Extending the Use of the Block-Block Bootstrap to AR(∞) Processes

In the context of limited dependence at large lags, Andrews (2002) showed the magnitudes of the error in rejection probabilities of the symmetric two-sided block bootstrap t, Wald and J tests. Andrews (2004) introduced the block-block bootstrap and proved that it obtained better asymptotic refinements than the block bootstrap. To date the ability to obtain asymptotic refinements with bootstrap methods has been restricted to data with very limited dependence. In this paper we show that the ability to obtain asymptotic refinements extends to the very important case of AR(∞) models. Specifically, we show that the block-block bootstrap can also provide refinements in the presence of AR(∞) models. We provide the assumptions under which those refinements are possible.