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

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

Research output: Contribution to journalArticlepeer-review

796 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)14889-14894
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume104
Issue number38
DOIs
StatePublished - 18 Sep 2007

Keywords

  • Empirical Mode Decomposition
  • Global warming
  • Intrinsic mode function
  • Intrinsic trend
  • Trend time scale

Fingerprint

Dive into the research topics of 'On the trend, detrending, and variability of nonlinear and nonstationary time series'. Together they form a unique fingerprint.

Cite this