Optimization Techniques for Solving Complex Problems

CHAPTER 15

Evolving Rules for Local Time Series Prediction

C. LUQUE, J. M. VALLS, and P. ISASI

Universidad Carlos III de Madrid, Spain

15.1 INTRODUCTION

A time series (TS) is a sequence of values of a variable obtained at successive, in most cases uniformly spaced, intervals of time. The goal is to predict future values of the variable y_i using D past values. In other words, the set {y₁, …, y_D} is used to predict y_{D + τ}, where τ is a nonnegative integer, which receives the name of the prediction horizon. In TS related to real phenomena, a good model needs to detect which elements in the data set can generate knowledge leading to refusing those that are noise. In this work a new model has been developed, based on evolutionary algorithms to search for rules to detect local behavior in a TS. That model allows us to improve the prediction level in these areas.

Previous studies have used linear stochastic models, mainly because they are simple models and their computational burden is low. Autoregressive moving average (ARMA) models using data as to air pressure and water level at Venice have been used to forecast the water level at the Venice lagoon [1]. Following this domain, Zaldívar et al. [2] used a TS analysis based on nonlinear dynamic systems theory, and multilayer neural network models can be found. This strategy is applied to the time sequence of water-level data recorded in ...