Long memory time series forecasting by using genetic programming

Real-world time series have certain properties, such as stationarity, seasonality, linearity, among others, which determine their underlying behaviour. There is a particular class of time series called long-memory processes, characterized by a persistent temporal dependence between distant observations, that is, the time series values depend not only on recent past values but also on observations of much prior time periods. The main purpose of this research is the development, application, and evaluation of a computational intelligence method specifically tailored for long memory time series forecasting, with emphasis on many-step-ahead prediction. The method proposed here is a hybrid combining genetic programming and the fractionally integrated (long-memory) component of autoregressive fractionally integrated moving average (ARFIMA) models. Another objective of this study is the discovery of useful comprehensible novel knowledge, represented as time series predictive models. In this respect, a new evolutionary multi-objective search method is proposed to limit complexity of evolved solutions and to improve predictive quality. Using these methods allows for obtaining lower complexity (and possibly more comprehensible) models with high predictive quality, keeping run time and memory requirements low, and avoiding bloat and over-fitting. The methods are assessed on five real-world long memory time series and their performance is compared to that of statistical models reported in the literature. Experimental results show the proposed methods’ advantages in long memory time series forecasting.