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Further Developments on the Henderson Trend-Cycle Filter

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Book cover Seasonal Adjustment Methods and Real Time Trend-Cycle Estimation

Part of the book series: Statistics for Social and Behavioral Sciences ((SSBS))

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Abstract

The linear filter developed by Henderson is the most widely applied to estimate the trend-cycle component in seasonal adjustment software such as the US Bureau of Census II-X11 and its variants, the X11/X12ARIMA. Major studies have been done on trend-cycle estimation during the last 20 years by making changes to the Henderson filters. The emphasis has been on determining the direction of the short-term trend for an early detection of a true turning point. This chapter introduces in detail three major contributions: (1) a nonlinear trend-cycle estimator also known as Nonlinear Dagum Filter (NLDF), (2) a Cascade Linear Filter (CLF) that closely approximates the NLDF, and (3) an approximation to the Henderson filter via the Reproducing Kernel Hilbert Space (RKHS) methodology.

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References

  1. Berlinet, A. (1993). Hierarchies of higher order kernels. Probability Theory and Related Fields, 94, 489–504.

    Article  MathSciNet  MATH  Google Scholar 

  2. Berlinet, A., & Devroye, L. (1994). A comparison of kernel density estimates. Publications de l’Institut de Statistique de l’Université de Paris, 38, 3–59.

    MathSciNet  MATH  Google Scholar 

  3. Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. San Francisco, CA, USA: Holden-Day (Second Edition 1976).

    Google Scholar 

  4. Castles, I. (1987). A guide to smoothing time series estimates of trend. Catalogue No. 1316. Australian Bureau.

    Google Scholar 

  5. Chhab, N., Morry, M., & Dagum, E. B. (1999). Results on alternative trend-cycle estimators for current economic analysis. Estadistica, 49–51, 231–257.

    Google Scholar 

  6. Cholette, P. A. (1981). A comparison of various trend-cycle estimators. In O. D. Anderson & M. R. Perryman (Eds.), Time series analysis (pp. 77–87). Amsterdam: North Holland.

    Google Scholar 

  7. Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal trend decomposition procedure based on LOESS. Journal of Official Statistics, 6(1), 3–33.

    Google Scholar 

  8. Dagum, E. B. (1988). The X11ARIMA/88 seasonal adjustment method-foundations and user’s manual. Ottawa, Canada: Time Series Research and Analysis Centre, Statistics Canada.

    Google Scholar 

  9. Dagum, E. B. (1996). A new method to reduce unwanted ripples and revisions in trend-cycle estimates from X11ARIMA. Survey Methodology, 22, 77–83.

    Google Scholar 

  10. Dagum, E. B., & Bianconcini, S. (2006). Local polynomial trend-cycle predictors in reproducing kernel Hilbert spaces for current economic analysis. Anales de Economia Aplicada, 1–22.

    Google Scholar 

  11. Dagum, E. B., & Bianconcini, S. (2008). The Henderson smoother in reproducing kernel Hilbert space. Journal of Business and Economic Statistics, 26(4), 536–545.

    Article  MathSciNet  Google Scholar 

  12. Dagum, E. B., Chhab, N., & Chiu, K. (1996). Derivation and analysis of the X11ARIMA and Census X11 linear filters. Journal of Official Statistics, 12(4), 329–347.

    Google Scholar 

  13. Dagum, E. B., & Laniel, N. (1987). Revisions of trend-cycle estimators of moving average seasonal adjustment methods. Journal of Business and Economic Statistics, 5, 177–189.

    Google Scholar 

  14. Dagum, E. B., & Luati, A. (2000). Predictive performance of some nonparametric linear and nonlinear smoothers for noisy data. Statistica, LX(4), 635–654.

    Google Scholar 

  15. Dagum, E. B., & Luati, A. (2004). A linear transformation and its properties with special applications in time series filtering. Linear Algebra and its Applications, 338, 107–117.

