Point Processes Modeling of Time Series Exhibiting Power-Law Statistics

TL;DR

This paper explores stochastic point processes that generate power-law behaviors in time series, applying them to model financial trading activity and word frequency distributions, revealing their broad applicability.

Contribution

It introduces a modeling framework for power-law time series using stochastic point processes, extending their application to finance and linguistics.

Findings

Power-law spectrum and distribution density in modeled time series

Effective modeling of financial trading activity

Accurate representation of word frequency distributions

Abstract

We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language.