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A Sequential Test For a Unit Root in Monitoring a p-th Order Autoregressive Process

Kohtaro Hitomi (Kyoto Institute of Technology, Kyoto, Japan)

Keiji Nagai (Yokohama National University, Yokohama, Japan)

Yoshihiko Nishiyama (Kyoto University, Kyoto, Japan)

Junfan Tao (Kyoto University, Kyoto, Japan)

Essays in Honor of Joon Y. Park: Econometric Theory

ISBN: 978-1-83753-209-4, eISBN: 978-1-83753-208-7

Publication date: 24 April 2023

Abstract

In this study, the authors investigate methods of sequential analysis to test prospectively for the existence of a unit root against stationary or explosive states in a p-th order autoregressive (AR) process monitored over time. Our sequential sampling schemes use stopping times based on the observed Fisher information of a local-to-unity parameter. In contrast to the Dickey–Fuller (DF) test statistic, the sequential test statistic has asymptotic normality. The authors derive the joint limit of the test statistic and the stopping time, which can be characterized using a 3/2-dimensional Bessel process driven by a time-changed Brownian motion. The authors obtain their limiting joint Laplace transform and density function under the null and local alternatives. In addition, simulations are conducted to show that the theoretical results are valid.

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Acknowledgements

Acknowledgments

We are grateful for the helpful comments and suggestions from the editor and an anonymous referee, which have significantly improved the structure and readability of this chapter. This study was supported by JSPS KAKENHI Grants Numbers JP17K03656, JP18K01543, JP19F19312, JP19H01473, JP19K21691, and JP20K01589.

Citation

Hitomi, K., Nagai, K., Nishiyama, Y. and Tao, J. (2023), "A Sequential Test For a Unit Root in Monitoring a p-th Order Autoregressive Process", Chang, Y., Lee, S. and Miller, J.I. (Ed.) Essays in Honor of Joon Y. Park: Econometric Theory (Advances in Econometrics, Vol. 45A), Emerald Publishing Limited, Leeds, pp. 115-153. https://doi.org/10.1108/S0731-90532023000045A004

Publisher

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Emerald Publishing Limited