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Bootstrapping Unit Root Tests with Covariates

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  • Chang, Yoosoon

    (Rice U)

  • Sickles, Robin
  • Song, Wonho

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 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 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 ADF test. We apply our testing procedures to the extended Nelson-Plosser data set for the post-1929 samples as well as postwar annual CPI-based real exchange rates for 14 OECD countries.

Suggested Citation

  • Chang, Yoosoon & Sickles, Robin & Song, Wonho, 2001. "Bootstrapping Unit Root Tests with Covariates," Working Papers 2001-07, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:2001-07
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    File URL: http://www.ruf.rice.edu/~econ/papers/2001papers/07Chang.pdf
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    References listed on IDEAS

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    1. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
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    5. DeJong, David N. & Nankervis, John C. & Savin, N. E. & Whiteman, Charles H., 1992. "The power problems of unit root test in time series with autoregressive errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 323-343.
    6. Alston Flynn, N. & Boucher, Janice L., 1993. "Tests of long-run Purchasing Power Parity using alternative methodologies," Journal of Macroeconomics, Elsevier, vol. 15(1), pages 109-122.
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    Cited by:

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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. 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.
    5. Chang, Yoosoon, 2003. "Nonlinear IV Panel Unit Root Tests," Working Papers 2003-06, Rice University, Department of Economics.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    14. Anton Skrobotov, 2022. "Testing for explosive bubbles: a review," Papers 2207.08249, arXiv.org.
    15. 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).

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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