Cross-correlations between volume change and price change

By Boris Podobnik, Davor Horvatic, Alexander M. Petersen, H. Eugene Stanley. Proceedings of the National Academy of Sciences of the United States of America, 2009

622 citations recorded by the source corpus.

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 R̃, 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 |R̃|, and their relationship to price changes |R|. We analyze 14,981 daily recordings of the Standard and Poor's (S & P) 500 Index over the 59-year period 1950–2009, and find power-law cross-correlations between |R| and |R̃| by using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these cross-correlations. Motivated by the relationship between |R| and |R̃|, we estimate the tail exponent α̃ of the probability density function P(|R̃|) ∼ |R̃|−1−α̃ 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 α̃, we calculate the time intervals τq between events where R̃ > q. We demonstrate that τ̃q, the average of τq, obeys τ̃q ∼ qα̃. We find α̃ ≈ 3. Furthermore, by aggregating all τq values of 28 global financial indices, we also observe an approximate inverse cubic law.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/99d38a01d23d671af23d4c0c41ceb9f2832de08d

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Citations in the corpus

Detrended cross-correlation analysis approach for assessing asymmetric multifractal detrended cross-correlations and their application to the Chinese financial market (2014, neutral): “MF-DCCA is used widely to detect the cross-correlation between financial markets [9–19].”
Nonlinear bivariate dependency of price–volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis (2011, methodology): “Various studies show that both price series [4–6] and volume series [7,8] are found to exhibit fractal and multifractal properties.”
Long memory and regime switching: A simulation study on the Markov Regime-Switching ARFIMA model (2015, background): “the ARFIMA model is stationary (−1/2 < d < 1/2), Sowell (1992) describes how to compute the exact maximum likelihood estimate (MLE) of d.”
Multifractal Detrended Fluctuation Analysis of the Chinese Stock Index Futures Market (2013, background): “Scholars have also studied the cross-correlations between two non-stationary time series [10-13] by generalising DFA and MF-DFA analyses with an emphasis on detrended covariance.”
Multifractal detrended cross-correlation analysis for power markets (2013, methodology): “To unveil the multifractal nature of the operating data in power market, multifractal detrended cross-correlation analysis (MF-DXA) [26] is applied here to study the degree of correlation between the price and the load series.”
Multifractal Detrended Cross-Correlation Analysis of agricultural futures markets (2011, methodology): “Many scholars have studied the cross-correlation among financial time series, such as stocks [5-9] and currencies [5], using the methods which assume that both of analyzed time series are stationary.”
A new approach to quantify power-law cross-correlation and its application to commodity markets (2011, methodology): “then apply their new method to uncover long-range power-law cross-correlations in the random part of the underlying stochastic process [24] and the cross-correlation between volume change and price change [25].”