Low Order Modeling of Seemingly Random Systems with Application to Stock Market Securities

Abstract

Even simple observation of stock price graphs can reveal dominant patterns. In our work, we will refer to such re-occurring, dominant patterns as “coherent structures”, a term borrowed from the theory of turbulence in fluid dynamics. Stock price performance exhibits coherent structures, which by definition make it non-random, although a price-versus-time graph might seem totally chaotic to the naked eye. A novel low-order modeling technique for systems that are seemingly random has been developed. Though stock market data is used for the formulation and verification of the technique, its application in diverse fields is verified. The dissertation discusses some of the salient features of the novel technique along with a dynamic system analogy. The technique reduces many of the significant limitations associated with traditional methods like Fourier analysis and digital filters. Application of the technique to a nonlinear dynamical system and meteorological data are presented as well as the primary application on stock market securities