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Dickey–Fuller, Lagrange Multiplier and Combined Tests for a Unit Root in Autoregressive Time Series

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  • Kosuke Oya
  • Hiro Toda

Abstract

In this paper we investigate (augmented) Dickey–Fuller (DF) and Lagrange multiplier (LM) type unit root tests for autoregressive time series through comprehensive Monte Carlo simulations. We consider two sorts of null and alternative hypotheses: a unit root without drift versus level stationarity and a unit root with drift versus trend stationarity. The DF‐type coef ficient tests are found to show the best overall performance in both cases, at least if the sample size is sufficiently large. How ever, it is also found that the DF and LM tests are roughly complementary with regard to their finite‐sample power. We therefore consider combining these two types of unit root tests to obtain (ad hoc‘but’) ‘robust’ test procedures. Critical values for the proposed tests are provided

Suggested Citation

  • Kosuke Oya & Hiro Toda, 1998. "Dickey–Fuller, Lagrange Multiplier and Combined Tests for a Unit Root in Autoregressive Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 325-347, May.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:3:p:325-347
    DOI: 10.1111/1467-9892.00095
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    Cited by:

    1. Luis C. Nunes & Paulo M. M. Rodrigues, 2011. "On LM‐type tests for seasonal unit roots in the presence of a break in trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(2), pages 108-134, March.
    2. Petrenko, Victoria (Петренко, ВИктория) & Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Maria (Турунцева, Мария), 2016. "Testing of Changes in Persistence and Their Effect on the Forecasting Quality [Тестирование Изменения Инерционности И Влияние На Качество Прогнозов]," Working Papers 542, Russian Presidential Academy of National Economy and Public Administration.
    3. Eiji Kurozumi, 2005. "Detection of Structural Change in the Long-run Persistence in a Univariate Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(2), pages 181-206, April.

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