Hybrid bootstrap aided unit root testing

• Published in: Computational statistics Vol. 27; no. 4; pp. 779 - 797
• Main Authors: Jentsch, C., Kreiss, J.-P., Mantalos, P., Paparoditis, E.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.12.2012; Springer Nature B.V
• Subjects: ADF tests; Approximation; Asymptotic properties; Bootstrap method; Computer simulation; Economic Theory/Quantitative Economics/Mathematical Methods; Hybrid bootstrap; Hypotheses; Mathematics and Statistics; Monte Carlo methods; Monte Carlo simulation; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Roots; Samples; Sieve bootstrap; Sieves; Statistical analysis; Statistical methods; Statistics; Statistik; Studies; Time series; Unit root testing; Hybrid bootstrap; Sieve bootstrap; Unit root testing; ADF tests
• ISSN: 0943-4062; 1613-9658; 1613-9658
• DOI: 10.1007/s00180-011-0290-0

In this paper, we propose a hybrid bootstrap procedure for augmented Dickey-Fuller (ADF) tests for the presence of a unit root. This hybrid proposal combines a time domain parametric autoregressive fit to the data and a nonparametric correction applied in the frequency domain to capture features that are possibly not represented by the parametric model. It is known that considerable size and power problems can occur in small samples for unit root testing in the presence of an MA parameter using critical values of the asymptotic Dickey-Fuller distribution. The benefit of the sieve bootstrap in this situation has been investigated by Chang and Park (J Time Ser Anal 24:379–400, 2003 ). They showed asymptotic validity as well as substantial improvements for small sample sizes, but the actual sizes of their bootstrap tests were still quite far away from the nominal size. The finite sample performances of our procedure are extensively investigated through Monte Carlo simulations and compared to the sieve bootstrap approach. Regarding the size of the tests, our results show that the hybrid bootstrap remarkably outperforms the sieve bootstrap.