Morphological-Rank-Linear Models for Financial Time Series Forecasting
Ricardo de A. Arajo, Glucio G. de M. Melo, Adriano L. I. Oliveira, Sérgio Soares · InTech eBooks · 2010
This work presented a new approach, referred to as Morpological-Rank-Linear Time-lag Added Forecasting (MRLTAEF) model, to overcome the RW dilemma for financial time series forecasting, which performs an evolutionary search for the minimum dimension to determining the characteristic phase space that generates the financial time series phenomenon. It is inspired on Takens Theorem and consists of an intelligent hybrid model composed of a Morpological-Rank-Linear (MRL) filter combined with a Modified Genetic Algorithm (MGA), which searches for the minimum number of time lags for a correct time series representation and estimates the initial (sub-optimal) parameters of the MRL filter (mixing parameter (), rank (r), linear Finite Impulse Response (FIR) filter (b) and the Morphological-Rank (MR) filter (a) coefficients). Each individual of the MGA population is trained by the averaged Least Mean Squares (LMS) algorithm to further improve the MRL filter parameters supplied by the MGA. After adjusting the model, it performs a behavioral statistical test and a phase fix procedure to adjust time phase distortions observed in financial time series. Five different metrics were used to measure the performance of the proposed MRLTAEF method for financial time series forecasting. A fitness function was designed with these five well-known statistic error measures in order to improve the description of the time series phenomenon as much as possible. The five different evaluation measures used to compose this fitness function can have different contributions to the final prediction, where a more sophisticated analysis must be done to determine the optimal combination of such metrics. An experimental validation of the method was carried out on four real world financial time series, showing the robustness of the MRLTAEF method through a comparison, according to five performance measures, of previous results found in the literature (MLP, MRL and TAEF models). This experimental investigation indicates a better, more consistent global performance of the proposed MRLTAEF method. In general, all generated predictive models with the MRLTAEF method using the phase fix procedure (to adjust time phase distortions) showed forecasting performance much better