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On causal and non‐causal cointegrated vector autoregressive time series

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  • Anders Rygh Swensen

Abstract

Previous‐30 treatments of multivariate non‐causal time series have assumed stationarity. In this article, we consider integrated processes in a non‐causal setting. We generalize the Johansen–Granger representation for causal vector autoregressive (VAR) models to allow for dependence on future errors and discuss how the parameters can be estimated. The asymptotic distribution of the trace statistic is also considered. Some Monte Carlo simulations are presented.

Suggested Citation

  • Anders Rygh Swensen, 2022. "On causal and non‐causal cointegrated vector autoregressive time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 178-196, March.
  • Handle: RePEc:bla:jtsera:v:43:y:2022:i:2:p:178-196
    DOI: 10.1111/jtsa.12607
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    References listed on IDEAS

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    1. Tom Engsted & Bent Nielsen, 2012. "Testing for rational bubbles in a coexplosive vector autoregression," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 226-254, June.
    2. Gourieroux, Christian & Jasiak, Joann, 2017. "Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation," Journal of Econometrics, Elsevier, vol. 200(1), pages 118-134.
    3. Søren Johansen, 2009. "Representation of Cointegrated Autoregressive Processes with Application to Fractional Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 121-145.
    4. Davis, Richard A. & Song, Li, 2020. "Noncausal vector AR processes with application to economic time series," Journal of Econometrics, Elsevier, vol. 216(1), pages 246-267.
    5. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164.
    6. Lanne, Markku & Saikkonen, Pentti, 2013. "Noncausal Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 29(3), pages 447-481, June.
    7. Nielsen, Bent, 2010. "Analysis Of Coexplosive Processes," Econometric Theory, Cambridge University Press, vol. 26(3), pages 882-915, June.
    8. Giuseppe Cavaliere & Heino Bohn Nielsen & Anders Rahbek, 2020. "Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(1), pages 55-67, January.
    9. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    10. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, vol. 74(6), pages 1699-1714, November.
    11. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    12. Peter Reinhard Hansen, 2005. "Granger's representation theorem: A closed-form expression for I(1) processes," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 23-38, March.
    13. Johansen, Søren & Juselius, Katarina, 2014. "An asymptotic invariance property of the common trends under linear transformations of the data," Journal of Econometrics, Elsevier, vol. 178(P2), pages 310-315.
    14. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 175-198, February.
    15. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2012. "Bootstrap Determination of the Co‐Integration Rank in Vector Autoregressive Models," Econometrica, Econometric Society, vol. 80(4), pages 1721-1740, July.
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