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Power Maximization and Size Control in Heteroskedasticity and Autocorrelation Robust Tests with Exponentiated Kernels

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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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File URL: http://cowles.econ.yale.edu/P/cd/d17a/d1749.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1749.

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Length: 50 pages
Date of creation: 2010
Date of revision:
Publication status: Published in Econometric Theory (December 2011), 27(6): 1320-1368
Handle: RePEc:cwl:cwldpp:1749

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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Asymptotic expansion; HAC estimation; Long run variance; Loss function; Optimal smoothing parameter; Power kernel; Power maximization; Size control; Type I error; Type II error;

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References

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  1. 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.
  2. Peter M. Robinson & Carlos Velasco, 2000. "Edgeworth expansions for spectral density estimates and studentized sample mean," LSE Research Online Documents on Economics 2148, London School of Economics and Political Science, LSE Library.
  3. 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.
  4. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2006. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Cowles Foundation Discussion Papers 1545, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. Peter C.B. Phillips & Chi-Young Choi & Donggyu Sul, 2004. "Prewhitening Bias in HAC Estimation," Yale School of Management Working Papers ysm426, Yale School of Management.
  7. Jong, R.M. de & Davidson, J., 1996. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Discussion Paper 1996-52, Tilburg University, Center for Economic Research.
  8. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
  9. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
  10. 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.
  11. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  12. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  13. 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.
  14. 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.
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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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