Local Functional Coefficient Autoregressive Model for Multistep Prediction of Chaotic Time Series

Liyun Su,Chenlong Li

doi:10.1155/2015/329487

Abstract

A new methodology, which combines nonparametric method based on local functional coefficient autoregressive (LFAR) form with chaos theory and regional method, is proposed for multistep prediction of chaotic time series. The objective of this research study is to improve the performance of long-term forecasting of chaotic time series. To obtain the prediction values of chaotic time series, three steps are involved. Firstly, the original time series is reconstructed inm-dimensional phase space with a time delayτby using chaos theory. Secondly, select the nearest neighbor points by using local method in them-dimensional phase space. Thirdly, we use the nearest neighbor points to get a LFAR model. The proposed model’s parameters are selected by modified generalized cross validation (GCV) criterion. Both simulated data (Lorenz and Mackey-Glass systems) and real data (Sunspot time series) are used to illustrate the performance of the proposed methodology. By detailed investigation and comparing our results with published researches, we find that the LFAR model can effectively fit nonlinear characteristics of chaotic time series by using simple structure and has excellent performance for multistep forecasting.

Highlights

In recent decades, researchers have paid much attention to chaos motion in many fields, such as meteorology, medicine, economics, signal processing, traffic flow, power load, Sunspot prediction, and many others [1,2,3,4,5,6,7,8,9,10,11,12] and bring about lots of new models for predicting chaotic time series
By detailed investigation and comparing our results with published researches, we find that the local functional coefficient autoregressive (LFAR) model can effectively fit nonlinear characteristics of chaotic time series by using simple structure and has excellent performance for multistep forecasting
Some researchers have been focusing on multistep prediction and using neural network (NN) or its extended models to improve the performance of multistep prediction [29,30,31]

Summary

Introduction

Researchers have paid much attention to chaos motion in many fields, such as meteorology, medicine, economics, signal processing, traffic flow, power load, Sunspot prediction, and many others [1,2,3,4,5,6,7,8,9,10,11,12] and bring about lots of new models for predicting chaotic time series. The direct and iterative methods are proposed as two main categories. Some researchers’ studies show that the accuracy of prediction can be improved by using hybrid technique, such as combined SVM and Neuro-Fuzzy [32] and neural network and Neuro-Fuzzy [25, 26]. Researchers’ studies show that hybrid technique can appear to have good performance by using the prediction error, such as the combined PCA and SVM [19] and ARMA and RESN [7]. The generalized nonlinear filtering methods are investigated for 5-step prediction of chaotic time series in [33].

Methods

Results

Conclusion