Multivariate Chaotic Time Series Prediction Based on Improved Grey Relational Analysis

In multivariate chaotic time series prediction, correlation analysis is important for reducing input dimensions and improving prediction performance. Grey relational analysis (GRA) has proved to be an effective method for data correlation analysis, especially for inexact data and incomplete data. In GRA, points are usually regarded as objects, and the distance between points or the concave and convex degree are mostly used to measure the correlations. However, with discrete variables, correlation analysis results always tend to have some deviations when using prior GRA methods. Furthermore, GRA methods cannot directly use vector datasets. Therefore, in this paper, an improved GRA method is proposed based on vector projections. The input and output variables are expressed as vectors by linking two adjacent points. The vectors, instants of the points, are regarded as the objects, and the projection length of input variables to output variables is used to measure the correlations. The smaller the difference between the projection length and the input variables, the higher the correlation. Then, a hybrid variable selection and prediction model is proposed based on the improved GRA method for multivariate chaotic time series predictions, in order to overcome the negative effects of irrelevant and redundant variables caused by phase-space reconstruction. The experimental results based on the gas furnace dataset and San Francisco river runoff dataset demonstrate that the improved GRA method is effective for data correlation analysis, and the prediction accuracy is better than prior GRA-based methods.

I. Introduction

Time series widely exist in the fields of hydrology, meteorology, signal processing, medical sciences, etc. The universal existence of time series determines the necessity of time series research [1]. For complex systems, multivariate time series are typically used. Prediction models based on multivariate time series can contain more information about a system and afford higher prediction accuracy [2]. Therefore, multivariate time series prediction is an important research direction in the field of time series. However, there are many limitations of multivariate time series prediction that need to be considered. Complex correlations always exist among multivariate time series. The correlations may not only limit the performance of the prediction model, but also enlarge the model size. Furthermore, complex correlations can also increase computational load, decrease prediction accuracy, and even result in the “curse of dimensionality” [3]. Therefore, it is essential to analyze correlations among multivariate time series, select appropriate input variables, and reduce input dimensions.