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Studying Co-Movements in Large Multivariate Data Prior to Multivariate Modelling

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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-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 nonparsimonious 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.

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  • Gianluca Cubadda & Alain Hecq & Franz C. Palm, 2008. "Studying Co-Movements in Large Multivariate Data Prior to Multivariate Modelling," CEIS Research Paper 125, Tor Vergata University, CEIS, revised 14 Jul 2008.
  • Handle: RePEc:rtv:ceisrp:125
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    21. Cubadda, Gianluca & Hecq, Alain & Palm, Franz C., 2008. "Macro-panels and reality," Economics Letters, Elsevier, vol. 99(3), pages 537-540, June.
    22. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
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    1. Gianluca Cubadda & Alain Hecq & Antonio Riccardo, 2018. "Forecasting Realized Volatility Measures with Multivariate and Univariate Models: The Case of The US Banking Sector," CEIS Research Paper 445, Tor Vergata University, CEIS, revised 30 Oct 2018.
    2. 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.
    3. Cubadda, Gianluca & Guardabascio, Barbara, 2012. "A medium-N approach to macroeconomic forecasting," Economic Modelling, Elsevier, vol. 29(4), pages 1099-1105.
    4. Chevillon, Guillaume & Hecq, Alain & Laurent, Sébastien, 2018. "Generating univariate fractional integration within a large VAR(1)," Journal of Econometrics, Elsevier, vol. 204(1), pages 54-65.
    5. Götz, Thomas B. & Knetsch, Thomas A., 2019. "Google data in bridge equation models for German GDP," International Journal of Forecasting, Elsevier, vol. 35(1), pages 45-66.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Franses, Ph.H.B.F., 2019. "Do African economies grow similarly?," Econometric Institute Research Papers EI2019-26, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Philip Hans Franses & Thomas Wiemann, 2020. "Intertemporal Similarity of Economic Time Series: An Application of Dynamic Time Warping," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 59-75, June.
    12. repec:gam:jecnmx:v:4:y:2016:i:2:p:21:d:67747 is not listed on IDEAS
    13. 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.
    14. Cubadda, Gianluca & Triacca, Umberto, 2011. "An alternative solution to the Autoregressivity Paradox in time series analysis," Economic Modelling, Elsevier, vol. 28(3), pages 1451-1454, May.
    15. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2019. "Granger Causality Testing in High-Dimensional VARs: a Post-Double-Selection Procedure," Papers 1902.10991, arXiv.org, revised Dec 2020.
    16. 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.
    17. Franses, Ph.H.B.F. & Wiemann, T., 2018. "Intertemporal Similarity of Economic Time Series," Econometric Institute Research Papers EI2018-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Nunzio Cappuccio & Diego Lubian, 2016. "Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series," Econometrics, MDPI, vol. 4(2), pages 1-11, April.

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    More about this item

    Keywords

    Interactions; multiple time series; co-movements; ARIMA; cointegration; common cycles; dynamic panel data.;
    All these keywords.

    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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