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

Proceedings of the National Academy of Sciences of the United States of America - Tập 104 Số 38 - Trang 14889-14894 - 2007
Zhaohua Wu1, Norden E. Huang2, Steven Long3, Chung‐Kang Peng4
1Center for Ocean-Land-Atmosphere Studies, 4041 Powder Mill Road, Suite 302, Calverton MD 20705, USA
2Research Center for Adaptive Data Analysis, National Central University, Chungli 32054, Taiwan, Republic of China;
3Ocean Sciences Branch, Code 614.2, National Aeronautics and Space Administration Goddard Space Flight Center, Wallops Flight Facility, Wallops Island, VA 23337; and
4Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA 02215

Tóm tắt

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.

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Thông tin xuất bản

Proceedings of the National Academy of Sciences of the United States of America

Tập 104 Số 38

14889-14894

Thông tin tác giả