Swingtum – A Computational Theory of Fractal Dynamic Swings and Physical Cycles of Stock Market in A Quantum Price-Time Space

This paper presents the basic framework of a comprehensive computational theory of stock market behavior, which we call Swingtum, taking multivariate stock index time series data as input, and producing probabilistic predictions of stock index movement at multiple time frames. The theory should also be applicable to other liquid markets. The Swingtum theory is based on the view that the movement of the stock market as a whole as represented by its benchmark index is driven by three types of forces: business dynamics, mass psychological dynamics, and news impacts, and consequently the market movement can be decomposed into four types of components: dynamical swings, physical cycles, abrupt momentums, and random walks. Dynamic swings include business cycles, stock life cycles, and Elliott waves of different levels, which typically have a fractal nature characterized by log-periodic power laws. Physical cycles includes anniversary days, seasonality cycles, and weekly cycles, which have relatively constant periodicity. Abrupt momentums may be caused by endogenous critical points or driven by exogenous news shocks or impacts. Random walks correspond to remaining randomness not explainable by any systematic force. The dynamic swings and physical cycles identified and modeled from the historical index time series will most likely define a quantum space of price and time in which the market will most likely travel from one quantum price level to another or from one time zone to another. There is a fundamental symmetry between price and time. The actual path is not only determined by dynamic swing phase and physical cycle phase, but also by the possible news impact. The more general theory of Swingtum extends the fractal and cyclical models of a univariate benchmark index to the multivariate time series models of intramarket and intermarket dynamical analysis.