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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. Copyright 2005 Blackwell Publishing Ltd.

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
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.0143-9782.2005.00462.x
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    References listed on IDEAS

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    1. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, pages 53-64.
    2. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, pages 2075-2088.
    3. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, pages 2075-2088.
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    Cited by:

    1. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60 Edward Elgar Publishing.
    2. Rünstler, Gerhard & Vlekke, Marente, 2016. "Business, housing and credit cycles," Working Paper Series 1915, European Central Bank.
    3. 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, pages 618-649.
    4. Joanne S. Ercolani, 2007. "Cyclical Trends in Continuous Time Models," Discussion Papers 07-13, Department of Economics, University of Birmingham.
    5. Dubovik, Andrei & Janssen, Maarten C.W., 2012. "Oligopolistic competition in price and quality," Games and Economic Behavior, Elsevier, pages 120-138.
    6. 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., pages 695-719.
    7. 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.
    8. 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, pages 207-219.
    9. Xiaoshan Chen & Terence Mills, 2012. "Measuring the Euro area output gap using a multivariate unobserved components model containing phase shifts," Empirical Economics, Springer, pages 671-692.
    10. 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.
    11. Alessandra Luati & Tommaso Proietti, 2010. "Hyper-spherical and elliptical stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, pages 169-181.
    12. Alessandra Luati & Tommaso Proietti, 2010. "Hyper-spherical and elliptical stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, pages 169-181.
    13. 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.).
    14. Trimbur, Thomas M., 2010. "Stochastic level shifts and outliers and the dynamics of oil price movements," International Journal of Forecasting, Elsevier, pages 162-179.
    15. 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.
    16. repec:psc:journl:v:9:y:2017:i:3:p:201-241 is not listed on IDEAS

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