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Analysis of Vector Autoregressions in the Presence of Shifts in Mean


  • Serena Ng

    () (Boston College)

  • Timothy J. Vogelsang

    (Cornell University)


This paper considers the implications of omitted mean shifts for estimation and inference in VARs. It is shown that the least squares estimates are inconsistent, and the F test for Granger causality diverges. While model selection rules have the tendency to incorrectly select a lag length that is too high, this over-parameterization can reduce size distortions in tests involving the inconsistent estimates. The practical issue of how to remove the breaks is shown to depend on whether the mean shifts are of the additive or innovational type in a multivariate setting. Under the additive outlier specification, the intercept in each equation of the VAR will be subject to multiple shifts when the break dates of the mean shifts to the univariate series do not coincide. Conversely, under the innovative outlier specification, the unconditional means of the univariate time series are subject to multiple shifts when mean shifts to the innovation processes occur at different dates: Techniques designed to detect multiple shifts are recommended when break dates do not coincide.

Suggested Citation

  • Serena Ng & Timothy J. Vogelsang, 1997. "Analysis of Vector Autoregressions in the Presence of Shifts in Mean," Boston College Working Papers in Economics 379, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:379

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    References listed on IDEAS

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    Cited by:

    1. Lumsdaine, Robin L. & Ng, Serena, 1999. "Testing for ARCH in the presence of a possibly misspecified conditional mean," Journal of Econometrics, Elsevier, vol. 93(2), pages 257-279, December.
    2. Marcos Sanso-Navarro, 2011. "Broken trend stationarity of hours worked," Post-Print hal-00712742, HAL.
    3. Nazlioglu, Saban & Gormus, N. Alper & Soytas, Uğur, 2016. "Oil prices and real estate investment trusts (REITs): Gradual-shift causality and volatility transmission analysis," Energy Economics, Elsevier, vol. 60(C), pages 168-175.
    4. Alfredo M. Pereira & Martin B. Schmidt, 2007. "Structural Breaks in Public Infrastructure Investment in the U.S," Working Papers 55, Department of Economics, College of William and Mary.
    5. PKG HARISCHANDRA & George CHOULIARAKIS, "undated". "Do Exchange Rate Regimes Matter for Inflation Persistence? Theory and Evidence from the History of UK and US Inflation," EcoMod2008 23800100, EcoMod.
    6. Mohsen Fardmanesh & Seymour Douglas, 2008. "Foreign Exchange Controls and the Parallel Market Premium," Review of Development Economics, Wiley Blackwell, vol. 12(1), pages 72-89, February.
    7. repec:kap:iecepo:v:14:y:2017:i:4:d:10.1007_s10368-016-0355-1 is not listed on IDEAS
    8. Thierno Balde & Gabriel Rodriguez, 2005. "Finite sample effects of additive outliers on the Granger-causality test with an application to money growth and inflation in Peru," Applied Economics Letters, Taylor & Francis Journals, vol. 12(13), pages 841-844.
    9. Salamaliki, Paraskevi K. & Venetis, Ioannis A., 2013. "Energy consumption and real GDP in G-7: Multi-horizon causality testing in the presence of capital stock," Energy Economics, Elsevier, vol. 39(C), pages 108-121.
    10. repec:kap:jfamec:v:38:y:2017:i:2:d:10.1007_s10834-016-9514-3 is not listed on IDEAS
    11. Yang Fan & Teng Jianzhou, 2011. "Studying on the monetary transmission mechanism in China in the presence of structural changes," China Finance Review International, Emerald Group Publishing, vol. 1(4), pages 334-357, September.

    More about this item


    trend shift; structural change; causality tests; lag length selection.;

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling


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