Parameter estimation for one-sided heavy-tailed distributions

Phillip Kerger; Kei Kobayashi

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arXiv · 2005.03662

Parameter estimation for one-sided heavy-tailed distributions

Phillip Kerger·Kei Kobayashi

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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.

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Phillip Kerger, Kei Kobayashi. 2020-05-07. Parameter estimation for one-sided heavy-tailed distributions. https://arxiv.org/abs/2005.03662

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