Power law for the calm-time interval of price changes

TL;DR

This study reveals that the calm-time intervals between significant stock price changes follow a power law distribution, with the exponent decreasing as the threshold for change increases, based on extensive analysis of Tokyo Stock Exchange data.

Contribution

It introduces a novel statistical property of stock price changes, demonstrating power law behavior in calm-time intervals across multiple companies and a major index over 27 years.

Findings

Calm-time intervals follow a power law decay.

Power-law exponent decreases with higher thresholds.

Results consistent across different companies and time periods.

Abstract

In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We conducted quantitative investigation of the {\it calm-time intervals} of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index over a 27-year period from January 4, 1975 to December 28, 2001. A calm-time interval is defined as the interval between two successive price changes above a fixed threshold. We found that the calm-time interval distribution of price changes obeys a power law decay. Furthermore, we show that the power-law exponent decreases monotonically with respect to the threshold. Keyword: econophysics, stock price changes, calm time interval, power-laws; PACS: 89.90.+n; 05.40.Df;