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Parameter estimation for one-sided heavy-tailed distributions

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  • Kerger, Phillip
  • Kobayashi, Kei

Abstract

Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant periods. The lengths of the constant periods follow a one-sided distribution which involves a parameter between 0 and 1 and whose first moment does not exist. This paper constructs an estimator for the parameter, applying the method of moments to the number of observed constant periods in a fixed time interval. The resulting estimator is asymptotically unbiased and consistent, and it is well-suited for situations where multiple observations of the same subdiffusion process are available. We present supporting numerical examples and an application to market price data for a low-volume stock.

Suggested Citation

  • Kerger, Phillip & Kobayashi, Kei, 2020. "Parameter estimation for one-sided heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301115
    DOI: 10.1016/j.spl.2020.108808
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    References listed on IDEAS

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