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Bootstrap determination of the co-integration rank in vector autoregressive models. (English) Zbl 1274.62223
Summary: This paper discusses a consistent bootstrap implementation of the likelihood ratio (LR) co-integration rank test and associated sequential rank determination procedure of S. Johansen [Likelihood-based inference in cointegrated vector autoregressive models. Oxford: Oxford Univ. Press (1995; Zbl 0928.62069)]. 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 [A. R. Swensen, Econometrica 74, No. 6, 1699–1714 (2006; Zbl 1187.62148)] 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.

62F40 Bootstrap, jackknife and other resampling methods
62F07 Statistical ranking and selection procedures
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C05 Monte Carlo methods
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