Prepivoted Augmented Dickey-Fuller Test with Bootstrap-Assisted Lag Length Selection

Abstract

We investigate the application of prepivoting in conjunction with lag length selection to correct the size and power performance of the Augmented Dickey-Fuller test for a unit root. The bootstrap methodology used to perform the prepivoting is a residual based AR bootstrap that ensures that bootstrap replicate time series are created under the null irrespective of whether the originally observed series obeys the null hypothesis or not. Simulation studies wherein we examine the performance of our proposed method are given; we evaluate our method’s performance on ARMA(1,1) models with varying configurations for size and power performance. We also propose a novel data dependent lag selection technique that uses bootstrap data under the null to select an optimal lag length; the performance of our method is compared to existing lag length selection criteria.

Keywords

• ADF test
• bootstrap
• hypothesis testing
• unit root
• ARMA models
• lag length selection