Abstract
This paper concerns the asymptotic properties of the quadratic functionals and associated ordinary least squares estimator in the explosive first-order Gaussian autoregressive process. By the deviation inequalities for multiple Wiener-Itô integrals and asymptotic analysis techniques, Cramér-type moderate deviations are achieved under the explosive and mildly explosive frameworks. As applications, the global and local powers for the unit root test are shown to approach one at exponential rates. Simulation experiments are conducted to confirm the theoretical results.
Funding Statement
Hui Jiang is partially supported by NSFC grant 11771209 and Guangyu Yang is partially supported by the Foundation of Young Scholar of the Educational Department of Henan Province grant 2019GGJS012.
Acknowledgements
We would like to express our great gratitude to the two anonymous referees and the AE for the careful reading and insightful comments, which surely lead to an improved presentation of this paper.
Citation
Hui Jiang. Yilong Wan. Guangyu Yang. "Deviation inequalities and Cramér-type moderate deviations for the explosive autoregressive process." Bernoulli 28 (4) 2634 - 2662, November 2022. https://doi.org/10.3150/21-BEJ1432
Information
