Abstract
In this article, the unit root test for the AR(1) model with dependent residuals is considered. We adopt a bootstrap procedure to bootstrap the residuals with bootstrap sample size m less than the size n of the original sample. Under the assumptions that m → ∞ and m/n → 0, the convergence in probability of the bootstrap distribution function is established.
Similar content being viewed by others
References
Arcones M, Giné E (1989) The bootstrap of the mean with arbitrary bootstrap sample size. Ann Inst H Poincaré 22:457–481
Arcones M, Giné E (1991) Additions and corrections to the bootstrap of the mean with arbitrary bootstrap sample size. Ann Inst H Poincaré 27:583–595
Basawa IV, Mallik AK, McCormick WP, Taylor RL (1991) Bootstrap test of significance and sequential bootstrap estimation for unstable first-order autoregressive processes. Comm Statist Theory Methods 20:1015–1026
Billingsley P (1968) Convergence of probability measure. Wiley, New York
Chan NH, Tran LT (1989) On the first-order autoregressive process with infinite variance. Econometric Theory 5:354–362
Datta SH (1996) On asymptotic properties of bootstrap for AR(1) processes. J Statist Plann Inference 53:361–374
Hall P, Heyde CC (1980) Martingale limit theory and its application. Academic Press, New York
Horváth L, Kokoszka P (2003) A bootstrap approximation to a unit root test statistic for heavy-tailed observations. Statist Probab Lett 62:163–173
Lai TL, Wei CZ (1982) Least-squares estimates in stochastic regression model with applications to identification and control of dynamical systems. Ann Statist 10:154–166
Newman CM, Wright AL (1981) An invariance principle for certain dependent sequeces. Ann Probab 9:671–675
Shao QM (2000) A comparison theorem on moment inqualities. J Theoret Probab 13:343–356
Su C, Zhao LC, Wang YB (1997) The moment inequalities and weak convergence for negatively associated sequences. Sci China 40(A):172–182
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported by National Natural Science Foundation of China (No. 10471126)
Rights and permissions
About this article
Cite this article
Zhang, LX., Yang, XR. The Limit Distribution of the Bootstrap for the Unit Root Test Statistic when the Residuals are Dependent. Metrika 65, 195–206 (2007). https://doi.org/10.1007/s00184-006-0070-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-006-0070-y