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GARCH, heteroscedasticity-consistent covariance matrix estimation and (non)linear unit root testing

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  • Steven Cook

Abstract

In previous research it has been shown that while the Dickey--Fuller unit root test exhibits oversizing in the presence of GARCH, this is reduced via the application of White's heteroscedasticity-consistent covariance matrix (HCCM). These findings provide the motivation for the present study. It is shown that the application of White's HCCM to the Dickey--Fuller test results in a shift of the finite-sample distribution of the test thereby necessitating the use of HCCM-specific critical values. Re-examination of the impact of GARCH upon the Dickey--Fuller test shows the combination of White's HCCM and HCCM-specific critical values leads to a marked improvement in empirical size. A similar analysis is performed for an alternative nonlinear unit root test. The results obtained show that in comparison to the Dickey--Fuller test, the distribution of this test is more sensitive to the use of White's HCCM while it also exhibits greater oversizing in the presence of GARCH. However, use of White's HCCM and HCCM-specific critical values are found to correct the size of the test. The results presented illustrate the usefulness of White's HCCM and HCCM-specific critical values when examining the unit root hypothesis in time series exhibiting GARCH.

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  • Steven Cook, 2006. "GARCH, heteroscedasticity-consistent covariance matrix estimation and (non)linear unit root testing," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 2(4), pages 217-222, July.
  • Handle: RePEc:taf:apfelt:v:2:y:2006:i:4:p:217-222
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    1. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    4. James G. MacKinnon, 1990. "Critical Values for Cointegration Tests," Working Papers 1227, Queen's University, Department of Economics.
    5. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October.
    6. Dirk Te Velde, 2001. "Balance of payments prospects in EMU," National Institute of Economic and Social Research (NIESR) Discussion Papers 178, National Institute of Economic and Social Research.
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    Cited by:

    1. Su, Jen-Je & Cheung, Adrian (Wai-Kong) & Roca, Eduardo, 2014. "Does Purchasing Power Parity hold? New evidence from wild-bootstrapped nonlinear unit root tests in the presence of heteroskedasticity," Economic Modelling, Elsevier, vol. 36(C), pages 161-171.
    2. Cook, Steven, 2008. "Joint maximum likelihood estimation of unit root testing equations and GARCH processes: Some finite-sample issues," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 109-116.

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