Generalized impulse response analysis in a fractionally integrated vector autoregressive model

We develop a generalized impulse response function for the fractionally integrated vector autoregressive (FIVAR) model using the Pesaran and Shin (1998) approach. Our method is different from the methodology shown in Chung (2001) since it does not require us to orthogonalize the error vector and, therefore, is independent of the ordering of the endogenous variables in the FIVAR. Being consistent with the long memory behaviour, we show that generalized and orthogonalized impulse responses of FIVAR evolve slowly at the same hyperbolic rates. However, we also note that they are different in a number of respects.

► We develop an impulse response function for a multivariate long memory process. ► This function is invariant to the ordering of endogenous variables in the system. ► The function evolves at slow hyperbolic rates as in Chung (2001). ► Our method and that of Chung (2001) are reformed to ease computer programming. ► Two methods give the same results for a shock in the 1st variable but different for others.