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Modeling Cyclical Behavior With Differential-Difference Equations In An Unobserved Components Framework

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  • Chambers, Marcus J.
  • McGarry, Joanne S.

Abstract

This paper considers a continuous time unobserved components model in which the cyclical component follows a differential-difference equation whereas the trend and seasonal components follow more standard differential equations. Estimation of the parameters of the model with either a stock or a flow variable is analyzed using a frequency domain Gaussian estimator whose asymptotic properties are derived paying particular attention to the role of a truncation parameter that arises in the practical computation of the spectral density function. The results of a simulation exercise, which assesses the finite sample performance of the estimator, are also provided.

Suggested Citation

  • Chambers, Marcus J. & McGarry, Joanne S., 2002. "Modeling Cyclical Behavior With Differential-Difference Equations In An Unobserved Components Framework," Econometric Theory, Cambridge University Press, vol. 18(2), pages 387-419, April.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:02:p:387-419_18
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    Cited by:

    1. Joanne S. McGarry & Marcus J. Chambers, 2004. "Party formation and coalitional bargaining in a model of proportional representation," Discussion Papers 04-07, Department of Economics, University of Birmingham.
    2. Joanne S. Ercolani, 2007. "Cyclical Trends in Continuous Time Models," Discussion Papers 07-13, Department of Economics, University of Birmingham.
    3. Eliana González & Luis F. Melo & Luis E. Rojas & Brayan Rojas, 2011. "Estimations of the Natural Rate of Interest in Colombia," Money Affairs, CEMLA, vol. 0(1), pages 33-75, January-J.
    4. Joanne S. Ercolani, 2014. "Cyclical Activity and Gestation Lags in Investment," Manchester School, University of Manchester, vol. 82(5), pages 620-630, September.
    5. Joanne S. Ercolani, 2010. "On the Asymptotic Properties of a Feasible Estimator of the Continuous Time Long Memory Parameter," Discussion Papers 10-09, Department of Economics, University of Birmingham.
    6. Tucker S. McElroy & Thomas M. Trimbur, 2007. "Continuous time extraction of a nonstationary signal with illustrations in continuous low-pass and band-pass filtering," Finance and Economics Discussion Series 2007-68, Board of Governors of the Federal Reserve System (U.S.).
    7. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.

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