Cross-correlations between volume change and price change

Abstract

In finance, one usually deals not with prices but with growth rates $R$, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate $\tilde{R}$, the difference in logarithm between two consecutive values of trading volume. To this end, we use several methods to analyze the properties of volume changes $|\tilde{R}|$, and their relationship to price changes $|R|$. We analyze $14,981$ daily recordings of the S\&P 500 index over the 59-year period 1950--2009, and find power-law {\it cross-correlations\/} between $|R|$ and $|\tilde{R}|$ using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these cross-correlations. Motivated by the relationship between $|R|$ and $|\tilde{R}|$, we estimate the tail exponent $\tilde{\alpha }$ of the probability density function $P(|\tilde{R}|)\sim |\tilde{R}{|}^{-1-\tilde{\alpha }}$ for both the S\&P 500 index as well as the collection of 1819 constituents of the New York Stock Exchange Composite index on 17 July 2009. As a new method to estimate $\tilde{\alpha }$, we calculate the time intervals ${\tau }_q$ between events where $\tilde{R}>q$. We demonstrate that ${\bar{\tau }}_q$, the average of ${\tau }_q$, obeys ${\bar{\tau }}_q\sim q^{\tilde{\alpha }}$. We find $\tilde{\alpha }\approx 3$. Furthermore, by aggregating all ${\tau }_q$ values of 28 global financial indices, we also observe an approximate inverse cubic law.

7 pages, 5 figures

References in corpus (2)

• Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series
• Indication of multiscaling in the volatility return intervals of stock markets

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