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A New Approach to Robust Inference in Cointegration

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Abstract
A new approach to robust testing in cointegrated systems is proposed using nonparametric HAC estimators without truncation. While such HAC estimates are inconsistent, they still produce asymptotically pivotal tests and, as in conventional regression settings, can improve testing and inference. The present contribution makes use of steep origin kernels which are obtained by exponentiating traditional quadratic kernels. Simulations indicate that tests based on these methods have improved size properties relative to conventional tests and better power properties than other tests that use Bartlett or other traditional kernels with no truncation.

Suggested Citation

  • Sainan Jin & Peter C.B. Phillips & Yixiao Sun, 2005. "A New Approach to Robust Inference in Cointegration," Cowles Foundation Discussion Papers 1538, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1538
    Note: CFP 1203.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d15/d1538.pdf
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    References listed on IDEAS

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    1. Nicholas M. Kiefer & Timothy J. Vogelsang, 2002. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation," Econometrica, Econometric Society, vol. 70(5), pages 2093-2095, September.
    2. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    3. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1350-1366, December.
    4. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    5. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, May.
    6. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation for Research in Economics, Yale University.
    7. 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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    Cited by:

    1. Hwang, Jungbin & Sun, Yixiao, 2018. "SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS," Econometric Theory, Cambridge University Press, vol. 34(5), pages 949-984, October.
    2. Javier Hualde & Fabrizio Iacone, 2015. "Small-b and Fixed-b Asymptotics for Weighted Covariance Estimation in Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 528-540, July.
    3. Pellatt, Daniel F. & Sun, Yixiao, 2023. "Asymptotic F test in regressions with observations collected at high frequency over long span," Journal of Econometrics, Elsevier, vol. 235(2), pages 1281-1309.
    4. Vogelsang, Timothy J. & Wagner, Martin, 2014. "Integrated modified OLS estimation and fixed-b inference for cointegrating regressions," Journal of Econometrics, Elsevier, vol. 178(2), pages 741-760.
    5. Qunyong Wang & Na Wu, 2012. "Long-run covariance and its applications in cointegration regression," Stata Journal, StataCorp LP, vol. 12(3), pages 525-542, September.
    6. Pellatt , Daniel & Sun, Yixiao, 2020. "Asymptotic F test in Regressions with Observations Collected at High Frequency over Long Span," University of California at San Diego, Economics Working Paper Series qt19f0d9wz, Department of Economics, UC San Diego.

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    More about this item

    Keywords

    Cointegration; HAC estimation; long-run covariance matrix; robust inference; steep origin kernel; fully modified estimation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric 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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