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Mathematical Problems in Engineering
Volume 2013, Article ID 516150, 7 pages
http://dx.doi.org/10.1155/2013/516150
Research Article

Set Pair Analysis Based on Phase Space Reconstruction Model and Its Application in Forecasting Extreme Temperature

1School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
2State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China
3Department of Mathematics and Statistics, Auburn University, Auburn, AL 36832, USA

Received 3 June 2013; Revised 16 July 2013; Accepted 19 July 2013

Academic Editor: Ming Li

Copyright © 2013 Yin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In order to improve the precision of forecasting a time series, set pair analysis based on phase space reconstruction (SPA-PSR) model is established. In the new model, by using chaos analysis, we reconstruct the phase space with delay time and embedding dimension. Based on it, we rebuilt history sets and current sets in the SPA-PSR model. Two cases of forecasting extreme temperature in Mount Wutai and Datong are taken to examine the performance of SPA-PSR model. The results indicate that the mean relative error (MRE) of SPA-PSR model has decreased by 65.97%, 59.32%, and 7.79% in the case of Mount Wutai and 29.11%, 32.82%, and 9.03% in the case of Datong, respectively, compared with autoregression (AR) model, rank set pair analysis (R-SPA) model, and Back-Propagation (BP) neural network model. It gives a theoretical support for set pair analysis and improves precision of numerical forecasting.