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Sequential test for unit root in AR(1) model

Keiji Nagai (), Yoshihiko Nishiyama () and Kohtaro Hitomi ()
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Keiji Nagai: Yokohama National University
Yoshihiko Nishiyama: Institute of Economic Research, Kyoto University
Kohtaro Hitomi: Kyoto Institute of Technology

No 1003, KIER Working Papers from Kyoto University, Institute of Economic Research

Abstract: We consider unit root tests under sequential sampling for an AR(1) process against both stationary and explosive alternatives. We propose three kinds of test, or t type, stopping time and Bonferroni tests, using the sequential coefficient estimator and the stopping time of Lai and Siegmund (1983). To examine the statistical properties, we obtain their weak joint limit by approximating the processes in D[0;∞) and using time change and a DDS (Dambis and Dubins-Schwarz) Brownian motion. The distribution of the stopping time is characterized by a Bessel process of dimension 3/2 with and without drift, while the esitimator is asymptotically normally distributed. We implement Monte Carlo simulations and numerical computations to examine their small sample properties.

Pages: 27 pages
Date: 2018-10
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