Cross-correlations between volume change and price change

Boris Podobnik; Davor Horvatic; Alexander M. Petersen; H. Eugene Stanley

doi:10.1073/pnas.0911983106

paper

Cross-correlations between volume change and price change

arXiv:1011.2674 · doi:10.1073/pnas.0911983106

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 $R ~$ , 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 $∣ R ~ ∣$ , 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 $∣ R ~ ∣$ using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these cross-correlations. Motivated by the relationship between $∣ R ∣$ and $∣ R ~ ∣$ , we estimate the tail exponent $α ~$ of the probability density function $P (∣ R ~ ∣) \sim ∣ R ~ ∣^{- 1 - α ~}$ 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 $α ~$ , we calculate the time intervals $τ_{q}$ between events where $R ~ > q$ . We demonstrate that $τ ˉ_{q}$ , the average of $τ_{q}$ , obeys $τ ˉ_{q} \sim q^{α ~}$ . We find $α ~ \approx 3$ . Furthermore, by aggregating all $τ_{q}$ values of 28 global financial indices, we also observe an approximate inverse cubic law.

7 pages, 5 figures

Cross-correlations between volume change and price change

Abstract

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