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A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation

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  • Estela Bee Dagum
  • Alessandra Luati

Abstract

The problem of identifying the direction of the short-term trend (nonstationary mean) of seasonally adjusted series contaminated by high levels of variability has become of relevant interest in recent years. In fact, major financial and economic changes of global character have introduced a large amount of noise in time series data, particularly, in socioeconomic indicators used for real time economic analysis. The aim of this study is to construct a cascade linear filter via the convolution of several noise suppression, trend estimation, and extrapolation linear filters. The cascading approach approximates the steps followed by the nonlinear Dagum (1996) trend-cycle estimator, a modified version of the 13-term Henderson filter. The former consists of first extending the seasonally adjusted series with ARIMA extrapolations, and then applying a very strict replacement of extreme values. The nonlinear Dagum filter has been shown to improve significantly the size of revisions and number of false turning points with respect to H13. We construct a linear approximation of the nonlinear filter because it offers several advantages. For one, its application is direct and hence does not require some knowledge on ARIMA model identification. Furthermore, linear filtering preserves the crucial additive constraint by which the trend of an aggregated variable should be equal to the algebraic addition of its component trends, thus avoiding the selection problem of direct versus indirect adjustments. Finally, the properties of a linear filter concerning signal passing and noise suppression can always be compared to those of other linear filters by means of spectral analysis.

Suggested Citation

  • Estela Bee Dagum & Alessandra Luati, 2009. "A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 40-59.
    • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:40-59
    DOI: 10.1080/07474930802387837
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    References listed on IDEAS

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    1. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
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    3. Zellner, Arnold & Hong, Chansik & Min, Chung-ki, 1991. "Forecasting turning points in international output growth rates using Bayesian exponentially weighted autoregression, time-varying parameter, and pooling techniques," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 275-304.
    4. Estela Bee Dagum & Alessandra Luati, 2002. "Global and local statistical properties of fixed-length nonparametric smoothers," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(3), pages 313-333, October.
    5. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
    6. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    7. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
    8. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
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    Cited by:

    1. Luis J. Álvarez, 2017. "Business Cycle Estimation with High-Pass and Band-Pass Local Polynomial Regression," Econometrics, MDPI, vol. 5(1), pages 1-11, January.
    2. Dagum, Estela Bee, 2010. "Business Cycles and Current Economic Analysis/Los ciclos económicos y el análisis económico actual," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 28, pages 577-594, Diciembre.
    3. Tommaso Proietti & Alessandra Luati, 2008. "Real Time Estimation in Local Polynomial Regression, with Application to Trend-Cycle Analysis," CEIS Research Paper 112, Tor Vergata University, CEIS, revised 14 Jul 2008.

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