Bootstrap determination of the co-integration rank in VAR models
AbstractThis 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 VAR model which obtain under the reduced rank null hypothesis. A full asymptotic theory is provided which 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.
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Bibliographic InfoPaper provided by Department of Statistics, University of Bologna in its series Quaderni di Dipartimento with number 9.
Date of creation: 2011
Date of revision:
Bootstrap; Co-integration; Trace statistic; Rank determination Cointegrazione; Statistica “traccia”; determinazione del rango;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-02-20 (All new papers)
- NEP-ECM-2012-02-20 (Econometrics)
- NEP-ETS-2012-02-20 (Econometric Time Series)
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- Anders Rahbek & Heino Bohn Nielsen, 2012.
"Unit root vector autoregression with volatility induced stationarity,"
12-02, University of Copenhagen. Department of Economics.
- Anders Rahbek & Heino Bohn Nielsen, 2012. "Unit Root Vector Autoregression with volatility Induced Stationarity," CREATES Research Papers 2012-29, School of Economics and Management, University of Aarhus.
- Cavaliere, Giuseppe & Taylor, A. M. Robert & Trenkler, Carsten, 2013. "Bootstrap Co-integration Rank Testing: The Effect of Bias-Correcting Parameter Estimates," Working Papers 32993, University of Mannheim, Department of Economics.
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