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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.

##### MSC:
 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
##### Keywords:
bootstrap; co-integration; trace statistic; rank determination
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