3 Morphological-Rank-Linear Models for Financial Time Series Forecasting

The financial time series forecasting is considered a rather difficult problem, due to the many complex features frequently present in such time series (irregularities, volatility, trends and noise). Several approaches have been studied for the development of predictive models able to predict time series, based on its past and present data. In the attempt to solve the time series prediction problem, a wide number of linear statistical models were proposed. Among them, the popular linear statistical approach based on Auto Regressive Integrated Moving Average (ARIMA) models [1] is one of the most common choices. However, since the ARIMA models are linear and most real world applications involve nonlinear problems, this can introduce an accuracy limitation of the generated forecasting models. In the attempt to overcome linear statistical models limitations, other nonlinear statistical approaches have been developed, such as the bilinear models [2], the threshold autoregressive models [3], the exponential autoregressive models [4], the general state dependent models [5], amongst others. The drawbacks of those nonlinear statistical models are the high mathematical complexity associated with them (resulting in many situations in similar performances to the linear models) and the need, most of the time, of a problem dependent specialist to validate the predictions generated by the model, limiting the development of an automatic forecast system [6]. Alternately, Artificial Neural Networks (ANNs) based approaches have been applied for nonlinear modeling of time series in the last two decades [7-14]. However, in order to define a solution to a given problem, ANNs require the setting up of a series of system parameters, some of them are not always easy to determine. The ANN topology, the number of processing units, the algorithm for ANN training (and its corresponding variables) are just some of the parameters that require definition. In addition to those, in the particular case of time series forecasting, another crucial element necessary to determine is the relevant time lags to represent the series [15]. In this context, evolutionary approaches for the definition of neural network parameters have produced interesting results [16{20]. Some of these works have focused on the evolution of the network weights whereas others aimed at evolving the network architecture.