Market Mill Dependence Pattern in the Stock Market: Multiscale Conditional Dynamics

Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a single time scale such as a characteristic shape of an asymmetry generating component of the conditional probability distribution result in the "elementary" market mill pattern. This asymmetry generating component matches the empirical distribution obtained from the market data. We discuss these properties as a mixture of trend-preserving and contrarian strategies used by market agents. Three basic types of asymmetry patterns characterizing individual stocks are outlined. Multiple time scale considerations make the resulting "composite" mill similar to the empirical market mill patterns. Multiscale model also reflects a multi-agent nature of the market.