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The accurate estimation of scaling exponents is central in the observationalstudy of scale-invariant phenomena. Natural systems unavoidably provideobservations over restricted intervals; consequently a stationary stochasticprocess (time series) can yield anomalous time variation in the scalingexponents, suggestive of non-stationarity. The variance in the estimates ofscaling exponents computed from an interval of N observations is known forfinite variance processes to vary as ~1/N as N goes to infinity for certainstatistical estimators; however, the convergence to this behaviour will dependon the details of the process, and may be slow. We study the variation in thescaling of second order moments of the time series increments with N, for avariety of synthetic and `real world' time series; and find that in particularfor heavy tailed processes, for realizable N, one is far from this 1/N limitingbehaviour. We propose a semi-empirical estimate for the minimum N needed tomake a meaningful estimate of the scaling exponents for model stochasticprocesses and compare these with some `real world' time series.

Pseudo-nonstationarity in the scaling exponents of finite interval time series