Title: Testing for co-integration rank in VAR models allowing for multiple breaks in trend and variance
Authors: Robert Taylor - University of Essex (United Kingdom) [presenting]
Giuseppe Cavaliere - University of Bologna (Italy)
David Harris - University of Melbourne (Australia)
Simon Price - University of Essex (United Kingdom)
Abstract: The problem of testing for the co-integration rank of a VAR process is considered in environments where multiple breaks can occur in the deterministic trend. Unlike existing procedures, we do not assume the break locations or the number of trend breaks to be known. Moreover, we allow the driving shocks to display non-stationary volatility and/or conditional heteroskedasticity, in each case of an unknown form. We use information criteria to select the VAR lag order and the number of trend breaks to fit, using likelihood-based break fraction estimators. Both the information criteria and the break fraction estimators are based around an adaptive (non-parametric) estimator of the variance matrix of the shocks to allow for any non-stationary volatility present. We show that our proposed adaptive information criterion consistently selects the lag length and the correct number of trend breaks in large samples, the locations of which are also consistently estimated. Based on these outcomes, wild bootstrap implementations of Johansen's likelihood ratio tests are then constructed. We show that these deliver asymptotically correctly sized and consistent inference on the co-integration rank regardless of the number of trend breaks present in the data and in the presence of heteroskedasticity.