Summary: In this article, we investigate and compare the behaviour of some bootstrap unit root tests in finite ARMA models with a constant and/or a trend and use them to obtain asymptotic results for the point optimal (hereafter PO) test, in terms of both size and power. We demonstrate the asymptotic validity of bootstrapping the PO test. We provide a feasible method for obtaining approximate critical values for the PO unit root test. Through simulations, we investigate how effective the bootstrap is in different sample sizes, correlative coefficients and close unity autoregressive roots in two different models. Our main objective is to show that the bootstrap PO test can be used in regression models with AR and MA errors and trending regressors. The results reported here provide an analytical investigation of the use of the bootstrap for PO tests with dependent data.
The main contribution of this article has two features. First, we choose the PO test and make this powerful but unfeasible procedure both powerful and feasible, by plugging in a consistent estimation of the coefficient structure, and we show that the bootstrap PO test provides asymptotically valid critical values. Second, through simulation, our numerical results suggest that the bootstrap PO test performs well in having the correct size properties and retaining good power in the parametric (and semi-parametric) bootstrap procedure.