arXiv subjects

Sergey Zaitsev

Publications and source records attributed to Sergey Zaitsev.

5 recordsLinked to original sources

arXiv2008

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.

q-fin.ST↗

arXiv2007

Market Mill Dependence Pattern in the Stock Market: Modeling of Predictability and Asymmetry via Multi-Component Conditional Distribution

Recent studies have revealed a number of striking dependence patterns in high frequency stock price dynamics characterizing probabilistic interrelation between two consequent price increments x (push) and y (response) as described by the bivariate probability distribution P(x,y) [1,2,3,4]. There are two properties, the market mill asymmetries of P(x,y) and predictability due to nonzero z-shaped mean conditional response, that are of special importance. Main goal of the present paper is to put together a model reproducing both the z-shaped mean conditional response and the market mill asymmetry of P(x,y) with respect to the axis y=0. We develop a probabilistic model based on a multi-component ansatz for conditional distribution P(y|x) with push-dependent weights and means describing both properties. A relationship between the market mill asymmetry and predictability is discussed. A possible connection of the model to agent-based picture is outlined.

physics.soc-ph↗

arXiv2006

Market Mill Dependence Pattern in the Stock Market: Individual Portraits

This paper continues a series of studies of dependence patterns following from properties of the bivariate probability distribution P(x,y) of two consecutive price increments x (push) and y (response). The paper focuses on individual differences of the P(x,y) for 2000 stocks using a methodology of identification of asymmetric market mill patterns developed in [1,2]. We show that individual asymmetry patterns (portraits) are remarkably stable over time and can be classified into three major groups - correlation, anticorrelation and market mill. We analyze the conditional dynamics resulting from the properties of P(x,y) for all groups and demonstrate that it is trend-following at small push magnitudes and contrarian at large ones

physics.soc-ph↗

arXiv2006

Market Mill Dependence Pattern in the Stock Market: Distribution Geometry, Moments and Gaussization

This paper continues a series of studies devoted to analysis of the bivariate probability distribution P(x,y) of two consecutive price increments x (push) and y (response) at intraday timescales for a group of stocks. Besides the asymmetry properties of P(x,y) such as Market Mill dependence patterns described in preceding paper [1], there are quite a few other interesting geometrical properties of this distribution discussed in the present paper, e.g. transformation of the shape of equiprobability lines upon growing distance from the origin of xy plane and approximate invariance of P(x,y) with respect to rotations at the multiples of $π/2$ around the origin of xy plane. The conditional probability distribution of response P(y|x) is found to be markedly non-gaussian at small magnitude of pushes and tending to more gauss-like behavior upon growing push magnitude. The volatility of P(y|,x) measured by the absolute value of the response shows linear dependence on the absolute value of the push, and the skewness of P(y|x) is shown to inherit a sign of the push. The conditional dynamics approach applied in this study is compared to regression models of AR-ARCH class.

physics.soc-ph↗

arXiv2006

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.

physics.soc-ph↗