Related Experiment Video
Updated: Jun 17, 2026
09:33
MRI Mapping of Cerebrovascular Reactivity via Gas Inhalation Challenges
Published on: December 17, 2014
Cross-correlations between volume change and price change.
Boris Podobnik1, Davor Horvatic, Alexander M Petersen
1Department of Physics, Center for Polymer Studies, Boston University, Boston, MA 02215, USA.
Summary
This study reveals power-law cross-correlations between trading volume growth rate and price changes in financial markets. An approximate inverse cubic law governs these relationships across global indices.
Area of Science:
- Quantitative Finance
- Financial Market Analysis
- Statistical Modeling
Background:
- Traditional financial analysis focuses on price changes, often overlooking trading volume dynamics.
- Understanding the relationship between volume and price fluctuations is crucial for market comprehension.
- Growth rates, derived from logarithmic differences, offer a robust measure for financial time series.
Purpose of the Study:
- To investigate the cross-correlations between volume growth rate and price change in financial markets.
- To model the observed cross-correlations using a joint stochastic process.
- To estimate the tail exponent (alpha) of the probability density function for volume and price changes.
Main Methods:
- Analysis of 14,981 daily Standard and Poor's (S&P) 500 Index recordings (1950-2009).
- Application of Detrended Cross-Correlation Analysis (DCCA) to identify power-law cross-correlations.
- Development of a new method to estimate the tail exponent (alpha) by analyzing time intervals (tau(q)) between events.
Main Results:
- Significant power-law cross-correlations were found between volume growth rate and price changes.
- A joint stochastic process was introduced to effectively model these cross-correlations.
- The tail exponent alpha was estimated to be approximately 3 for both S&P 500 and NYSE Composite constituents, indicating an approximate inverse cubic law.
Conclusions:
- The study establishes a quantifiable relationship between volume and price dynamics in financial markets.
- The findings suggest universal statistical properties in financial markets, evidenced by the consistent inverse cubic law across global indices.
- The novel method for estimating the tail exponent provides a valuable tool for financial risk assessment.
Related Concept Videos
01:09Correlation
In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
01:15Scatter Plot
The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a relationship between the variables. A clear direction happens when there is either:
01:26Unsoundness of Aggregate due to Volume Change
Unsoundness in aggregates due to volume changes is primarily caused by the physical alterations aggregates undergo, such as freezing and thawing, thermal changes, and wetting and drying. Unsound aggregates, when subjected to these changes, result in volume change upon disintegration. This, in turn, contributes to the deterioration of concrete, including scaling, pop-outs, and cracking. Particular types of aggregates, such as porous flints, cherts, and those containing clay minerals, are...
01:17Work Done During Volume Change
In mechanics, work is done on an object when the force acting on it displaces the object. In thermodynamics, work done on a system can be estimated when the system's volume changes during any thermodynamic process.
Consider a gas confined to a cylinder fitted with a movable piston at one end. If the gas expands from volume V1 to volume V2, it exerts a force on the piston, such that the piston moves by a distance dr.
The work done by the gas on the piston can be expressed as
Consider a gas confined to a cylinder fitted with a movable piston at one end. If the gas expands from volume V1 to volume V2, it exerts a force on the piston, such that the piston moves by a distance dr.
The work done by the gas on the piston can be expressed as
02:32Le Chatelier's Principle: Changing Volume (Pressure)
For gas-phase equilibria, changes in the concentrations of reactants and products can occur with altered volume and pressure. The partial pressure, P, of an ideal gas is proportional to its molar concentration, M.
01:24Finding Volume Using Cross-Sectional Area
For solids whose cross-sectional areas vary in a predictable way, volume can be determined by integrating these areas along an axis perpendicular to the slices. This approach is particularly useful for polyhedral solids, where classical geometric formulas may not be immediately applicable. A tetrahedron provides a clear example of how cross-sectional integration can be applied to a three-dimensional object with continuously changing geometry.Consider a tetrahedron with height h and a base that...