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Results On Estimation And Testing For A Unit Root In The Nonstationary Autoregressive Moving‐Average Model

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  • Sook Fwe Yap
  • Gregory C. Reinsel

Abstract

. We review the limiting distribution theory for Gaussian estimation of the univariate autoregressive moving‐average (ARMA) model in the presence of a unit root in the autoregressive (AR) operator, and present the asymptotic distribution of the associated likelihood ratio (LR) test statistic for testing for a unit root in the ARMA model. The finite sample properties of the LR statistic as well as other unit root test procedures for the ARMA model are examined through a limited simulation study. We conclude that, for practical empirical work that relies on standard computations, the LR test procedure generally performs better than other standard procedures in the presence of a substantial moving‐average component in the ARMA model.

Suggested Citation

  • Sook Fwe Yap & Gregory C. Reinsel, 1995. "Results On Estimation And Testing For A Unit Root In The Nonstationary Autoregressive Moving‐Average Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 339-353, May.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:3:p:339-353
    DOI: 10.1111/j.1467-9892.1995.tb00238.x
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    References listed on IDEAS

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    1. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    2. Pantula, Sastry G. & Hall, Alastair, 1991. "Testing for unit roots in autoregressive moving average models : An instrumental variable approach," Journal of Econometrics, Elsevier, vol. 48(3), pages 325-353, June.
    3. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    4. Dolado, Juan J. & Hidalgo-Moreno, Javier, 1990. "The Asymptotic Distribution of the Iterated Gauss-Newton Estimators of an ARIMA Process," Econometric Theory, Cambridge University Press, vol. 6(04), pages 490-494, December.
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    1. Taiyeong Lee & David A. Dickey, 2004. "Limiting distributions of unconditional maximum likelihood unit root test statistics in seasonal time–series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 551-561, July.
    2. Shin, Dong Wan & So, Beong-Soo, 1997. "Semiparametric unit root tests based on symmetric estimators," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 177-184, April.
    3. Ismael Sánchez, 2004. "Implementing unit roost tests in ARMA models of unknow order," Statistical Papers, Springer, vol. 45(2), pages 249-266, April.
    4. Ling, Shiqing & Zhu, Ke & Yee, Chong Ching, 2013. "Diagnostic checking for non-stationary ARMA models with an application to financial data," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 624-639.
    5. Müller, Christian & Hahn, Elke, 2000. "Money demand in Europe: Evidence from the past," SFB 373 Discussion Papers 2000,35, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Neil Kellard & Denise Osborn & Jerry Coakley & Marcus J. Chambers, 2015. "Testing for a Unit Root in a Near-Integrated Model with Skip-Sampled Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 630-649, September.
    7. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.

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