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Sequential test for unit root in AR(1) model

Author

Listed:
  • Keiji Nagai

    (Yokohama National University)

  • Yoshihiko Nishiyama

    (Institute of Economic Research, Kyoto University)

  • Kohtaro Hitomi

    (Kyoto Institute of Technology)

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.

Suggested Citation

  • Keiji Nagai & Yoshihiko Nishiyama & Kohtaro Hitomi, 2018. "Sequential test for unit root in AR(1) model," KIER Working Papers 1003, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:1003
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP1003.pdf
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    References listed on IDEAS

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    1. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. Chang, Yoosoon & Park, Joon Y., 2004. "Taking a New Contour: A Novel View on Unit Root Test," Working Papers 2004-10, Rice University, Department of Economics.
    5. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    6. Galtchouk, L. & Konev, V., 2004. "On uniform asymptotic normality of sequential least squares estimators for the parameters in a stable AR(p)," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 119-142, November.
    7. Galtchouk, Leonid & Konev, Victor, 2010. "On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2616-2636, November.
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    Cited by:

    1. Jianwei Jin & Keiji Nagai, 2022. "Sequential unit root test for first-order autoregressive processes with initial values," KIER Working Papers 1085, Kyoto University, Institute of Economic Research.
    2. Kohtaro Hitomi & Keiji Nagai & Yoshihiko Nishiyama & Junfan Tao, 2021. "Joint Asymptotic Properties of Stopping Times and Sequential Estimators for Stationary First-order Autoregressive Models," KIER Working Papers 1060, Kyoto University, Institute of Economic Research.
    3. Kohtaro Hitomi & Jianwei Jin & Keiji Nagai & Yoshihiko Nishiyama & Junfan Tao, 2022. "Unit root tests considering initial values and a concise method for computing powers," KIER Working Papers 1084, Kyoto University, Institute of Economic Research.

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