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


  • Theodore Alexandrov
  • Silvia Bianconcini
  • Estela Bee Dagum
  • Peter Maass
  • Tucker S. McElroy


This article presents a review of some modern approaches to trend extraction for one-dimensional time series, which is one of the major tasks of time series analysis. The trend of a time series is usually defined as a smooth additive component which contains information about the time series global change, and we discuss this and other definitions of the trend. We do not aim to review all the novel approaches, but rather to observe the problem from different viewpoints and from different areas of expertise. The article contributes to understanding the concept of a trend and the problem of its extraction. We present an overview of advantages and disadvantages of the approaches under consideration, which are: the model-based approach (MBA), nonparametric linear filtering, singular spectrum analysis (SSA), and wavelets. The MBA assumes the specification of a stochastic time series model, which is usually either an autoregressive integrated moving average (ARIMA) model or a state space model. The nonparametric filtering methods do not require specification of model and are popular because of their simplicity in application. We discuss the Henderson, LOESS, and Hodrick--Prescott filters and their versions derived by exploiting the Reproducing Kernel Hilbert Space methodology. In addition to these prominent approaches, we consider SSA and wavelet methods. SSA is widespread in the geosciences; its algorithm is similar to that of principal components analysis, but SSA is applied to time series. Wavelet methods are the de facto standard for denoising in signal procession, and recent works revealed their potential in trend analysis.

Suggested Citation

  • Theodore Alexandrov & Silvia Bianconcini & Estela Bee Dagum & Peter Maass & Tucker S. McElroy, 2012. "A Review of Some Modern Approaches to the Problem of Trend Extraction," Econometric Reviews, Taylor & Francis Journals, vol. 31(6), pages 593-624, November.
  • Handle: RePEc:taf:emetrv:v:31:y:2012:i:6:p:593-624
    DOI: 10.1080/07474938.2011.608032

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    Cited by:

    1. Vasilios Plakandaras & Theophilos Papadimitriou & Periklis Gogas, 2015. "Forecasting Daily and Monthly Exchange Rates with Machine Learning Techniques," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(7), pages 560-573, November.
    2. Huang, Xu & Hassani, Hossein & Ghodsi, Mansi & Mukherjee, Zinnia & Gupta, Rangan, 2017. "Do trend extraction approaches affect causality detection in climate change studies?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 604-624.
    3. Yoon, Gawon, 2015. "Locating change-points in Hodrick–Prescott trends with an application to US real GDP: A generalized unobserved components model approach," Economic Modelling, Elsevier, vol. 45(C), pages 136-141.
    4. Michel Grun-Rehomme & OLGA VASYECHKO, 2013. "Methodes De Lissage D’Une Serie Temporelle :Le Probleme Des Extremites," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 56(2), pages 163-174.
    5. Huang, Xuan & An, Haizhong & Gao, Xiangyun & Hao, Xiaoqing & Liu, Pengpeng, 2015. "Multiresolution transmission of the correlation modes between bivariate time series based on complex network theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 493-506.
    6. Wildi Marc & McElroy Tucker, 2016. "Optimal Real-Time Filters for Linear Prediction Problems," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 155-192, July.
    7. Tung-Lam Dao, 2014. "Momentum Strategies with L1 Filter," Papers 1403.4069,
    8. Trimbur Thomas & McElroy Tucker, 2017. "Signal Extraction for Nonstationary Time Series with Diverse Sampling Rules," Journal of Time Series Econometrics, De Gruyter, vol. 9(1), pages 1-37, January.
    9. Herman Stekler & Yongchen Zhao, 2016. "Predicting U.S. Business Cycle Turning Points Using Real-Time Diffusion Indexes Based on a Large Data Set," Working Papers 2016-15, Towson University, Department of Economics, revised Sep 2016.
    10. Dagum, Estela Bee, 2010. "Business Cycles and Current Economic Analysis/Los ciclos económicos y el análisis económico actual," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 28, pages 577-594, Diciembre.
    11. Luis Francisco Rosales & Tatyana Krivobokova, 2012. "Instant Trend-Seasonal Decomposition of Time Series with Splines," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 131, Courant Research Centre PEG.
    12. Anusha, "undated". "Evaluating reliability of some symmetric and asymmetric univariate filters," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2015-030, Indira Gandhi Institute of Development Research, Mumbai, India.

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