Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (5): 1364-1376.

• Articles • Previous Articles     Next Articles

Nonstationarity Measure of Data Stream

 DING Yi-Ming, FAN Wen-Tao, TAN Qiu-Heng, WU Ke-Kun, ZOU Yong-Jie   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071|Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071|Graduate School of the Chinese Academy of Sciences, The Chinese Academy of Sciences, Beijing 100049|School of Sciences, |Wuhan University of Technology, Wuhan 430070
  • Received:2010-10-08 Online:2010-10-25 Published:2010-10-25
  • Supported by:

    国家自然科学基金(Nos.70571079, 60534080)资助

Abstract:

We study the nonstationarity measure for data streams by integration ideas from ergodic theory, coarse grain and information theory. We introduce nonstationarity measure for data streams. An effective approximation algorithm is designed for implementation. The nonstationarity measure is a real number between 0 and 1. The nonstationarity measure is smaller for a more stationary data stream. We apply the nonstationarity measure to model selection, and propose a criterion for model selection which requires least nonstationarity measure for residual sequence. Numerical experiments are performed to test our approximation algorithm and to validate the least nonstationarity measure as a criterion for model selection. The numerical results indicate that the nonstationarity measure is a sound index to compare the level of
nonstationarity among data streams. By comparing the nonstationarity measure, we can distinguish trend-stationary process and difference-stationary process effectively, and discern i.i.d. sequence, white noise sequence and martingale difference sequence.

Key words: Data analysis, Nonstationarity measure, Model selection, Stable set, Shannon entropy

CLC Number: 

  • 62M10
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