How to implement the Bootstrap in Static or Stable Dynamic Regression Models

By combining two alternative formulations of a test statistic with two alternative resamplingschemes we obtain four different bootstrap tests. In the context of static linear regression modelstwo of these are shown to have serious size and power problems, whereas the remaining two areadequate and in fact equivalent. The equivalence between the two valid implementations is shown tobreak down in dynamic regression models. Then the procedure based on the test statistic approachperforms best, at least in the AR(l)-model. Similar finite-sample phenomena are illustrated in theARMA(l,l)-model through a small-scale Monte Carlo study and an empirical example.