On the trend, detrending, and variability of nonlinear and nonstationary time series

Zhaohua Wu, Norden E. Huang, Steven R. Long, Chung Kang Peng

研究成果: 雜誌貢獻期刊論文同行評審

773 引文 斯高帕斯(Scopus)


Determining trend and implementing detrending operations are important steps in data analysis. Yet there is no precise definition of "trend" nor any logical algorithm for extracting it. As a result, various ad hoc extrinsic methods have been used to determine trend and to facilitate a detrending operation. In this article, a simple and logical definition of trend is given for any nonlinear and nonstationary time series as an intrinsically determined monotonic function within a certain temporal span (most often that of the data span), or a function in which there can be at most one extremum within that temporal span. Being intrinsic, the method to derive the trend has to be adaptive. This definition of trend also presumes the existence of a natural time scale. All these requirements suggest the Empirical Mode Decomposition (EMD) method as the logical choice of algorithm for extracting various trends from a data set. Once the trend is determined, the corresponding detrending operation can be implemented. With this definition of trend, the variability of the data on various time scales also can be derived naturally. Climate data are used to illustrate the determination of the intrinsic trend and natural variability.

頁(從 - 到)14889-14894
期刊Proceedings of the National Academy of Sciences of the United States of America
出版狀態已出版 - 18 9月 2007


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