On the Vector Autoregressive Sieve Bootstrap

The concept of autoregressive sieve bootstrap is investigated for the case of vector autoregressive (VAR) time series. This procedure fits a finite‐order VAR model to the given data and generates residual‐based bootstrap replicates of the time series. The paper explores the range of validity of this resampling procedure and provides a general check criterion, which allows to decide whether the VAR sieve bootstrap asymptotically works for a specific statistic or not. In the latter case, we will point out the exact reason that causes the bootstrap to fail. The developed check criterion is then applied to some particularly interesting statistics