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Multivariate Trend‐Cycle‐Seasonal Decompositions with Correlated Innovations

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  • Jing Tian
  • Jan P.A.M. Jacobs
  • Denise R. Osborn

Abstract

Multivariate analysis can help to focus on important phenomena, including trend and cyclical movements, but any economic information in seasonality is typically ignored. The present paper aims to more fully exploit time series information through a multivariate unobserved component model for quarterly data that exhibits seasonality together with cross‐variable component correlations. We show that economic restrictions, including common trends, common cycles and common seasonals can aid identification. The approach is illustrated using Italian GDP and consumption data.

Suggested Citation

  • Jing Tian & Jan P.A.M. Jacobs & Denise R. Osborn, 2024. "Multivariate Trend‐Cycle‐Seasonal Decompositions with Correlated Innovations," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(5), pages 1260-1289, October.
    • Handle: RePEc:bla:obuest:v:86:y:2024:i:5:p:1260-1289
    DOI: 10.1111/obes.12602
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    References listed on IDEAS

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    1. Matas-Mir, Antonio & Osborn, Denise R., 2004. "Does seasonality change over the business cycle? An investigation using monthly industrial production series," European Economic Review, Elsevier, vol. 48(6), pages 1309-1332, December.
    2. Siem Jan Koopman & Kai Ming Lee, 2009. "Seasonality with trend and cycle interactions in unobserved components models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 427-448, September.
    3. Clark, Peter K., 1989. "Trend reversion in real output and unemployment," Journal of Econometrics, Elsevier, vol. 40(1), pages 15-32, January.
    4. Barend Abeln & Jan P. A. M. Jacobs, 2023. "Seasonal Adjustment Without Revisions," SpringerBriefs in Economics, Springer, number 978-3-031-22845-2, February.
    5. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    6. Pesaran, H. Hashem & Shin, Yongcheol, 1998. "Generalized impulse response analysis in linear multivariate models," Economics Letters, Elsevier, vol. 58(1), pages 17-29, January.
    7. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    8. Trenkler, Carsten & Weber, Enzo, 2016. "On the identification of multivariate correlated unobserved components models," Economics Letters, Elsevier, vol. 138(C), pages 15-18.
    9. Krane, Spencer & Wascher, William, 1999. "The cyclical sensitivity of seasonality in U.S. employment," Journal of Monetary Economics, Elsevier, vol. 44(3), pages 523-553, December.
    10. M. Dungey & J. P. A. M. Jacobs & J. Tian & S. van Norden, 2013. "On the correspondence between data revision and trend-cycle decomposition," Applied Economics Letters, Taylor & Francis Journals, vol. 20(4), pages 316-319, March.
    11. Tucker McElroy, 2017. "Multivariate Seasonal Adjustment, Economic Identities, and Seasonal Taxonomy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 611-625, October.
    12. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    13. Barend Abeln & Jan P. A. M. Jacobs, 2023. "CAMPLET: Seasonal Adjustment Without Revisions," SpringerBriefs in Economics, in: Seasonal Adjustment Without Revisions, chapter 0, pages 7-29, Springer.
    14. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-266, October-D.
    15. James C. Morley, 2007. "The Slow Adjustment of Aggregate Consumption to Permanent Income," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(2‐3), pages 615-638, March.
    16. Tara M. Sinclair, 2009. "The Relationships between Permanent and Transitory Movements in U.S. Output and the Unemployment Rate," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(2-3), pages 529-542, March.
    17. Jun Ma & Mark E. Wohar, 2013. "An Unobserved Components Model that Yields Business and Medium-Run Cycles," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(7), pages 1351-1373, October.
    18. Cecchetti, Stephen G. & Kashyap, Anil K, 1996. "International cycles," European Economic Review, Elsevier, vol. 40(2), pages 331-360, February.
    19. Dungey, Mardi & Jacobs, Jan P.A.M. & Tian, Jing & van Norden, Simon, 2015. "Trend In Cycle Or Cycle In Trend? New Structural Identifications For Unobserved-Components Models Of U.S. Real Gdp," Macroeconomic Dynamics, Cambridge University Press, vol. 19(4), pages 776-790, June.
    20. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, January.
    21. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-389, October.
    22. Jean-Marie Dufour & Denis Pelletier, 2022. "Practical Methods for Modeling Weak VARMA Processes: Identification, Estimation and Specification With a Macroeconomic Application," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1140-1152, June.
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