A Moving Average Sieve Bootstrap for Unit Root Tests'', working paper

This paper considers the use of bootstrap methods for the test of the unit root hypothesis for a time series with a first difference that can be written as a general linear process admitting an infinite moving average (MA(∞)) representation. The standard test procedure for such cases is the augmented Dickey Fuller (ADF) test introduced by Said and Dickey (1984). However, it is well known that this test’s true rejection probability under the unit root null hypothesis is often quite differ-ent from what asymptotic theory predicts. The bootstrap is a natural solution to such error in rejection probability (ERP) problems and ADF tests are consequently often based on block bootstrap or autoregressive (AR) sieve bootstrap distribu-tions. In this paper, we propose the use of moving average (MA) sieve bootstrap distributions. To justify this, we derive an invariance principle for sieve bootstrap samples based on MA approximations. Also, we demonstrate that the ADF test based on this MA sieve bootstrap is consistent. Similar results have been proved for the AR sieve bootstrap by Park (2002) and Chang and Park (2003). The finite sample performances of the MA sieve bootstrap ADF test are investigated through simulations. Our main conclusions are that it is often, though not always, more ac-curate than the AR sieve bootstrap or the block bootstrap, that it requires smaller parametric orders to achieve comparable or better accuracy than the AR sieve and that it is more robust than the block bootstrap to the choice of approximation order or block length and slightly more robust to the data generating process. I am very grateful to my thesis director, professor Russell Davidson, for suggesting this research and for his constant guidance and support. I also thank professors John Galbraith and Victoria Zinde-Walsh for their very insightful comments