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Trend filtering via empirical mode decompositions

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  • Moghtaderi, Azadeh
  • Flandrin, Patrick
  • Borgnat, Pierre

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 Vélo’v).

Suggested Citation

  • Moghtaderi, Azadeh & Flandrin, Patrick & Borgnat, Pierre, 2013. "Trend filtering via empirical mode decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 114-126.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:114-126
    DOI: 10.1016/j.csda.2011.05.015
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    References listed on IDEAS

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    1. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    2. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 393-419, August.
    3. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
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    Cited by:

    1. Jason Angelopoulos, 2017. "Time–frequency analysis of the Baltic Dry Index," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 19(2), pages 211-233, June.
    2. Plakandaras, Vasilios & Gupta, Rangan & Gogas, Periklis & Papadimitriou, Theophilos, 2015. "Forecasting the U.S. real house price index," Economic Modelling, Elsevier, vol. 45(C), pages 259-267.
    3. Bangzhu Zhu & Ping Wang & Julien Chevallier & Yiming Wei, 2015. "Carbon Price Analysis Using Empirical Mode Decomposition," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 195-206, February.
    4. repec:ipg:wpaper:2014-473 is not listed on IDEAS
    5. Yujia Ge & Yurong Nan & Lijun Bai, 2019. "A Hybrid Prediction Model for Solar Radiation Based on Long Short-Term Memory, Empirical Mode Decomposition, and Solar Profiles for Energy Harvesting Wireless Sensor Networks," Energies, MDPI, vol. 12(24), pages 1-21, December.
    6. Wang, Yalin & Xu, Yan & Liu, Minghui & Guo, Yao & Wu, Yonglin & Chen, Chen & Chen, Wei, 2022. "Cumulative residual symbolic dispersion entropy and its multiscale version: Methodology, verification, and application," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Alejandra Carmona & Germán Poveda, 2014. "Detection of long-term trends in monthly hydro-climatic series of Colombia through Empirical Mode Decomposition," Climatic Change, Springer, vol. 123(2), pages 301-313, March.
    8. Lisi, Francesco & Nan, Fany, 2014. "Component estimation for electricity prices: Procedures and comparisons," Energy Economics, Elsevier, vol. 44(C), pages 143-159.
    9. Jason Angelopoulos, 2017. "Creating and assessing composite indicators: Dynamic applications for the port industry and seaborne trade," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 19(1), pages 126-159, March.

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