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Exact distribution and critical values of a unit root test when error terms are serially correlated

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  • Junya Masuda
  • Kazuhiro Ohtani

Abstract

In this article we consider the unit root test based on the ordinary least squares (OLSs) estimator for a coefficient of a lagged dependent variable when the error terms are serially correlated. Using Imhof's (1961) method, we show how we numerically evaluate the exact distribution function of the unit root test when the error terms are serially correlated. Our numerical results show that when the error terms are serially correlated, the size distortion is not small even if the sample size is considerably large. Also, based on the distribution function, we evaluate numerically exact critical values when the sample size is small and moderate.

Suggested Citation

  • Junya Masuda & Kazuhiro Ohtani, 2008. "Exact distribution and critical values of a unit root test when error terms are serially correlated," Applied Economics Letters, Taylor & Francis Journals, vol. 15(5), pages 359-362.
    • Handle: RePEc:taf:apeclt:v:15:y:2008:i:5:p:359-362
    DOI: 10.1080/13504850600706131
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    References listed on IDEAS

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    1. Kazuhiro Ohtani, 2002. "Exact critical values of unit root tests with drift and trend," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 137-145.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Kazuhiro Ohtani, 2000. "Exact and bootstrap distributions of a unit root test," Applied Economics Letters, Taylor & Francis Journals, vol. 7(7), pages 463-466.
    4. Kazuhiro Ohtani, 2004. "Exact distribution and critical values of a unit root test in the presence of change in variance," Applied Economics Letters, Taylor & Francis Journals, vol. 11(14), pages 855-860.
    5. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    6. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
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