    Article  MathSciNet  MATH  Google Scholar 

  16. Dagum, E. B., & Luati, A. (2009). A cascade linear filter to reduce revisions and turning points for real time trend-cycle estimation. Econometric Reviews, 28(1–3), 40–59.

    MathSciNet  MATH  Google Scholar 

  17. Dalton, P., & Keogh, G. (2000). An experimental indicator to forecast turning points in the Irish business cycle. Journal of the Statistical and Social Inquiry Society of Ireland, XXIX, 117–176.

    Google Scholar 

  18. Darnè, O. (2002). La dèsaisonnalisation des chroniques économiques: analyse des conditions conjuncturelles (Ph.D. dissertation, Department of Economics, University of Montpellier 1, France).

    Google Scholar 

  19. Findley, D. F., & Martin, D. E. K. (2006). Frequency domain analysis of SEATS and X-11/X-12-ARIMA seasonal adjustment filters for short and moderate length time series. Journal of Official Statistics, 22, 1–34.

    Google Scholar 

  20. Findley, D. F., Monsell, B. C., Bell, W. R., Otto, M. C., & Chen, B. C. (1998). New capabilities and methods of the X12ARIMA seasonal adjustment program. Journal of Business and Economic Statistics, 16(2), 127–152.

    Google Scholar 

  21. Gray, A., & Thomson, P. (1996). Design of moving-average trend filters using fidelity and smoothness criteria. In P. M. Robinson & M. Rosenblatt (Eds.), Time series analysis (in memory of E.J. Hannan). Vol. II. Lecture notes in statistics (Vol. 115, pp. 205–219). New York: Springer.

    Google Scholar 

  22. Henderson, R. (1916). Note on graduation by adjusted average. Transaction of Actuarial Society of America, 17, 43–48.

    Google Scholar 

  23. Kenny, P., & Durbin, J. (1982). Local trend estimation and seasonal adjustment of economic and social time series. Journal of the Royal Statistical Society A, 145, 1–41.

    Article  Google Scholar 

  24. Ladiray, D., & Quenneville, B. (2001). Seasonal adjustment with the X-11 method. Lecture notes in statistics (Vol. 158). New York: Springer.

    Google Scholar 

  25. Loader, C. (1999). Local regression and likelihood. New York: Springer.

    MATH  Google Scholar 

  26. Müller, H. G. (1984). Smooth optimum kernel estimators of regression curves, densities and modes. Annals of Statistics, 12, 766–774.

    Article  MathSciNet  MATH  Google Scholar 

  27. Musgrave, J. (1964). A set of end weights to end all end weights. Working Paper. U.S. Bureau of Census, Washington DC.

    Google Scholar 

  28. Priestley, M. B. (1981). Spectral analysis and time series. Probability and mathematical statistics. New York: Academic Press.

    Google Scholar 

  29. Quenneville, B., Ladiray, D., & Lefrancois, B. (2003). A note on Musgrave asymmetrical trend-cycle filters. International Journal of Forecasting, 19(4), 727–734.

    Article  Google Scholar 

  30. Shiskin, J., Young, A. H., & Musgrave, J. C. (1967). The X-11 variant of the Census Method II seasonal adjustment program. Technical Paper 15 (revised). US Department of Commerce, Bureau of the Census, Washington, DC.

    Google Scholar 

  31. Wahba, G. (1990). Spline models for observational data. Philadelphia: SIAM.

    Book  MATH  Google Scholar 

  32. Zellner, A., Hong, C., & Min, C. (1991). Forecasting turning points in international output growth rates using Bayesian exponentially weighted autoregression, time-varying parameter and pooling techniques. Journal of Econometrics, 48, 275–304.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Statistical Sciences, University of Bologna, Bologna, Italy

    Estela Bee Dagum & Silvia Bianconcini

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  1. Estela Bee Dagum
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  2. Silvia Bianconcini
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Bee Dagum, E., Bianconcini, S. (2016). Further Developments on the Henderson Trend-Cycle Filter. In: Seasonal Adjustment Methods and Real Time Trend-Cycle Estimation. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-31822-6_8

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