Multifractality in the stock market: price increments versus waiting times

TL;DR

This study applies multifractal analysis to high-frequency stock data, revealing multiscaling in price changes and waiting times, and explores their origins and implications for financial modeling.

Contribution

It demonstrates that both price increments and inter-trade intervals exhibit multifractality due to long-range correlations and non-Gaussian distributions, providing insights into market dynamics.

Findings

Both quantities show multiscaling across different stocks.

Long-range correlations and non-Gaussian fluctuations cause multifractality.

Price increments and waiting times are largely independent.

Abstract

By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche B\"orse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities reveal multiscaling and that this result holds across different stocks. The origin of the multifractal character of the corresponding dynamics is, among others, the long-range correlations in price increments and in inter-trade time intervals as well as the non-Gaussian distributions of the fluctuations. Since the transaction-to-transaction price increments do not strongly depend on or are almost independent of the inter-trade waiting times, both can be sources of the observed multifractal behaviour of the fixed-delay returns and volatility. The results presented also allow one to evaluate the applicability of the Multifractal Model of Asset Returns in the case of tick-by-tick data.