Title: Bootstrap Determination of the Co-Integration Rank in Vector Autoregressive Models
Abstract: EconometricaVolume 80, Issue 4 p. 1721-1740 Bootstrap Determination of the Co-Integration Rank in Vector Autoregressive Models Giuseppe Cavaliere, Giuseppe Cavaliere Dept. of Statistical Sciences, University of Bologna, via delle Belle Arti 41, I-40126 Bologna, Italy; [email protected]Search for more papers by this authorAnders Rahbek, Anders Rahbek Dept. of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K, Denmark; [email protected]Search for more papers by this authorA. M. Robert Taylor, A. M. Robert Taylor School of Economics, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom; [email protected] We thank a co-editor and four anonymous referees for their very helpful and constructive comments on previous versions of this paper. We also thank Iliyan Georgiev, Niels Haldrup, Bent Nielsen, Heino Bohn Nielsen, Søren Johansen, and Anders Swensen for many useful discussions on this work. Parts of this paper were written while Cavaliere and Rahbek both visited CREATES, whose hospitality is gratefully acknowledged. Rahbek gratefully acknowledges funding from the Danish Council for Independent Research, Social Sciences (Grant 10-07977). Rahbek is also affiliated with CREATES, funded by the Danish National Research Foundation.Search for more papers by this author Giuseppe Cavaliere, Giuseppe Cavaliere Dept. of Statistical Sciences, University of Bologna, via delle Belle Arti 41, I-40126 Bologna, Italy; [email protected]Search for more papers by this authorAnders Rahbek, Anders Rahbek Dept. of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K, Denmark; [email protected]Search for more papers by this authorA. M. Robert Taylor, A. M. Robert Taylor School of Economics, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom; [email protected] We thank a co-editor and four anonymous referees for their very helpful and constructive comments on previous versions of this paper. We also thank Iliyan Georgiev, Niels Haldrup, Bent Nielsen, Heino Bohn Nielsen, Søren Johansen, and Anders Swensen for many useful discussions on this work. Parts of this paper were written while Cavaliere and Rahbek both visited CREATES, whose hospitality is gratefully acknowledged. Rahbek gratefully acknowledges funding from the Danish Council for Independent Research, Social Sciences (Grant 10-07977). Rahbek is also affiliated with CREATES, funded by the Danish National Research Foundation.Search for more papers by this author First published: 25 July 2012 https://doi.org/10.3982/ECTA9099Citations: 79 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract This paper discusses a consistent bootstrap implementation of the likelihood ratio (LR) co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying vector autoregressive (VAR) model that obtain under the reduced rank null hypothesis. A full asymptotic theory is provided that shows that, unlike the bootstrap procedure in Swensen (2006) where a combination of unrestricted and restricted estimates from the VAR model is used, the resulting bootstrap data are I(1) and satisfy the null co-integration rank, regardless of the true rank. This ensures that the bootstrap LR test is asymptotically correctly sized and that the probability that the bootstrap sequential procedure selects a rank smaller than the true rank converges to zero. Monte Carlo evidence suggests that our bootstrap procedures work very well in practice. References Andrews, D. W. K., and M. Buchinsky (2000): "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, 68, 23–51. DOI: 10.1111/1468-0262.00092 Cavaliere, G., A. Rahbek, and A. M. R. Taylor (2010a): "Co-Integration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, 26, 1719–1760. DOI: 10.1017/S0266466609990776 Cavaliere, G., A. Rahbek, and A. M. R. Taylor (2010b): "Testing for Co-Integration in Vector Autoregressions With Non-Stationary Volatility," Journal of Econometrics, 158, 7–24. DOI: 10.1016/j.jeconom.2010.03.003 Hansen, B. E. (1996): "Inference When a Nuisance Parameter is Not Identified Under the Null Hypothesis," Econometrica, 64, 413–430. DOI: 10.2307/2171789 Johansen, S. (1996): Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford : Oxford University Press. DOI: 10.1093/0198774508.001.0001 Johansen, S. (2002): "A Small Sample Correction of the Test for Cointegrating Rank in the Vector Autoregressive Model," Econometrica, 70, 1929–1961. DOI: 10.1111/1468-0262.00358 Park, J. Y. (2003): "Bootstrap Unit Root Tests," Econometrica, 71, 1845–1895. DOI: 10.1111/1468-0262.00471 Rahbek, A., H. C. Kongsted, and C. Jørgensen (1999): "Trend Stationarity in the I(2) Cointegration Model," Journal of Econometrics, 90, 265–289. DOI: 10.1016/S0304-4076(98)00044-X Swensen, A. R. (2006): "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models," Econometrica, 74, 1699–1714. DOI: 10.1111/j.1468-0262.2006.00723.x Swensen, A. R. (2009): "Corrigendum to 'Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models'," Econometrica, 77, 1703–1704. DOI: 10.3982/ECTA8201 Trenkler, C. (2009): "Bootstrapping Systems Cointegration Tests With a Prior Adjustment for Deterministic Terms," Econometric Theory, 25, 243–269. DOI: 10.1017/S0266466608090087 Van Giersbergen, N. P. A. (1996): "Bootstrapping the Trace Statistic in VAR Models: Monte Carlo Results and Applications," Oxford Bulletin of Economics and Statistics, 58, 391–408. Citing Literature Volume80, Issue4July 2012Pages 1721-1740 ReferencesRelatedInformation
Publication Year: 2012
Publication Date: 2012-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 107
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