Computation of the Beveridge–Nelson decomposition for multivariate economic time series

This note shows how the result of Newbold (1990) [Newbold, P., 1990. Precise and efficient computation of the Beveridge–Nelson decomposition of economic time series. Journal of Monetary Economics 26, 453-457] can be extended to the computation of the Beveridge–Nelson decomposition in the multivariate case, where series are generated by vector ARIMA models. A separate treatment is provided for the cointegrated case.