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Studying co-movements in large multivariate data prior to multivariate modelling

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  • Cubadda, Gianluca
  • Hecq, Alain
  • Palm, Franz C.

Abstract

For non-stationary vector autoregressive models (VAR hereafter, or VAR with moving average, VARMA hereafter), we show that the presence of common cyclical features or cointegration leads to a reduction of the order of the implied univariate autoregressive-integrated-moving average (ARIMA hereafter) models. This finding can explain why we identify parsimonious univariate ARIMA models in applied research although VAR models of typical order and dimension used in macroeconometrics imply non-parsimonious univariate ARIMA representations. Next, we develop a strategy for studying interactions between variables prior to possibly modelling them in a multivariate setting. Indeed, the similarity of the autoregressive roots will be informative about the presence of co-movements in a set of multiple time series. Our results justify both the use of a panel setup with homogeneous autoregression and heterogeneous cross-correlated vector moving average errors and a factor structure, and the use of cross-sectional aggregates of ARIMA series to estimate the homogeneous autoregression.

Suggested Citation

  • Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2009. "Studying co-movements in large multivariate data prior to multivariate modelling," Journal of Econometrics, Elsevier, vol. 148(1), pages 25-35, January.
  • Handle: RePEc:eee:econom:v:148:y:2009:i:1:p:25-35
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    1. Maravall, Agustin & Mathis, Alexandre, 1994. "Encompassing univariate models in multivariate time series : A case study," Journal of Econometrics, Elsevier, vol. 61(2), pages 197-233, April.
    2. Ralf BRUEGGEMANN & Hans-Martin KROLZIG & Helmut LUETKEPOHL, 2002. "Comparison of Model Reduction Methods for VAR Processes," Economics Working Papers ECO2002/19, European University Institute.
    3. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    4. Centoni, Marco & Cubadda, Gianluca & Hecq, Alain, 2007. "Common shocks, common dynamics, and the international business cycle," Economic Modelling, Elsevier, vol. 24(1), pages 149-166, January.
    5. ZELLNER, Arnold & PALM, Franz, 1975. "Time series and structural analysis of monetary models of the U.S. economy," CORE Discussion Papers RP 247, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    7. Palm, Franz, 1977. "On univariate time series methods and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 5(3), pages 379-388, May.
    8. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2008. "Macro-panels and reality," Economics Letters, Elsevier, vol. 99(3), pages 537-540, June.
    9. 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.
    10. Cubadda, Gianluca & Hecq, Alain, 2001. "On non-contemporaneous short-run co-movements," Economics Letters, Elsevier, vol. 73(3), pages 389-397, December.
    11. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    12. Cubadda, Gianluca, 2007. "A unifying framework for analysing common cyclical features in cointegrated time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 896-906, October.
    13. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    14. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
    15. Christoph Schleicher, 2007. "Codependence in cointegrated autoregressive models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 137-159.
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    18. Vahid, Farshid & Engle, Robert F., 1997. "Codependent cycles," Journal of Econometrics, Elsevier, vol. 80(2), pages 199-221, October.
    19. Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2002. "Separation, Weak Exogeneity, And P-T Decomposition In Cointegrated Var Systems With Common Features," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 273-307.
    20. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    21. Palm, Franz & Zellner, Arnold, 1981. "Large sample estimation and testing procedures for dynamic equation systems," Journal of Econometrics, Elsevier, vol. 17(1), pages 131-138, September.
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    23. Wallis, Kenneth F, 1977. "Multiple Time Series Analysis and the Final Form of Econometric Models," Econometrica, Econometric Society, vol. 45(6), pages 1481-1497, September.
    24. Zellner,Arnold & Palm,Franz C. (ed.), 2004. "The Structural Econometric Time Series Analysis Approach," Cambridge Books, Cambridge University Press, number 9780521814072, April.
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    Citations

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    Cited by:

    1. Cubadda, Gianluca & Guardabascio, Barbara & Hecq, Alain, 2017. "A vector heterogeneous autoregressive index model for realized volatility measures," International Journal of Forecasting, Elsevier, vol. 33(2), pages 337-344.
    2. Götz, Thomas B. & Knetsch, Thomas A., 2017. "Google data in bridge equation models for German GDP," Discussion Papers 18/2017, Deutsche Bundesbank.
    3. Gianluca Cubadda & Alain Hecq, 2011. "Testing for common autocorrelation in data‐rich environments," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(3), pages 325-335, April.
    4. repec:gam:jecnmx:v:4:y:2016:i:2:p:21:d:67747 is not listed on IDEAS
    5. Stephan Smeekes & Jean-Pierre Urbain, 2014. "On the Applicability of the Sieve Bootstrap in Time Series Panels," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 139-151, February.
    6. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "The conditional autoregressive Wishart model for multivariate stock market volatility," Journal of Econometrics, Elsevier, vol. 167(1), pages 211-223.
    7. Nunzio Cappuccio & Diego Lubian, 2016. "Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-11, April.
    8. Marco Centoni & Gianluca Cubadda, 2011. "Modelling comovements of economic time series: a selective survey," Statistica, Department of Statistics, University of Bologna, vol. 71(2), pages 267-294.
    9. Cubadda, Gianluca & Guardabascio, Barbara, 2012. "A medium-N approach to macroeconomic forecasting," Economic Modelling, Elsevier, vol. 29(4), pages 1099-1105.
    10. Chevillon, Guillaume & Hecq , Alain & Laurent, Sébastien, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," ESSEC Working Papers WP1507, ESSEC Research Center, ESSEC Business School.
    11. Mitchell, James & Robertson, Donald & Wright, Stephen, 2016. "What univariate models tell us about multivariate macroeconomic models," EMF Research Papers 08, Economic Modelling and Forecasting Group.

    More about this item

    Keywords

    Interactions Multiple time series Co-movements ARIMA Cointegration Common cycles Dynamic panel data;

    JEL classification:

    • 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

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