Record statistics of financial time series and geometric random walks

TL;DR

This paper investigates the record statistics of stock market data and geometric random walks, revealing power-law distributions for record ages and extreme value behavior, with empirical and simulated data showing strong agreement.

Contribution

It provides a detailed analysis of record age distributions and their extreme value properties in financial and geometric random walk series, supported by simulations and empirical data.

Findings

Record ages follow a power-law distribution with exponent 1.5 to 1.8.

Longest record ages follow the Fréchet distribution.

Empirical stock data matches geometric random walk predictions.

Abstract

The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent $\alpha$ lying in the range $1.5 \le \alpha \le 1.8$. Further, the longest record ages follow the Fr\'{e}chet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that from the empirical stock data.