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

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…

• NS
  National Science Foundation

  Awards: 0342104, 0653123
• NA
  National Aeronautics and Space Administration
• UO
  University of Washington
• NS
  National Science Council
• TS
  Taiwan Semiconductor Manufacturing Company
• NC
  National Central University
• NI
  National Institutes of Health

  Award: P41-RR13622
• NC
  National Center for Research Resources

  Award: P41-RR13622