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Separation, Weak Exogeneity and P-T Decomposition in Cointegrated VAR Systems with Common Features

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  • Alain Hecq
  • Franz Palm
  • Jean-Pierre Urbain

Abstract

The aim of this paper is to study the concept of separability in multiple nonstationary time series displaying both common stochastic trends and common stochastic cycles. When modeling the dynamics of multiple time series for a panel of several entities such as countries, sectors, firms, imposing some form of separability and commonalities is often required to restrict the dimension of the parameter space. For this purpose we introduce the concept of common feature separation and investigate the relationships between separation in cointegration and separation in serial correlation common features. Loosely speaking we investigate whether a set of time series can be partitioned into subsets such that there are serial correlation common features in the sub-groups and that there do not exist linear combinations of the common cycles which are white noise. The paper investigates three issues. First, it provides conditions for separating joint cointegrating vectors into marginal cointegrating vectors as well as separating joint short-term dynamics into marginal short-term dynamics. Second, conditions for making permanent-transitory decompositions based on marginal systems are given. Third, issues of weak exogeneity are considered. Likelihood ratio type tests for the different hypotheses under study are proposed. An empirical analysis of the link between economic fluctuations in the U.S. and Canada shows the practical relevance of the approach proposed in this paper.

Suggested Citation

  • Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2002. "Separation, Weak Exogeneity and P-T Decomposition in Cointegrated VAR Systems with Common Features," CESifo Working Paper Series 660, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_660
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    1. repec:kap:iaecre:v:14:y:2008:i:3:p:280-290 is not listed on IDEAS
    2. Cubadda, Gianluca & Hecq, Alain, 2003. "The Role of Common Cyclical Features for Coincident and Leading Indexes Building," Economics & Statistics Discussion Papers esdp03002, University of Molise, Dept. EGSeI.
    3. Narayan, Paresh Kumar, 2008. "An investigation of the behaviour of Australia's business cycle," Economic Modelling, Elsevier, vol. 25(4), pages 676-683, July.
    4. Balcilar, Mehmet & Gupta, Rangan & Wohar, Mark E., 2017. "Common cycles and common trends in the stock and oil markets: Evidence from more than 150years of data," Energy Economics, Elsevier, vol. 61(C), pages 72-86.
    5. Paresh Narayan, 2008. "Common Trends and Common Cycles in Per Capita GDP: The Case of the G7 Countries, 1870–2001," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 14(3), pages 280-290, August.
    6. Narayan, Paresh Kumar, 2008. "Estimating exchange rate responsiveness to shocks," Review of Financial Economics, Elsevier, vol. 17(4), pages 338-351, December.
    7. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, pages 143-168.
    8. Christophe Rault, 2004. "Further results on weak-exogeneity in vector error correction models," Econometric Society 2004 Far Eastern Meetings 402, Econometric Society.
    9. Christophe Rault, 2007. "Une synthèse de l'exogénéité dans les modèles vectoriels à correction d'erreurs," Post-Print halshs-00202651, HAL.
    10. Paresh Kumar Narayan & Seema Narayan, 2008. "The role of permanent and transitory shocks in explaining international health expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 17(10), pages 1171-1186.
    11. Narayan, Paresh Kumar, 2008. "Understanding the importance of permanent and transitory shocks at business cycle horizons for the UK," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2879-2888.
    12. Paruolo Paolo, 2002. "Testing for common trends in conditional I(2) VAR models," Economics and Quantitative Methods qf0216, Department of Economics, University of Insubria.
    13. Cengiz Arikan & Yeliz Yalcin, 2013. "Determining the Exogeneity of Tax Components with Respect to GDP," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 3(3), pages 242-255, July.
    14. Franchi, Massimo & Paruolo, Paolo, 2011. "A characterization of vector autoregressive processes with common cyclical features," Journal of Econometrics, Elsevier, vol. 163(1), pages 105-117, July.
    15. Gengenbach Christian & Palm Franz C. & Urbain Jean-Pierre, 2005. "Panel Cointegration Testing in the Presence of Common Factors," Research Memorandum 050, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. Marçal, Emerson Fernandes & Zimmermann, Beatrice Aline & Mendonça, Diogo de Prince & Merlin, Giovanni Tondin, 2015. "Assessing interdependence among countries' fundamentals and its implications for exchange rate misalignment estimates: An empirical exercise based on GVAR," Textos para discussão 384, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    17. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, pages 25-35.
    18. Hecq, Alain & Palm, Franz C. & Urbain, Jean-Pierre, 2006. "Common cyclical features analysis in VAR models with cointegration," Journal of Econometrics, Elsevier, vol. 132(1), pages 117-141, May.

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