Stock Market Index Dynamics and Market Activity

This paper proposes a parsimonious model for stock market index dynamics grounded in information theory. It models market activity, the derivative of the market time, as a linear function of the squared derivative of an exponential moving average from a proxy of the single driving Brownian motion. The normalized index is following in market time a Cox–Ingersoll–Ross process with dimension 4. In calendar time, major shifts in the driving Brownian motion cause spikes in market activity. Applied to S&P500 data, the model accurately extracts the potential driving Brownian motion, which withstands rejection as a Brownian motion by a joint variance ratio test, providing a realistic representation of the stock index dynamics.