Market Mill Dependence Pattern in the Stock Market: Asymmetry Structure, Nonlinear Correlations and Predictability

An empirical study of joint bivariate probability distribution of two consecutive price increments for a set of stocks at time scales ranging from one minute to thirty minutes reveals asymmetric structures with respect to the axes y=0, y=x, x=0 and y=-x. All four asymmetry patterns remarkably resemble a four-blade mill called market mill pattern. The four market mill patterns characterize different aspects of interdependence between past (push) and future (response) price increments. When analyzed in appropriate coordinates, each pattern corresponds to a particular nonlinear dependence between the push and conditional mean of response. Qualitative interpretation of each pattern is discussed. The market mill pattern is an evidence of complex dependence properties relating past and future price increments resulting in various types of nonlinear correlation and predictability.