Inference for Impulse Response Coefficients from Multivariate Fractionally Integrated Processes

This paper 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 paper extends the univariate analysis recently provided by Baillie and Kapetanios (2013), and uses a semi parametric, time domain estimator, based on a vector autoregression (VAR) approximation. There are theoretical reasons for making the lag length of the VAR proportional to [ln(T)^2]. Results are also derived for the orthogonalized estimated IRs which are generally more practically relevant. Simulation evidence strongly indicates the desirability for applying the Kilian small sample bias correction, which is found to improve both the estimated orthogonalized and the non-orthogonalized IRs. The most appropriate order of the VAR turns out to be relevant for the lag length of the IR being estimated.