Title: Adaptive information-based methods for determining the co-integration rank in heteroskedastic VAR models
Authors: Luca De Angelis - University of Bologna (Italy) [presenting]
Robert Taylor - University of Essex (United Kingdom)
Giuseppe Cavaliere - University of Bologna (Italy)
Peter Boswijk - University of Amsterdam (Netherlands)
Abstract: Standard methods for determining the co-integration rank of vector autoregressive (VAR) systems of variables integrated of order one are affected by the presence of heteroskedasticity with sequential procedures based on Johansen's (pseudo-)likelihood ratio [PLR] test being significantly over-sized in finite samples and even asymptotically. Notable solutions to this problem are the wild bootstrap applied to the PLR test or an information criterion such as BIC. However, although asymptotically valid, these methods may show low power in small samples as they do not exploit the potential efficiency gains provided by the adaptation with respect to the volatility process. Adaptive methods where the covariance matrix is estimated non-parametrically can be particularly useful in the determination of the co-integration rank in VAR models driven by heteroskedastic innovations. Adaptive information criteria-based approaches can also been used to jointly determine the co-integration rank and the VAR lag length. It is in fact well-known that an incorrect selection of the number of lags has a relevant impact on the efficacy of information criteria as well as standard and bootstrap PLR tests in determining the co-integration rank in finite samples. We show that adaptive information criteria are weakly consistent for co-integration rank and lag length determination in the presence of non-stationary unconditional heteroskedasticity, provided the usual conditions on the penalty term hold.