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A Closed Form Multivariate Linear Filter

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  • Mr. Francis Vitek

Abstract

This paper considers the problem of jointly decomposing a set of time series variables into cyclical and trend components, subject to sets of stochastic linear restrictions among these cyclical and trend components. We derive a closed form solution to an ordinary problem featuring homogeneous penalty term difference orders and static restrictions, as well as to a generalized problem featuring heterogeneous penalty term difference orders and dynamic restrictions. We use our Generalized Multivariate Linear Filter to jointly estimate potential output, the natural rate of unemployment and the natural rate of interest, conditional on selected equilibrium conditions from a calibrated New Keynesian model.

Suggested Citation

  • Mr. Francis Vitek, 2018. "A Closed Form Multivariate Linear Filter," IMF Working Papers 2018/275, International Monetary Fund.
    • Handle: RePEc:imf:imfwpa:2018/275
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    References listed on IDEAS

    as
    1. Mr. Francis Vitek, 2012. "Policy Analysis and Forecasting in the World Economy: A Panel Unobserved Components Approach," IMF Working Papers 2012/149, International Monetary Fund.
    2. Lucas, Robert E, Jr, 1980. "Two Illustrations of the Quantity Theory of Money," American Economic Review, American Economic Association, vol. 70(5), pages 1005-1014, December.
    3. Clark, Peter K., 1989. "Trend reversion in real output and unemployment," Journal of Econometrics, Elsevier, vol. 40(1), pages 15-32, January.
    4. James D. Hamilton, 2017. "Why You Should Never Use the Hodrick-Prescott Filter," NBER Working Papers 23429, National Bureau of Economic Research, Inc.
    5. 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.
    6. Thomas Laubach & John C. Williams, 2003. "Measuring the Natural Rate of Interest," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 1063-1070, November.
    7. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    8. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
    9. Mr. Francis Vitek, 2009. "Monetary Policy Analysis and Forecasting in the World Economy: A Panel Unobserved Components Approach," IMF Working Papers 2009/238, International Monetary Fund.
    10. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
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