstationarity in the scaling exponents of finite-interval time series
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.
Privacy & Cookies Policy
Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.