Overlapping subsampling and invariance to initial conditions

This article studies the use of the overlapping blocking scheme in unit root autoregression. When the underlying process is that of a random walk, the blocks’ initial conditions are not fixed, but are equal to the sum of all the previous observations’ error terms. When non overlapping subsamples are used, these initial conditions do not disappear asymptotically. In this article, we show that a simple way of overcoming this issue is to use overlapping blocks. By doing so, the effect of these initial conditions vanishes asymptotically. An application of these findings to jackknife estimators indicates that an estimator based on moving blocks is able to provide obvious reductions to the mean square error. Also results are shown to be robust to local-to-unity frameworks, when the autoregressive parameter is unknown.