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Bootstrapping Unit Root Tests with Covariates

Author

Listed:
  • Chang, Yoosoon

    (IN University)

  • Sickles, Robin C.

    (Rice University)

  • Song, Wonho

    (Chung-Ang University)

Abstract

We consider the bootstrap method for the covariates augmented Dickey-Fuller (CADF) unit root test suggested in Hansen (1995) which uses related variables to improve the power of univariate unit root tests. It is shown that there are substantial power gains from including correlated covariates. The limit distribution of the CADF test, however, depends on the nuisance parameter that represents the correlation between the equation error and the covariates. Hence, inference based directly on the CADF test is not possible. To provide a valid inferential basis for the CADF test, we propose to use the parametric bootstrap procedure to obtain critical values, and establish the asymptotic validity of the bootstrap CADF test. Simulations show that the bootstrap CADF test significantly improves the asymptotic and the finite sample size performances of the CADF test, especially when the covariates are highly correlated with the error. Indeed, the bootstrap CADF test offers drastic power gains over the conventional unit root tests. Our testing procedures are applied to the extended Nelson and Plosser data set.

Suggested Citation

  • Chang, Yoosoon & Sickles, Robin C. & Song, Wonho, 2014. "Bootstrapping Unit Root Tests with Covariates," Working Papers 15-009, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:15-009
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    2. Bruggeman, Annick & Donati, Paola & Warne, Anders, 2003. "Is the demand for euro area M3 stable?," Working Paper Series 255, European Central Bank.
    3. Astill, Sam & Taylor, A.M. Robert & Kellard, Neil & Korkos, Ioannis, 2023. "Using covariates to improve the efficacy of univariate bubble detection methods," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 342-366.
    4. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    5. Omtzigt Pieter & Fachin Stefano, 2002. "Bootstrapping and Bartlett corrections in the cointegrated VAR model," Economics and Quantitative Methods qf0212, Department of Economics, University of Insubria.
    6. Nguyen Dinh Hoan, 2022. "Nexus among Green Energy Investment, World Oil Price, Monetary Policy and Business Performance: Evidence from Energy Companies on the Vietnamese Stock Exchange," International Journal of Energy Economics and Policy, Econjournals, vol. 12(6), pages 404-411, November.
    7. Yang, Yang & Zhao, Zhao, 2020. "Quantile nonlinear unit root test with covariates and an application to the PPP hypothesis," Economic Modelling, Elsevier, vol. 93(C), pages 728-736.
    8. Jitendra Kumar & Ashok Kumar & Varun Agiwal, 2024. "Bayesian Estimation of Multiple Covariate of Autoregressive (MC-AR) Model," Annals of Data Science, Springer, vol. 11(4), pages 1291-1301, August.
    9. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    10. Anton Skrobotov, 2022. "Testing for explosive bubbles: a review," Papers 2207.08249, arXiv.org.
    11. Sadiq, Muhammad & Chavali, Kavita & Kumar, V.V. Ajith & Wang, Kuan-Ting & Nguyen, Phong Thanh & Ngo, Thanh Quang, 2023. "Unveiling the relationship between environmental quality, non-renewable energy usage and natural resource rent: Fresh insights from ten asian economies," Resources Policy, Elsevier, vol. 85(PA).
    12. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
    13. Hsu, Ching-Chi, 2023. "Influence of climate finance and natural resource consumption on the mitigation of climate change in developed countries in the Pre-COP26 era," Resources Policy, Elsevier, vol. 83(C).
    14. Shahbaz, Muhammad & Abbas Rizvi, Syed Kumail & Dong, Kangyin & Vo, Xuan Vinh, 2022. "Fiscal decentralization as new determinant of renewable energy demand in China: The role of income inequality and urbanization," Renewable Energy, Elsevier, vol. 187(C), pages 68-80.
    15. Tsong Ching-Chuan & Lee Cheng-Feng & Tsai Li Ju, 2019. "A parametric stationarity test with smooth breaks," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(2), pages 1-14, April.
    16. Ho, Tsung-wu, 2015. "Income inequality may not converge after all: Testing panel unit roots in the presence of cross-section cointegration," The Quarterly Review of Economics and Finance, Elsevier, vol. 56(C), pages 68-79.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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