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Cyclical Trends in Continuous Time Models


  • Joanne S. Ercolani


It is undoubtedly desirable that econometric models capture the dynamic behaviour,like trends and cycles, observed in many economic processes. Building models with such capabilities has been an important objective in the continuous time econometrics literature, see for instance the cyclical growth models of Bergstrom (1966), the complete economy-wide macroeconometric models of, for example, Bergstrom and Wymer (1976), unobserved stochastic trends of Harvey and Stock (1988 and 1993) and Bergstrom (1997), and differential-difference equations of Chambers and McGarry (2002). This paper’s contribution is to examine cyclical trends formulated in continuous time, which complement the trend-plus-cycle models that are frequently used in the unobserved components literature.

Suggested Citation

  • Joanne S. Ercolani, 2007. "Cyclical Trends in Continuous Time Models," Discussion Papers 07-13, Department of Economics, University of Birmingham.
  • Handle: RePEc:bir:birmec:07-13

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    References listed on IDEAS

    1. Harvey, A. C. & Stock, James H., 1988. "Continuous time autoregressive models with common stochastic trends," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 365-384.
    2. Bergstrom, A.R., 1997. "Gaussian Estimation of Mixed-Order Continuous-Time Dynamic Models with Unobservable Stochastic Trends from Mixed Stock and Flow Data," Econometric Theory, Cambridge University Press, vol. 13(04), pages 467-505, August.
    3. Bergstrom, A. R. & Nowman, K. B. & Wymer, C. R., 1992. "Gaussian estimation of a second order continuous time macroeconometric model of the UK," Economic Modelling, Elsevier, vol. 9(4), pages 313-351, October.
    4. Bergstrom,Albert Rex & Nowman,Khalid Ben, 2012. "A Continuous Time Econometric Model of the United Kingdom with Stochastic Trends," Cambridge Books, Cambridge University Press, number 9781107411234, March.
    5. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    6. Ercolani, Joanne S. & Chambers, Marcus J., 2006. "Estimation Of Differential-Difference Equation Systems With Unknown Lag Parameters," Econometric Theory, Cambridge University Press, vol. 22(03), pages 483-498, June.
    7. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
    8. 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.
    9. 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(02), pages 387-419, April.
    10. A. R. Bergstrom, 2001. "Stability and wage acceleration in macroeconomic models of cyclical growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 327-340.
    11. Thomas M. Trimbur, 2006. "Properties of higher order stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 1-17, January.
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    More about this item


    Cyclical Trends; continuous time models; stochastic differential equations; differential-difference equations;

    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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