On distribution of number of trades in different time windows in the stock market

TL;DR

This paper investigates the statistical properties and multifractal nature of trade counts in intraday stock market data, proposing an evolution equation to model these distributions based on capital turnover.

Contribution

It introduces an evolution equation linking capital turnover and trade counts, inspired by particle physics, to describe distribution features in stock trading.

Findings

Distributions exhibit multifractal characteristics.

Correlation patterns show peculiar changes.

Proposed model can describe observed distribution features.

Abstract

Properties of distributions of the number of trades in different intraday time intervals for five stocks traded in MICEX are studied. The dependence of the mean number of trades on the capital turnover is analyzed. Correlation analysis using factorial and $H_q$ moments demonstrates the multifractal nature of these distributions as well as some peculiar changes in the correlation pattern. Guided by the analogy with the analysis of particle multiplicity distributions in multiparticle production at high energies, an evolution equation relating changes in capital turnover and a number of trades is proposed. We argue that such equation can describe the observed features of the distribution of the number of trades in the stock market.