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Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration

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  • Dimitrios D. Thomakos

    (University of Peloponnese, Greece and The Rimini Centre for Economic Analysis)

Abstract

In this paper I propose a novel optimal linear filter for smoothing, trend and signal extraction for time series with a unit root. The filter is based on the Singular Spectrum Analysis (SSA) methodology, takes the form of a particular moving average and is different from other linear filters that have been used in the existing literature. To best of my knowledge this is the first time that moving average smoothing is given an optimality justification for use with unit root processes. The frequency response function of the filter is examined and a new method for selecting the degree of smoothing is suggested. I also show that the filter can be used for successfully extracting a unit root signal from stationary noise. The proposed methodology can be extended to also deal with two cointegrated series and I show how to estimate the cointegrating coefficient using SSA and how to extract the common stochastic trend component. A simulation study explores some of the characteristics of the filter for signal extraction, trend prediction and cointegration estimation for univariate and bivariate series. The practical usefulness of the method is illustrated using data for the US real GDP and two financial time series.

Suggested Citation

  • Dimitrios D. Thomakos, 2008. "Optimal Linear Filtering, Smoothing and Trend Extraction for Processes with Unit Roots and Cointegration," Working Paper series 14_08, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:14_08
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    References listed on IDEAS

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    1. Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," Discussion Papers in Economics 304, University of Munich, Department of Economics.
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    Cited by:

    1. 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.
    2. Papailias, Fotis & Liu, Jiadong & Thomakos, Dimitrios D., 2019. "Return Signal Momentum," QBS Working Paper Series 2019/04, Queen's University Belfast, Queen's Business School.
    3. D.S. Poskitt, 2016. "Singular Spectrum Analysis of Grenander Processes and Sequential Time Series Reconstruction," Monash Econometrics and Business Statistics Working Papers 15/16, Monash University, Department of Econometrics and Business Statistics.
    4. Papailias, Fotis & Liu, Jiadong & Thomakos, Dimitrios D., 2021. "Return signal momentum," Journal of Banking & Finance, Elsevier, vol. 124(C).
    5. Khan, M. Atikur Rahman & Poskitt, D.S., 2017. "Forecasting stochastic processes using singular spectrum analysis: Aspects of the theory and application," International Journal of Forecasting, Elsevier, vol. 33(1), pages 199-213.

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