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

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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Paper provided by Tor Vergata University, CEIS in its series CEIS Research Paper with number 125.

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Length: 26 pages
Date of creation: 14 Jul 2008
Date of revision: 14 Jul 2008
Handle: RePEc:rtv:ceisrp:125
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Keywords: Interactions; multiple time series; co-movements; ARIMA; cointegration; common cycles; dynamic panel data.;

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Find related papers by 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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  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.
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  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.
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  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.
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  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.
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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. 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. 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, 02.
  5. 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.
  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. 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.
  8. 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.
  9. repec:gam:jecnmx:v:4:y:2016:i:2:p:21:d:67747 is not listed on IDEAS
  10. 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.

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