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Forecasting and signal extraction with misspecified models

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  • Tommaso Proietti

    (Università di Udine, Italy)

Abstract

This paper evaluates multistep estimation for the purposes of signal extraction, and in particular the separation of the trend from the cycle in economic time series, and long-range forecasting, in the presence of a misspecified, but simply parameterized model. Our workhorse models are two popular unobserved components models, namely the local level and the local linear model. The paper introduces a metric for assessing the accuracy of the unobserved components estimates and concludes that multistep estimation can be valuable. However, its performance depends crucially on the properties of the series and the paper explores the role of the order of integration and the relative size of the cyclical variation. On the contrary, cross-validation is usually not suitable for the purposes considered. Copyright © 2005 John Wiley & Sons, Ltd.

Suggested Citation

  • Tommaso Proietti, 2005. "Forecasting and signal extraction with misspecified models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(8), pages 539-556.
    • Handle: RePEc:jof:jforec:v:24:y:2005:i:8:p:539-556
    DOI: 10.1002/for.970
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    References listed on IDEAS

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    1. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    2. Clements, Michael P & Hendry, David F, 1996. "Multi-step Estimation for Forecasting," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 657-684, November.
    3. Peter Young, 1999. "Recursive and en-bloc approaches to signal extraction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 103-128.
    4. 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.
    5. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    6. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May.
    7. J. Haywood & G. Tunnicliffe Wilson, 1997. "Fitting Time Series Models by Minimizing Multistep‐ahead Errors: a Frequency Domain Approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 237-254.
    8. Tommaso Proietti, 2003. "Leave‐K‐Out Diagnostics In State‐Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 221-236, March.
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    Cited by:

    1. Kauermann Goeran & Krivobokova Tatyana & Semmler Willi, 2011. "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-28, March.
    2. Eliud Silva & Víctor M. Guerrero, 2017. "Penalized least squares smoothing of two-dimensional mortality tables with imposed smoothness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1662-1679, July.
    3. Blöchl, Andreas, 2014. "Penalized Splines as Frequency Selective Filters - Reducing the Excess Variability at the Margins," Discussion Papers in Economics 20687, University of Munich, Department of Economics.
    4. Tommaso Proietti, 2009. "Structural Time Series Models for Business Cycle Analysis," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 9, pages 385-433, Palgrave Macmillan.
    5. McElroy, Tucker S. & Wildi, Marc, 2020. "The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions," Econometrics and Statistics, Elsevier, vol. 14(C), pages 112-130.
    6. Flaig Gebhard, 2015. "Why We Should Use High Values for the Smoothing Parameter of the Hodrick-Prescott Filter," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 235(6), pages 518-538, December.
    7. Pollock, D.S.G., 2006. "Introduction to the special issue on statistical signal extraction and filtering," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2137-2145, May.
    8. Bloechl, Andreas, 2014. "Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter," Discussion Papers in Economics 21406, University of Munich, Department of Economics.
    9. Proietti, Tommaso, 2008. "Band spectral estimation for signal extraction," Economic Modelling, Elsevier, vol. 25(1), pages 54-69, January.
    10. 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.
    11. Göran Kauermann & Timo Teuber & Peter Flaschel, 2012. "Exploring US Business Cycles with Bivariate Loops Using Penalized Spline Regression," Computational Economics, Springer;Society for Computational Economics, vol. 39(4), pages 409-427, April.
    12. Harvey, Andrew C. & Delle Monache, Davide, 2009. "Computing the mean square error of unobserved components extracted by misspecified time series models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 283-295, February.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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