An Investigation of Stretched Exponential Function in Quantifying Long-Term Memory of Extreme Events Based on Artificial Data following Lévy Stable Distribution

HongGuang Sun, Lin Yuan, Yong Zhang and Nicholas Privitera

Complexity, 2018, vol. 2018, 1-7

Abstract:

Extreme events, which are usually characterized by generalized extreme value (GEV) models, can exhibit long-term memory, whose impact needs to be quantified. It was known that extreme recurrence intervals can better characterize the significant influence of long-term memory than using the GEV model. Our statistical analyses based on time series datasets following the Lévy stable distribution confirm that the stretched exponential distribution can describe a wide spectrum of memory behavior transition from exponentially distributed intervals (without memory) to power-law distributed ones (with strong memory or fractal scaling property), extending the previous evaluation of the stretched exponential function using Gaussian/exponential distributed random data. Further deviation and discussion of a historical paradox (i.e., the residual waiting time tends to increase with an increasing elapsed time under long-term memory) are also provided, based on the theoretical analysis of the Bayesian law and the stretched exponential distribution.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:5913976

DOI: 10.1155/2018/5913976

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