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On the detection of superdiffusive behaviour in time series
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Gottwald, Georg A. and Melbourne, Ian (2016) On the detection of superdiffusive behaviour in time series. Journal of Statistical Mechanics: Theory and Experiment, 2016 . 123205. doi:10.1088/1742-5468/aa4f0f ISSN 1742-5468.
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Official URL: https://doi.org/10.1088/1742-5468/aa4f0f
Abstract
We present a new method for detecting superdiffusive behaviour and for determining rates of superdiffusion in time series data. Our method applies equally to stochastic and deterministic time series data (with no prior knowledge required of the nature of the data) and relies on one realisation (ie one sample path) of the process. Linear drift effects are automatically removed without any preprocessing. We show numerical results for time series constructed from i.i.d. α-stable random variables and from deterministic weakly chaotic maps. We compare our method with the standard method of estimating the growth rate of the mean-square displacement as well as the p-variation method, maximum likelihood, quantile matching and linear regression of the empirical characteristic function.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Journal or Publication Title: | Journal of Statistical Mechanics: Theory and Experiment | ||||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||||
| ISSN: | 1742-5468 | ||||||
| Official Date: | 19 December 2016 | ||||||
| Dates: |
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| Volume: | 2016 | ||||||
| Article Number: | 123205 | ||||||
| DOI: | 10.1088/1742-5468/aa4f0f | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 1 December 2016 | ||||||
| Date of first compliant Open Access: | 19 December 2017 |
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