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Forecasting and Signal Extraction with Misspecified Models


  • Tommaso Proietti

    (Dipartimento di Scienze Statistiche, Università di Udine)


The paper illustrates and compares estimation methods alternative to maximum likelihood, among which multistep estimation and leave-one-out cross-validation, 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 parameterised 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 cross- validation is not a suitable estimation criterion for the purpose considered, whereas multistep estimation can be valuable. Finally, we propose a local likelihood estimator in the frequency domain that provides a simple and alternative way of making operative the notion of emphasising the long-run properties of a time series.

Suggested Citation

  • Tommaso Proietti, 2004. "Forecasting and Signal Extraction with Misspecified Models," Econometrics 0401002, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0401002
    Note: Type of Document - ; prepared on WinXP; pages: 34; figures: 9

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    References listed on IDEAS

    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. Peter Young, 1999. "Recursive and en-bloc approaches to signal extraction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 103-128.
    3. 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.
    4. 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.
    5. 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.
    6. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May.
    7. 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. 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.
    2. Proietti, Tommaso, 2008. "Structural Time Series Models for Business Cycle Analysis," MPRA Paper 6854, University Library of Munich, Germany.
    3. 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.
    4. 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.
    5. Bloechl, Andreas, 2014. "Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter," Discussion Papers in Economics 21406, University of Munich, Department of Economics.
    6. Proietti, Tommaso, 2008. "Band spectral estimation for signal extraction," Economic Modelling, Elsevier, vol. 25(1), pages 54-69, January.
    7. 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.
    8. 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.

    More about this item


    Business cycles; Unobserved components models; Cross- validation; Smoothing; Hodrick-Prescott filter; Multistep estimation.;

    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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