A Review of Some Modern Approaches to the Problem of Trend Extraction

Alexandrov, Theodore; Bianconcini, Silvia; Dagum, Estela Bee; Maaß, Peter; McElroy, Tucker

doi:10.1080/07474938.2011.608032

Cited by 121 publications

(97 citation statements)

References 62 publications

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“…Furthermore, while the above definition of trend seems to be generally accepted in the climate science community, other communities have a different understanding of trend. For example, in economics the annual cycle is usually referred to as a trend (Alexandrov et al 2008). In the climate community this is seen as being an oscillatory mode and part of the intrinsic climate variability.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

2012

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This study investigates the significance of trends of four temperature time series-Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

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Section: Introductionmentioning

confidence: 99%

“…If the observed warming is due to external forcing then we will call this a deterministic trend; on the other hand, if the warming is due to intrinsic climate variability we will call this a stochastic trend (Alexandrov et al 2008;Fatichi et al 2009). …”

Section: Introductionmentioning

confidence: 99%

Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

2012

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“…Indeed, given a time series generated by a particular physical system, it may be clear (based on physical intuition) how to solve the trend filtering problem. In the absence of physical intuition, it may still be possible to solve the trend filtering problem, provided one makes an ad hoc definition of trend; see (Alexandrov et al, 2008). Such definitions may require extra assumptions concerning the nature of the time series.…”

Section: Introductionmentioning

confidence: 99%

Trend filtering via empirical mode decompositions

Moghtaderi

Flandrin

Borgnat

2013

Computational Statistics & Data Analysis

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The present work is concerned with the problem of extracting low-frequency trend from a given time series. To solve this problem, the authors develop a nonparametric technique called empirical mode decomposition (EMD) trend filtering. A key assumption is that the trend is representable as the sum of intrinsic mode functions produced by the EMD. Based on an empirical analysis of the EMD, the authors propose an automatic procedure for selecting the requisite intrinsic mode functions. To illustrate the effectiveness of the technique, the authors apply it to simulated time series containing different types of trend, as well as real-world data collected from an environmental study (atmospheric carbon dioxide levels at Mauna Loa Observatory) and from a large-scale bicycle rental service (rental numbers of Grand Lyon Vélo'v).

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“…In the present approach, we choose to work directly on the phase signal so that the low-pass filter step becomes a trend detection step. For that purpose, several techniques exist such as the Hodrick-Prescott filter [7] .…”

Section: Instantaneous Phase/frequency and Mode Deflection Shapes Calmentioning

confidence: 99%

Identification of a Time-Varying Beam Using Hilbert Vibration Decomposition

Bertha

Golinval

2014

Topics in Modal Analysis II, Volume 8

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The present work is concerned by modal identification of time-varying systems. For this purpose, a method based on instantaneous frequency identification and synchronous demodulation is used to extract modal components from recorded signals. The proposed method of iterated sifting process is based on the Hilbert Vibration Decomposition (HVD) technique which is used to extract the instantaneous dominant vibrating component at each iteration. A source separation preprocessing step is introduced to treat multiple degree-of-freedom systems in an optimal way. Sources are used as reference signals to get a single instantaneous frequency of each mode for the demodulation on all the channels. The algorithm is presented and is applied to numerical simulation of a randomly excited time-varying structure for illustration purpose. The investigated structure is made up of a beam on which a non-negligible mass is traveling. The variable location of the mass results in changes in modal parameters.

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A Review of Some Modern Approaches to the Problem of Trend Extraction

Cited by 121 publications

References 62 publications

Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

Trend filtering via empirical mode decompositions

Identification of a Time-Varying Beam Using Hilbert Vibration Decomposition

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