Asymptotic standard errors for common trends linear combinations in I(2) VAR systems

This paper provides asymptotic standard errors for the moving average (MA) impact matrix for the second differences of a vector autoregressive (VAR) process integrated of order 2,I(2). Standard errors of the row space of the MA impact matrix are also provided; bases of this row space define the common I(2) trends linear combinations. These standard errors are then used to formulate Wald type tests. The MA impact matrix is shown to be linked to impact factors which measure the total effect of disequilibrium errors on the growth rate of the system. Most of the relevant limit distributions are Gaussian, and we report artificial regressions that can be used to calculate the estimators of the asymptotic variances. The use of the techniques proposed in the paper are illustrated on UK money data.