Online Forecasting of Synchronous Time Series Based on Evolving Linear Models

Abstract

This paper suggests evolving linear models as a powerful alternative for online forecasting of synchronous time series. First, using a priori knowledge of an expert, all known possible features are clustered in some categories so that each category includes homogeneous features. Then, a novel evolving correlation-based forward subset selection technique is used to determine relevant features from each category. Next, based on the selected features, an estimation of the output of the system is modeled through an evolving adaptive linear regression model. In evolving systems, selected features and their associated weights could vary over time based on new incoming data samples which contain new information. Finally, a soft combination of output estimations of all categories, in a new sense of Takagi–Sugeno fuzzy system, gives the prediction of the output of the system at each sampling time. The approach offers a certain new view at the enhancement of evolving forecasting models. The proposed approach embodies recursive learning and one-step-ahead incremental algorithms that progressively modify the model to ensure continuous learning, and self-organization of the model structure and its parameters. Two real-world problems, forecasting electricity load of the Electric Reliability Council of Texas region and stock price forecasting of technology sector of Standard & Poor’s 500 index, are provided to validate the developed method. Pros and cons of the proposed approach are comprehensively discussed and shown through simulation results and comparisons with other state-of-the-art techniques.