Dynamics of the Number of Trades of Financial Securities

TL;DR

This paper analyzes the spectral density of stock prices and trading activity, revealing distinct power-law behaviors that enhance understanding of market dynamics.

Contribution

It provides a comparative spectral analysis of stock prices and trading volume, highlighting different power-law behaviors in financial market data.

Findings

Spectral density of log stock prices follows a 1/f^2 pattern.

Spectral density of daily trading numbers exhibits a 1/f-like pattern.

Different power-law behaviors suggest distinct underlying market processes.

Abstract

We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-law behavior. We confirm the $1/f^2$ behavior for the spectral density of the logarithm of stock price whereas we detect a $1/f$-like behavior for the spectral density of the daily number of trades.