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Bayesian analysis of seasonally cointegrated VAR models

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  • Wróblewska, Justyna

Abstract

The aim is to develop a Bayesian seasonally cointegrated model for quarterly data. Relevant prior structure is proposed, and the set of full conditional posterior distributions is derived, enabling us to employ the Gibbs sampler for posterior inference. The identification of cointegrating spaces is obtained by orthonormality restrictions imposed on vectors spanning them. The point estimation of the cointegrating spaces is also discussed. In the presence of a seasonal pattern with one cycle per year, the cointegrating vectors belong to the complex space, which should be taken into account in the identification scheme. The methodology is illustrated by the analysis of money and prices in the Polish economy.

Suggested Citation

  • Wróblewska, Justyna, 2025. "Bayesian analysis of seasonally cointegrated VAR models," Econometrics and Statistics, Elsevier, vol. 35(C), pages 55-70.
    • Handle: RePEc:eee:ecosta:v:35:y:2025:i:c:p:55-70
    DOI: 10.1016/j.ecosta.2023.02.002
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    1. Cubadda, Gianluca, 1999. "Common Cycles in Seasonal Non-stationary Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 273-291, May-June.
    2. Robert Engle & Clive Granger, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    3. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    4. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2011. "Bayesian inference in a time varying cointegration model," Journal of Econometrics, Elsevier, vol. 165(2), pages 210-220.
    5. John Geweke & Gianni Amisano, 2011. "Hierarchical Markov normal mixture models with applications to financial asset returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 1-29, January/F.
    6. Anna Pajor & Justyna Wróblewska, 2022. "Forecasting performance of Bayesian VEC-MSF models for financial data in the presence of long-run relationships," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 427-448, September.
    7. Hallman, Jeffrey J & Porter, Richard D & Small, David H, 1991. "Is the Price Level Tied to the M2 Monetary Aggregate in the Long Run?," American Economic Review, American Economic Association, vol. 81(4), pages 841-858, September.
    8. Geweke, John, 2001. "Bayesian econometrics and forecasting," Journal of Econometrics, Elsevier, vol. 100(1), pages 11-15, January.
    9. Hecq, Alain, 1998. "Does seasonal adjustment induce common cycles?," Economics Letters, Elsevier, vol. 59(3), pages 289-297, June.
    10. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    11. James D. Hamilton, 2018. "Why You Should Never Use the Hodrick-Prescott Filter," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 831-843, December.
    12. Josu Arteche, 2007. "The Analysis of Seasonal Long Memory: The Case of Spanish Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(6), pages 749-772, December.
    13. Reimers, Hans-Eggert, 1997. "Forecasting of seasonal cointegrated processes," International Journal of Forecasting, Elsevier, vol. 13(3), pages 369-380, September.
    14. Chikuse, Yasuko, 1990. "The matrix angular central Gaussian distribution," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 265-274, May.
    15. Abeysinghe, Tilak, 1994. "Deterministic seasonal models and spurious regressions," Journal of Econometrics, Elsevier, vol. 61(2), pages 259-272, April.
    16. Mark Meyer & Peter Winker*, 2005. "Using HP Filtered Data for Econometric Analysis: Some Evidence from Monte Carlo Simulations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(3), pages 303-320, August.
    17. Kunst, Robert M, 1993. "Seasonal Cointegration in Macroeconomic Systems: Case Studies for Small and Large European Countries," The Review of Economics and Statistics, MIT Press, vol. 75(2), pages 325-330, May.
    18. Philip Hans Franses & Robert M. Kunst, 1999. "On the Role of Seasonal Intercepts in Seasonal Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(3), pages 409-433, August.
    19. Rodney Strachan & Herman K. van Dijk, "undated". "Bayesian Model Averaging in Vector Autoregressive Processes with an Investigation of Stability of the US Great Ratios and Risk of a Liquidity Trap in the USA, UK and Japan," MRG Discussion Paper Series 1407, School of Economics, University of Queensland, Australia.
    20. repec:bla:germec:v:7:y:2006:i::p:65-86 is not listed on IDEAS
    21. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
    22. Granger, C. W. J. & Siklos, Pierre L., 1995. "Systematic sampling, temporal aggregation, seasonal adjustment, and cointegration theory and evidence," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 357-369.
    23. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
    24. Geisel, Martin S, 1973. "Bayesian Comparisons of Simple Macroeconomic Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 5(3), pages 751-772, August.
    25. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679.
    26. Sung K. Ahn & Sinsup Cho & B. Chan Seong, 2004. "Inference of Seasonal Cointegration: Gaussian Reduced Rank Estimation and Tests for Various Types of Cointegration," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(2), pages 261-284, May.
    27. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    28. Karl-Heinz Tödter & Hans-Eggert Reimers, 1994. "P-Star as a link between money and prices in Germany," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 130(2), pages 273-289, June.
    29. Justyna Wróblewska, 2009. "Bayesian Model Selection in the Analysis of Cointegration," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 1(1), pages 57-69, March.
    30. Gerlach, Stefan & Svensson, Lars E. O., 2003. "Money and inflation in the euro area: A case for monetary indicators?," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1649-1672, November.
    31. Cubadda, Gianluca & Omtzigt, Pieter, 2005. "Small-sample improvements in the statistical analysis of seasonally cointegrated systems," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 333-348, April.
    32. repec:bla:obuest:v:61:y:1999:i:3:p:409-33 is not listed on IDEAS
    33. Helmut Herwartz & Hans‐Eggert Reimers, 2006. "Long‐Run Links among Money, Prices and Output: Worldwide Evidence," German Economic Review, Verein für Socialpolitik, vol. 7(1), pages 65-86, February.
    34. Jacek Kotlowski, 2005. "Money and prices in the Polish economy. Seasonal cointegration approach," Working Papers 20, Department of Applied Econometrics, Warsaw School of Economics.
    35. Gianluca Cubadda, 2001. "Complex Reduced Rank Models For Seasonally Cointegrated Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 63(4), pages 497-511, September.
    36. Lof, Marten & Hans Franses, Philip, 2001. "On forecasting cointegrated seasonal time series," International Journal of Forecasting, Elsevier, vol. 17(4), pages 607-621.
    37. Rudebusch, Glenn D. & Svensson, Lars E. O., 2002. "Eurosystem monetary targeting: Lessons from U.S. data," European Economic Review, Elsevier, vol. 46(3), pages 417-442, March.
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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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