Improved Forecasting of Time Series Data of Real System Using Genetic Programming

摘要

A study is made to improve short term forecasting of time series data of real system using Genetic Programming (GP) under the framework of time delayed embedding technique. GP based approach is used to make analytical model of time series data of real system using embedded vectors that help reconstruct the phase space. The map equations, involving non-linear symbolic expressions in the form of binary trees comprising of time delayed components in the immediate past, are first obtained by carrying out single-step GP fit for the training data set and usually they are found to give good fitness as well as single-step predictions. However while forecasting the time series based on multi-step predictions in the out-of-sample region in an iterative manner, these solutions often show rapid deterioration as we dynamically forward the solution in future time. With a view to improve on this limitation, it is shown that if the multi-step aspect is incorporated while making the GP fit itself, the corresponding GP solutions give multi-step predictions that are improved to a fairly good extent for around those many multi-steps as incorporated during the multi-step GP fit. Two different methods for multi-step fit are introduced, and the corresponding prediction results are presented. The modified method is shown to make better forecast for out-of-sample multi-step predictions for the time series of a real system, namely Electroencephelograph (EEG) signals.