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


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  • 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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 31 (2012)
Issue (Month): 6 (November)
Pages: 593-624

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Handle: RePEc:taf:emetrv:v:31:y:2012:i:6:p:593-624

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Cited by:
  1. Papadimitriou, Theophilos & Gogas, Periklis & Plakandaras, Vasilios, 2013. "Forecasting daily and monthly exchange rates with machine learning techniques," DUTH Research Papers in Economics 3-2013, Democritus University of Thrace, Department of Economics, revised 26 Sep 2013.
  2. 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.
  3. 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.
  4. Tung-Lam Dao, 2014. "Momentum Strategies with L1 Filter," Papers 1403.4069,


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