Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and volume int
eract, particularly when the levels of both are high. We find that the distribution of the volume-conditional volatility is well fit by a power-law function with an exponential cutoff. We find that the volume-conditional volatility distribution scales with volume, and collapses these distributions to a single curve. We exploit the characteristics of the volume-volatility scatter plot to find a strong correlation between logarithmic volume and a quantity we define as local maximum volatility (LMV), which indicates the largest volatility observed in a given range of trading volumes. This finding supports our empirical analysis showing that volume is an excellent predictor of the maximum value of volatility for both same-day and near-future time periods. We also use a joint conditional probability that includes both volatility and volume to demonstrate that invoking both allows us to better predict the largest next-day volatility than invoking either one alone.
In a highly interdependent economic world, the nature of relationships between financial entities is becoming an increasingly important area of study. Recently, many studies have shown the usefulness of minimal spanning trees (MST) in extracting inte
ractions between financial entities. Here, we propose a modified MST network whose metric distance is defined in terms of cross-correlation coefficient absolute values, enabling the connections between anticorrelated entities to manifest properly. We investigate 69 daily time series, comprising three types of financial assets: 28 stock market indicators, 21 currency futures, and 20 commodity futures. We show that though the resulting MST network evolves over time, the financial assets of similar type tend to have connections which are stable over time. In addition, we find a characteristic time lag between the volatility time series of the stock market indicators and those of the EU CO2 emission allowance (EUA) and crude oil futures (WTI). This time lag is given by the peak of the cross-correlation function of the volatility time series EUA (or WTI) with that of the stock market indicators, and is markedly different (>20 days) from 0, showing that the volatility of stock market indicators today can predict the volatility of EU emissions allowances and of crude oil in the near future.
