On the Trend, Detrending and Variability of Nonlinear and Non-stationary Time Series
Wednesday, September 7, 2011 - 10:45am - 11:25am
Determining trend and implementing detrending operations are important steps in data analysis. Traditionally, various extrinsic methods have been used to determine the trend, and to facilitate a detrending operation. In this talk, a simple and logical definition of trend is given for any nonlinear and non-stationary 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 timescale. All these requirements suggest the Empirical Mode Decomposition method (EMD) 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 timescales can also be derived naturally. Climate data are used to illustrate the determination of the intrinsic trend and natural variability.