Bootstrapping autoregressive and moving average parameter estimates of infinite order vector autoregressive processes

We consider an r-dimensional multivariate time series {y(t), t is an element of Z} which is generated by an infinite order vector autoregressive process. We show that a bootstrap procedure which works by generating time series replicates via an estimated finite k-order vector autoregressive process (k --> infinity at an appropriate rate with the sample size) gives asymptotically valid approximations to the joint distribution of the growing set of estimated autoregressive coefficients and to the corresponding set of estimated moving average coefficients (impuls responses). (C) 1996 Academic Press, Inc.