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Determining the Cointegration Rank in Heteroskedastic VAR Models of Unknown Order

Author

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  • Cavaliere, G
  • De Angelis, L
  • Rahbek, A
  • Taylor, AMR
Abstract
We investigate the asymptotic and finite sample properties of a number of methods for estimating the cointegration rank in integrated vector autoregressive systems of unknown autoregressive order driven by heteroskedastic shocks. We allow for both conditional and unconditional heteroskedasticity of a very general form. We establish the conditions required on the penalty functions such that standard information criterion-based methods, such as the Bayesian information criterion [BIC], when employed either sequentially or jointly, can be used to consistently estimate both the cointegration rank and the autoregressive lag order. In doing so we also correct errors which appear in the proofs provided for the consistency of information-based estimators in the homoskedastic case by Aznar and Salvador (2002). We also extend the corpus of available large sample theory for the conventional sequential approach of Johansen (1995) and the associated wild bootstrap implementation thereof of Cavaliere, Rahbek and Taylor (2014) to the case where the lag order is unknown. In particular, we show that these methods remain valid under heteroskedasticity and an unknown lag length provided the lag length is first chosen by a consistent method, again such as the BIC. The relative finite sample properties of the different methods discussed are investigated in a Monte Carlo simulation study. The two best performing methods in this study are a wild bootstrap implementation of the Johansen (1995) procedure implemented with BIC selection of the lag length and joint IC approach (cf. Phillips, 1996) which uses the BIC to jointly select the lag order and the cointegration rank.

Suggested Citation

  • Cavaliere, G & De Angelis, L & Rahbek, A & Taylor, AMR, 2016. "Determining the Cointegration Rank in Heteroskedastic VAR Models of Unknown Order," Essex Finance Centre Working Papers 17454, University of Essex, Essex Business School.
    • Handle: RePEc:esy:uefcwp:17454
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    Cited by:

    1. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    2. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.
    3. She, Rui & Ling, Shiqing, 2020. "Inference in heavy-tailed vector error correction models," Journal of Econometrics, Elsevier, vol. 214(2), pages 433-450.
    4. Anna Pajor & Justyna Wróblewska, 2022. "Forecasting performance of Bayesian VEC-MSF models for financial data in the presence of long-run relationships," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 427-448, September.
    5. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    6. Helmut Lütkepohl & Aleksei Netšunajev, 2018. "The Relation between Monetary Policy and the Stock Market in Europe," Econometrics, MDPI, vol. 6(3), pages 1-14, August.
    7. H. Peter Boswijk & Giuseppe Cavaliere & Luca De Angelis & A. M. Robert Taylor, 2023. "Adaptive information-based methods for determining the co-integration rank in heteroskedastic VAR models," Econometric Reviews, Taylor & Francis Journals, vol. 42(9-10), pages 725-757, November.
    8. Gianluca Cubadda & Marco Mazzali, 2024. "The vector error correction index model: representation, estimation and identification," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 126-150.
    9. Motegi, Kaiji & Iitsuka, Yoshitaka, 2023. "Inter-regional dependence of J-REIT stock prices: A heteroscedasticity-robust time series approach," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    10. Guillermo Carlomagno & Antoni Espasa, 2021. "Discovering Specific Common Trends in a Large Set of Disaggregates: Statistical Procedures, their Properties and an Empirical Application," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(3), pages 641-662, June.

    More about this item

    Keywords

    Cointegration rank; Information criteria; Wild bootstrap; Trace statistic; Lag length; Heteroskedasticity;
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