Patrick Richard () (GREDI, Département d'économique, Université de Sherbrooke)
Abstract
We study the use of the sieve bootstrap to conduct ADF unit root tests when the time series' first difference is a general linear process that admits an infinite moving average form. The work of Park (2002) and Chang and Park (2003) suggest that the usual autoregressive (AR) sieve bootstrap provides some accuracy gains under the null hypothesis. The magnitude of this amelioration, however, depends on the nature of the true DGP. For example, the AR sieve test over-rejects almost as much as the asymptotic one when the DGP contains a strong negative moving average root. This lack of robustness is, of course, caused by the poor quality of the AR approximation. We attempt to reduce this problem by proposing to use sieve bootstraps based on moving average (MA) and autoregressive-moving average (ARMA) approximations. Though this is a natural generalisation of the standard AR sieve bootstrap, it has never been suggested in the econometrics literature. Two important theoretical results are shown. First, we establish invariance principles for the partial sum processes built from invertible MA and stationary and invertible ARMA sieve bootstrap DGPs. Second, these are used to provide a proof of the asymptotic validity of the resulting ADF bootstrap tests. Through Monte Carlo experiments, we find that the rejection probability of the MA sieve bootstrap is more robust to the DGP than that of the AR sieve bootstrap. We also find that the ARMA sieve bootstrap requires only a very parsimonious specification to achieve excellent results.
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Publisher Info
Paper provided by Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke in its series Cahiers de recherche with number
07-05.
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