An increasing hybrid morphological-linear perceptron with pseudo-gradient-based learning and phase adjustment for financial time series prediction

Financial time series exhibit a mixture of linear and nonlinear components as indicated by the corresponding lagplots. As we will explain in this paper, certain financial time series can be approximated by increasing functions of a fixed number of time lags or antecedents. This work presents a suitable model for dealing with financial prediction problems, called increasing hybrid morphological-linear perceptron (IHMP). A pseudo-gradient steepest descent method is presented to design the IHMP (learning process), using the back-propagation algorithm and a systematic approach to overcome the problem of nondifferentiability of morphological operations. The learning process includes an automatic phase correction step that is geared at eliminating the time phase distortions that typically occur in financial time series prediction (“random walk dilemma”). Furthermore, we compare the proposed IHMP with other neural and statistical models using three complex nonlinear problems of financial time series prediction.