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A Comparison of Sequential and Information-based Methods for Determining the Co-integration Rank in Heteroskedastic VAR Models

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  • Giuseppe Cavaliere
  • Luca De Angelis
  • Anders Rahbek
  • A. M. Robert Taylor

Abstract

type="main" xml:id="obes12051-abs-0001"> In this article, we investigate the behaviour of a number of methods for estimating the co-integration rank in VAR systems characterized by heteroskedastic innovation processes. In particular, we compare the efficacy of the most widely used information criteria, such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) , with the commonly used sequential approach of Johansen [Likelihood-based Inference in Cointegrated Vector Autoregressive Models (1996)] based around the use of either asymptotic or wild bootstrap-based likelihood ratio type tests. Complementing recent work done for the latter in Cavaliere, Rahbek and Taylor [Econometric Reviews (2014) forthcoming], we establish the asymptotic properties of the procedures based on information criteria in the presence of heteroskedasticity (conditional or unconditional) of a quite general and unknown form. The relative finite-sample properties of the different methods are investigated by means of a Monte Carlo simulation study. For the simulation DGPs considered in the analysis, we find that the BIC-based procedure and the bootstrap sequential test procedure deliver the best overall performance in terms of their frequency of selecting the correct co-integration rank across different values of the co-integration rank, sample size, stationary dynamics and models of heteroskedasticity. Of these, the wild bootstrap procedure is perhaps the more reliable overall as it avoids a significant tendency seen in the BIC-based method to over-estimate the co-integration rank in relatively small sample sizes.

Suggested Citation

  • Giuseppe Cavaliere & Luca De Angelis & Anders Rahbek & A. M. Robert Taylor, 2015. "A Comparison of Sequential and Information-based Methods for Determining the Co-integration Rank in Heteroskedastic VAR Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(1), pages 106-128, February.
    • Handle: RePEc:bla:obuest:v:77:y:2015:i:1:p:106-128
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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. 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.
    3. Pajor Anna & Wróblewska Justyna, 2017. "VEC-MSF models in Bayesian analysis of short- and long-run relationships," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-22, June.
    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. Gianluca Cubadda & Marco Mazzali, 2023. "The Vector Error Correction Index Model: Representation, Estimation and Identification," CEIS Research Paper 556, Tor Vergata University, CEIS, revised 04 Apr 2023.

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