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Unit Root Tests Based on Unconditional Maximum Likelihood Estimation for the Autoregressive Moving Average

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  • Dong Wan Shin
  • Wayne Fuller

Abstract

Unconditional maximum likelihood estimation is considered for an autoregressive moving average that may contain an autoregressive unit root. The limiting distribution of the normalized maximum likelihood estimator of the unit root is shown to be the same as that of the estimator for the first‐order autoregressive process. A likelihood ratio test based on unconditional maximum likelihood estimation is proposed. In a Monte Carlo study for the autoregressive moving‐average model of order (1, 1), the new test is shown to have better size and power than those of several other tests.

Suggested Citation

  • Dong Wan Shin & Wayne Fuller, 1998. "Unit Root Tests Based on Unconditional Maximum Likelihood Estimation for the Autoregressive Moving Average," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 591-599, September.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:5:p:591-599
    DOI: 10.1111/1467-9892.00110
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    1. Kerry Patterson & Michael A. Thornton, 2013. "A review of econometric concepts and methods for empirical macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 2, pages 4-42, Edward Elgar Publishing.
    2. Sánchez, Ismael, 2000. "Spectral density estimators at frequency zero for nonstationarity tests in arma models," DES - Working Papers. Statistics and Econometrics. WS 10132, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Garcia-Hiernaux, Alfredo & Guerrero, David E., 2021. "Price convergence: Representation and testing," Economic Modelling, Elsevier, vol. 104(C).
    4. García-Hiernaux, Alfredo & Guerrero, David E. & McAleer, Michael, 2016. "Market integration dynamics and asymptotic price convergence in distribution," Economic Modelling, Elsevier, vol. 52(PB), pages 913-925.
    5. George, Halkos & Ilias, Kevork, 2005. "Το Υπόδειγμα Τυχαίου Περιπάτου Με Αυτοπαλίνδρομα Σφάλματα [The random walk model with autoregressive errors]," MPRA Paper 33312, University Library of Munich, Germany.
    6. Rafael, Dobado-González & Alfredo, García-Hiernaux & David, Guerrero-Burbano, 2013. "West versus East: Early Globalization and the Great Divergence," MPRA Paper 48773, University Library of Munich, Germany.
    7. Alfredo García-Hiernaux & David E. Guerrero, 2011. "Convergence and Cointegration," Documentos de Trabajo del ICAE 2011-22, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    8. 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.
    9. Ismael Sánchez, 2004. "Implementing unit roost tests in ARMA models of unknow order," Statistical Papers, Springer, vol. 45(2), pages 249-266, April.
    10. Alfredo García Hiernaux & David Esteban Guerrero Burbano, 2015. "Price-Level Convergence in the Eurozone," Documentos de Trabajo del ICAE 2015-05, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    11. Garcia-Hiernaux, Alfredo & Gonzalez-Perez, Maria T. & Guerrero, David E., 2023. "Eurozone prices: A tale of convergence and divergence," Economic Modelling, Elsevier, vol. 126(C).

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