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 rateR, 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 Standard and Poor's (S & P) 500 Index over the 59-year period 1950-2009, and find power-law cross-correlations between |R| and |R| by using detrended cross-correlation analysis (DCCA). We introduce a joint stochastic process that models these crosscorrelations. Motivated by the relationship between |R| and |R|, we estimate the tail exponentα of the probability density function P(|R|) ∼ |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 estimateα, we calculate the time intervals τ q between events whereR > q. We demonstrate thatτ q , the average of τ q , obeysτ q ∼ qα. We findα ≈ 3. Furthermore, by aggregating all τ q values of 28 global financial indices, we also observe an approximate inverse cubic law. econophysics | finance | volatility There is a saying on Wall Street that "it takes volume to move stock prices." A number of studies have analyzed the relationship between price changes and the trading volume in financial markets (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). Some of these studies (1, 3-6) have found a positive relationship between price change and the trading volume. In order to explain this relationship, Clarke assumed that the daily price change is the sum of a random number of uncorrelated intraday price changes (3), so predicted that the variance of the daily price change is proportional to the average number of daily transactions. If the number of transactions is proportional to the trading volume, then the trading volume is proportional to the variance of the daily price change.The cumulative distribution function (cdf) of the absolute logarithmic price change |R| obeys a power lawIt is believed (15-18) that α ≈ 3 ("inverse cubic law"), outside the range α < 2 characterizing a Lévy distribution (18,19). A parallel analysis of Q, the volume traded, yields a power law (20-28)To our knowledge, the logarithmic volume change-R and its relation to the logarithmic price change R-has not been analyzed, and this analysis is our focus here. For each of the 1,819 companies and 28 indices, we calculate over the time interval of one day the logarithmic change in price S(t), Data Analyzedand also the logarithmic change in trading volume Q(t) (29),For each of the 3,694 time series, we also calculate the absolute values |R t | and |R t | and define the "price volatility" (30) and "volume volatility," respectively,andwhere σ R ≡ ( |R t | 2 − |R t | 2 ) 1/2 and σR ≡ ( |R t | 2 − |R t | 2 ) 1/2 are the respective standard deviat...

Revisiting Covered Interest Parity in the European Union: the DCCA Approach

“…6 Originally used to explain behavior in natural science phenomena, both techniques could also be applied to economic time series, namely financial data (see, for example, Podobnik, Horvatic, Petersen, & Stanley, 2009, or Wang, Wei, & Wu, 2013.…”

Statistical regularities of Carbon emission trading market: Evidence from European Union allowances

“…In order to evaluate the risk of diversified investment, quantitative evaluation for the cross correlation of price change between different financial assets is considered as a useful method [11][12][13][14][15][16]. In this section we quantitatively evaluate the cross correlation of price change (return) time series, between EUA and other financial assets including stock market indicators, traditional commodities, and currency futures.…”

Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations

“…This approach was introduced in a context of autocorrelations in [11] as the detrended fluctuation analysis (DFA) and immediately gained popularity among the researchers working with empirical data across many disciplines. The modification of DFA oriented towards detection of the powerlaw cross-correlations is known as the detrended crosscorrelation analysis (DCCA) [12] and it can be used in analysis of bivariate and multivariate empirical data [13][14][15][16].…”