Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes

We consider anr-dimensional multivariate time series {yt, t∈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 finitek-order vector autoregressive process (k→∞ 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).