Cross-Correlations between Volume Change and Price Change

Proceedings of the National Academy of Sciences of the United States of America, Vol. 106, No. 52, pp. 22079-22084, December 2009

7 Pages Posted: 11 Nov 2010

See all articles by Boris Podobnik

Boris Podobnik

Boston University; University of Rijeka

Davor Horvatic

Theoretical Physics Department, University of Zagreb

Alexander Michael Petersen

University of California Merced, Ernest and Julio Gallo Management Program

H. Eugene Stanley

Boston University - Center for Polymer Studies

Date Written: DEC 29, 2009

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 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 [alpha] of the probability density function P(|R̃|) ∼ |R̃|−1−[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 [alpha], we calculate the time intervals τq between events where R̃ > q. We demonstrate that [tau with tilde]q, the average of τq, obeys [tau with tilde]q ∼ q[alpha]. We find [alpha] ≈ 3. Furthermore, by aggregating all τq values of 28 global financial indices, we also observe an approximate inverse cubic law.

Keywords: econophysics, finance, volatility

Suggested Citation

Podobnik, Boris and Horvatic, Davor and Petersen, Alexander Michael and Stanley, H. Eugene, Cross-Correlations between Volume Change and Price Change (DEC 29, 2009). Proceedings of the National Academy of Sciences of the United States of America, Vol. 106, No. 52, pp. 22079-22084, December 2009 , Available at SSRN: https://ssrn.com/abstract=1706275

Boris Podobnik (Contact Author)

Boston University ( email )

University of Rijeka ( email )

Rijeka, 51000
Croatia

Davor Horvatic

Theoretical Physics Department, University of Zagreb ( email )

Trg maršala Tita 14
Zagreb
Croatia

Alexander Michael Petersen

University of California Merced, Ernest and Julio Gallo Management Program ( email )

School of Engineering
Science & Engineering 2, Suite 315
Merced, CA 95343
United States

H. Eugene Stanley

Boston University - Center for Polymer Studies ( email )

Boston, MA 02215
United States

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