# Asymptotic distribution of time-series intermittency estimates: applications to economic and clinical data

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- Elsevier B.V.
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## Abstract

The intermittency of a time series can be defined as its normalized difference in scaling parameters. We establish the central limit theorem for the estimates of intermittency under the null hypothesis of a random walk. Simulations of random walks indicate that the distribution of intermittency estimates is slightly negatively skewed and positively biased, but that the skewness and bias approach zero as the length n of the random walks increases. We provide a formula by which the sample variance of the intermittency estimates of these simulations can be used to approximate the standard error of the intermittency for any large n. These results can be used to test whether the intermittency estimate of an observed long time series is significantly greater than zero, the intermittency of a random walk. This test reveals that the intermittency estimates of the S& P 500 index and of the heart rate of a human adult are significantly positive. The hypothesis testing proposed in this paper can also be applied to other observed time series to determine whether their intermittency estimates are sufficiently high for the series to be considered intermittent, or whether their estimates are small enough to be consistent with a random walk.

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