September 18, 2007 | Zhaohua Wu*, Norden E. Huang†, Steven R. Long‡, and Chung-Kang Peng§¶
This article discusses the challenges of defining and extracting trends from nonlinear and nonstationary time series data. Traditional methods for trend detection, such as linear regression or moving averages, often fail because they assume stationarity and linearity, which are not always valid for real-world data. The authors propose a new definition of trend as an intrinsically determined monotonic function or a function with at most one extremum within a given data span. This definition is intrinsic, meaning it is derived from the data itself and is adaptive to the data's characteristics. The Empirical Mode Decomposition (EMD) method is suggested as the logical choice for extracting trends because it is adaptive and can handle nonlinear and nonstationary data.
The EMD method decomposes a time series into intrinsic mode functions (IMFs), which are oscillatory components that represent different time scales of the data. The trend is then identified as the overall adaptive trend derived from the IMFs. The variability of the data on various time scales is also derived naturally from the EMD decomposition.
The article uses climate data, specifically the annual global surface temperature anomalies (GSTA), to illustrate the determination of the intrinsic trend and natural variability. The GSTA data are decomposed into IMFs using EMD, and the results show that the first four IMFs are not statistically significant, while the fifth IMF represents multidecadal variability and the residual represents the overall trend. The overall adaptive trend is found to be highly robust and reliable, with a time scale of approximately 65 years.
The article concludes that the EMD method provides a more accurate and reliable way to analyze nonlinear and nonstationary data compared to traditional methods. The method is adaptive, allowing it to capture the intrinsic properties of the data, and it is particularly useful for climate data analysis. The results demonstrate that the EMD method can reveal important intrinsic properties of the data and provide a more accurate understanding of trends and variability in nonlinear and nonstationary systems.This article discusses the challenges of defining and extracting trends from nonlinear and nonstationary time series data. Traditional methods for trend detection, such as linear regression or moving averages, often fail because they assume stationarity and linearity, which are not always valid for real-world data. The authors propose a new definition of trend as an intrinsically determined monotonic function or a function with at most one extremum within a given data span. This definition is intrinsic, meaning it is derived from the data itself and is adaptive to the data's characteristics. The Empirical Mode Decomposition (EMD) method is suggested as the logical choice for extracting trends because it is adaptive and can handle nonlinear and nonstationary data.
The EMD method decomposes a time series into intrinsic mode functions (IMFs), which are oscillatory components that represent different time scales of the data. The trend is then identified as the overall adaptive trend derived from the IMFs. The variability of the data on various time scales is also derived naturally from the EMD decomposition.
The article uses climate data, specifically the annual global surface temperature anomalies (GSTA), to illustrate the determination of the intrinsic trend and natural variability. The GSTA data are decomposed into IMFs using EMD, and the results show that the first four IMFs are not statistically significant, while the fifth IMF represents multidecadal variability and the residual represents the overall trend. The overall adaptive trend is found to be highly robust and reliable, with a time scale of approximately 65 years.
The article concludes that the EMD method provides a more accurate and reliable way to analyze nonlinear and nonstationary data compared to traditional methods. The method is adaptive, allowing it to capture the intrinsic properties of the data, and it is particularly useful for climate data analysis. The results demonstrate that the EMD method can reveal important intrinsic properties of the data and provide a more accurate understanding of trends and variability in nonlinear and nonstationary systems.