Inference for impulse response coefficients from multivariate fractionally integrated processes

This article considers a multivariate system of fractionally integrated time series and investigates the most appropriate way for estimating Impulse Response (IR) coefficients and their associated confidence intervals. The article extends the univariate analysis recently provided by Baillie and Kapetanios (2013), and uses a semiparametric, time domain estimator, based on a vector autoregression (VAR) approximation. Results are also derived for the orthogonalized estimated IRs which are generally more practically relevant. Simulation evidence strongly indicates the desirability of applying the Kilian small sample bias correction, which is found to improve the coverage accuracy of confidence intervals for IRs. The most appropriate order of the VAR turns out to be relevant for the lag length of the IR being estimated.