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Power Maximization And Size Control In Heteroskedasticity And Autocorrelation Robust Tests With Exponentiated Kernels

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  • Sun, Yixiao
  • Phillips, Peter C.B.
  • Jin, Sainan

Abstract

Using the power kernels of Phillips, Sun and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (rho). We show that the nonstandard fixed-rho limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-rho limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large-rho asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central concern of hypothesis testing: the selected power parameter is test-optimal in the sense that it minimizes the type II error while controlling for the type I error. A plug-in procedure for implementing the test-optimal power parameter is suggested. Simulations indicate that the new test is as accurate in size as the nonstandard test of Kiefer and Vogelsang (2002a, 2002b; KV), and yet it does not incur the power loss that often hurts the performance of the latter test. The new test therefore combines the advantages of the KV test and the standard (MSE optimal) HAC test while avoiding their main disadvantages (power loss and size distortion, respectively). The results complement recent work by Sun, Phillips and Jin (2008) on conventional and bT HAC testing.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 06 (December)
Pages: 1320-1368

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Handle: RePEc:cup:etheor:v:27:y:2011:i:06:p:1320-1368_00

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  1. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, 01.
  2. Kiefer, Nicholas M., 2001. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using the Bartlett Kernel without Truncation," Working Papers 01-13, Cornell University, Center for Analytic Economics.
  3. Phillips, Peter C.B. & Sun, Yixiao & Jin, Sainan, 2004. "Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," University of California at San Diego, Economics Working Paper Series qt6mf9q2rt, Department of Economics, UC San Diego.
  4. Donggyu Sul & Peter C. B. Phillips & Chi-Young Choi, 2005. "Prewhitening Bias in HAC Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(4), pages 517-546, 08.
  5. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
  6. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation for Research in Economics, Yale University.
  7. Sun, Yixiao, 2003. "Estimation of the Long-run Average Relationship in Nonstationary Panel Time Series," University of California at San Diego, Economics Working Paper Series qt5002z0pn, Department of Economics, UC San Diego.
  8. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June.
  9. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  10. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests," Working Papers 05-08, Cornell University, Center for Analytic Economics.
  11. Surajit Ray & N. E. Savin, 2008. "The performance of heteroskedasticity and autocorrelation robust tests: a Monte Carlo study with an application to the three-factor Fama-French asset-pricing model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 91-109.
  12. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
  13. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
  14. Wouter J. Den Haan & Andrew T. Levin, 1996. "A Practitioner's Guide to Robust Covariance Matrix Estimation," NBER Technical Working Papers 0197, National Bureau of Economic Research, Inc.
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Cited by:
  1. Sun, Yixiao, 2013. "Fixed-smoothing Asymptotics in a Two-step GMM Framework," University of California at San Diego, Economics Working Paper Series qt64x4z265, Department of Economics, UC San Diego.
  2. Preinerstorfer, David & Pötscher, Benedikt M., 2013. "On Size and Power of Heteroscedasticity and Autocorrelation Robust Tests," MPRA Paper 45675, University Library of Munich, Germany.

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