Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/205333 
Year of Publication: 
2019
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2019-043/III
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
Abstract: 
This paper generalises Boswijk and Zu (2018)'s adaptive unit root test for time series with nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix of a vector autoregressive model lead to size distortions in conventional cointegration tests, which may be resolved using the wild bootstrap, as shown by Cavaliere et al. (2010, 2014). We show that it also leads to the possibility of constructing tests with higher power, by taking the time-varying volatilities and correlations into account in the formulation of the likelihood function and the resulting likelihood ratio test statistic. We find that under suitable conditions, adaptation with respect to the volatility process is possible, in the sense that nonparametric volatility matrix estimation does not lead to a loss of asymptotic local power relative to the case where the volatilities are observed. The asymptotic null distribution of the test is nonstandard and depends on the volatility process; we show that various bootstrap implementations may be used to conduct asymptotically valid inference. Monte Carlo simulations show that the resulting test has good size properties, and higher power than existing tests. Two empirical examples illustrate the applicability of the tests.
Subjects: 
Adaptive estimation
Nonparametric volatility estimation
Wild bootstrap
JEL: 
C32
C12
Document Type: 
Working Paper

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