Trend filtering via empirical mode decompositions

Authors:
Azadeh Moghtaderi;Patrick Flandrin;Pierre Borgnat
Affiliations:
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada K7L 3N6 and CNRS, ícole Normale Supérieure de Lyon, Laboratoire de Physique, 46 allée d'Itali ...;CNRS, ícole Normale Supérieure de Lyon, Laboratoire de Physique, 46 allée d'Italie 69364 Lyon CEDEX 07, France;CNRS, ícole Normale Supérieure de Lyon, Laboratoire de Physique, 46 allée d'Italie 69364 Lyon CEDEX 07, France
Venue:
Computational Statistics & Data Analysis
Year:
2013

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Abstract

The problem of filtering low-frequency trend from a given time series is considered. In order to solve this problem, a nonparametric technique called empirical mode decomposition trend filtering is developed. A key assumption is that the trend is representable as the sum of intrinsic mode functions produced by the empirical mode decomposition (EMD) of the time series. Based on an empirical analysis of the EMD, an automatic procedure for selecting the requisite intrinsic mode functions is proposed. To illustrate the effectiveness of the technique, it is applied 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 bicycle rental service (rental numbers of Grand Lyon Velo'v).