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Properties of higher order stochastic cycles

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  • Thomas M. Trimbur

Abstract

. This article investigates a general class of stochastic cycles, presenting the main properties in the time and frequency domains. Harvey and Trimbur [Review of Economics and statistics (2003) Vol. 85, pp. 244–55] showed how generalized cyclical processes may be used in unobserved components models to extract smoother cycles in economic series. The stochastic cycle models allow for a flexible description of periodic behaviour in time series data. In the frequency domain, a wide variety of peaked spectral shapes, characteristic of time‐varying cyclical dynamics, is produced. The parameters have a direct interpretation, so cyclical behaviour may be studied directly; in a Bayesian approach, the researcher may implement prior views on the period in a consistent way. Extensions to multivariate models are possible.

Suggested Citation

  • Thomas M. Trimbur, 2006. "Properties of higher order stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 1-17, January.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:1:p:1-17
    DOI: 10.1111/j.0143-9782.2005.00462.x
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    1. Harvey, A. & TTrimbur, T. & van Dijk, H., 2003. "Cyclical Components in Economic Time Series: a Bayesian Approach," Cambridge Working Papers in Economics 0302, Faculty of Economics, University of Cambridge.
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    Cited by:

    1. Gerhard Rünstler & Marente Vlekke, 2018. "Business, housing, and credit cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(2), pages 212-226, March.
    2. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60, Edward Elgar Publishing.
    3. Drew Creal & Siem Jan Koopman & Eric Zivot, 2008. "The Effect of the Great Moderation on the U.S. Business Cycle in a Time-varying Multivariate Trend-cycle Model," Tinbergen Institute Discussion Papers 08-069/4, Tinbergen Institute.
    4. Rodrigo Barbone Gonzalez & Joaquim Lima & Leonardo Marinho, 2015. "Business and Financial Cycles: an estimation of cycles’ length focusing on Macroprudential Policy," Working Papers Series 385, Central Bank of Brazil, Research Department.
    5. Kum Hwa Oh & Eric Zivot & Drew Creal, 2006. "The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks," Working Papers UWEC-2006-16-FC, University of Washington, Department of Economics.
    6. Alessandra Luati & Tommaso Proietti, 2010. "Hyper‐spherical and elliptical stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 169-181, May.
    7. Łukasz Lenart, 2018. "Bayesian inference for deterministic cycle with time-varying amplitude: the case of growth cycle in European countries," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 10(3), pages 233-262, September.
    8. Trimbur, Thomas M., 2010. "Stochastic level shifts and outliers and the dynamics of oil price movements," International Journal of Forecasting, Elsevier, vol. 26(1), pages 162-179, January.
    9. Harvey, A.C. & Trimbur, T.M. & van Dijk, H.K., 2004. "Bayes estimates of the cyclical component in twentieth centruy US gross domestic product," Econometric Institute Research Papers EI 2004-45, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Xiaoshan Chen & Terence Mills, 2012. "Measuring the Euro area output gap using a multivariate unobserved components model containing phase shifts," Empirical Economics, Springer, vol. 43(2), pages 671-692, October.
    11. Łukasz Lenart & Mateusz Pipień, 2017. "Non-Parametric Test for the Existence of the Common Deterministic Cycle: The Case of the Selected European Countries," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(3), pages 201-241, September.
    12. Harvey, Andrew C. & Trimbur, Thomas M. & Van Dijk, Herman K., 2007. "Trends and cycles in economic time series: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 618-649, October.
    13. Joanne S. Ercolani, 2007. "Cyclical Trends in Continuous Time Models," Discussion Papers 07-13, Department of Economics, University of Birmingham.
    14. Drew Creal & Siem Jan Koopman & Eric Zivot, 2010. "Extracting a robust US business cycle using a time-varying multivariate model-based bandpass filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 695-719.
    15. Oh, Kum Hwa & Zivot, Eric & Creal, Drew, 2008. "The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics," Journal of Econometrics, Elsevier, vol. 146(2), pages 207-219, October.
    16. Li, Yunhan & Shonkwiler, J. Scott, 2021. "The Vanishing U.S. Cattle Cycle: A Stochastic Cycle Approach," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 46(3), September.
    17. 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.).

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