An information theory approach to stock market liquidity

A novel methodology is introduced to dynamically analyze the complex scaling behavior of financial data across various investment horizons. This approach comprises two steps: (a) the application of a distribution-based method for the estimation of time-varying self-similarity matrices. These matrices consist of entries that represent the scaling parameters relating pairs of distributions of price changes constructed for different temporal scales (or investment horizons); (b) the utilization of information theory, specifically the Normalized Compression Distance, to quantify the relative complexity and ascertain the similarities between pairs of self-similarity matrices. Through this methodology, distinct patterns can be identified and they may delineate the levels and the composition of market liquidity. An application to the U.S. stock index S&P500 shows the effectiveness of the proposed methodology.