Market mill dependence pattern in the stock market: Multiscale conditional dynamics

摘要

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. 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.Interpretation of variations of asymmetry patterns of individual stocks in terms of specific deformations of the fundamental market mill asymmetry patterns is described.