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A Two-Stage Plug-In Bandwidth Selection And Its Implementation For Covariance Estimation

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  • Hirukawa, Masayuki

Abstract

The two most popular bandwidth choice rules for kernel HAC estimation have been proposed by Andrews (1991) and Newey and West (1994). This paper suggests an alternative approach that estimates an unknown quantity in the optimal bandwidth for the HAC estimator (called normalized curvature) using a general class of kernels, and derives the optimal bandwidth that minimizes the asymptotic mean squared error of the estimator of normalized curvature. It is shown that the optimal bandwidth for the kernel-smoothed normalized curvature estimator should diverge at a slower rate than that of the HAC estimator using the same kernel. An implementation method of the optimal bandwidth for the HAC estimator, which is analogous to the one for probability density estimation by Sheather and Jones (1991), is also developed. The finite sample performance of the new bandwidth choice rule is assessed through Monte Carlo simulations.

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  • Hirukawa, Masayuki, 2010. "A Two-Stage Plug-In Bandwidth Selection And Its Implementation For Covariance Estimation," Econometric Theory, Cambridge University Press, vol. 26(3), pages 710-743, June.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:710-743_99
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    Cited by:

    1. Hirukawa, Masayuki, 2011. "How useful is yet another data-driven bandwidth in long-run variance estimation?: A simulation study on cointegrating regressions," Economics Letters, Elsevier, vol. 111(2), pages 170-172, May.
    2. Pedro H. Albuquerque, 2020. "Optimal Time Interval Selection in Long-Run Correlation Estimation," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(1), pages 53-79, March.
    3. 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.
    4. Bruce E. Hansen & Ananth Seshadri, 2014. "Uncovering the Relationship between Real Interest Rates and Economic Growth," Working Papers wp303, University of Michigan, Michigan Retirement Research Center.
    5. Gregory Rice & Han Lin Shang, 2017. "A Plug-in Bandwidth Selection Procedure for Long-Run Covariance Estimation with Stationary Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 591-609, July.
    6. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    7. Kin Wai Chan & Chun Yip Yau, 2017. "High-order Corrected Estimator of Asymptotic Variance with Optimal Bandwidth," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 866-898, December.
    8. Pavel Yaskov, 2010. "Testing for predictive ability in the presence of structural breaks (in Russian)," Quantile, Quantile, issue 8, pages 127-135, July.

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