Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T02:32:51.967Z Has data issue: false hasContentIssue false
  • English
  • Français

POWER MAXIMIZATION AND SIZE CONTROL IN HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS WITH EXPONENTIATED KERNELS

Published online by Cambridge University Press:  17 May 2011

Yixiao Sun,
Peter C.B. Phillips and
Sainan Jin
Yixiao Sun*
Affiliation:
University of California, San Diego
Peter C.B. Phillips
Affiliation:
Yale University, University of Auckland, University of Southampton, Singapore Management University
Sainan Jin
Affiliation:
Singapore Management University
*
*Address correspondence to Yixiao Sun, Department of Economics, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0508; e-mail: yisun@ucsd.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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 (ρ). We show that the nonstandard fixed-ρ limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-ρ 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-ρ 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), and yet it does not incur the power loss that often hurts the performance of the latter test. The results complement recent work by Sun, Phillips, and Jin (2008) on conventional and bT HAC testing.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 6 , December 2011, pp. 1320 - 1368
Copyright
Copyright © Cambridge University Press 2011

References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–854.CrossRefGoogle Scholar
Andrews, D.W.K. & Monahan, J.C. (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953–966.CrossRefGoogle Scholar
de Jong, R.M. & Davidson, J. (2000) Consistency of kernel estimators of heteroskedastic and autocorrelated covariance matrices. Econometrica 68, 407–424.CrossRefGoogle Scholar
den Haan, W.J. & Levin, A. (1997) A practitioner’s guide to robust covariance matrix estimation. In Maddala, G. and Rao, C. (eds.), Handbook of Statistics: Robust Inference, vol. 15. Elsevier.Google Scholar
Hansen, B.E. (1992) Consistent covariance matrix estimation for dependent heterogenous processes. Econometrica 60, 967–972.CrossRefGoogle Scholar
Hong, Y. & Lee, J. (2001) Wavelet-Based Estimation for Heteroskedastic and Autocorrelation Consistent Variance-covariance Matrices. Working paper, Cornell University.Google Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 1449–1459.CrossRefGoogle Scholar
Jansson, M. (2004) On the error of rejection probability in simple autocorrelation robust tests. Econometrica 72, 937–946.CrossRefGoogle Scholar
Kiefer, N.M. & Vogelsang, T.J. (2002a) Heteroskedasticity-autocorrelation robust standard errors using the bartlett kernel without truncation. Econometrica 70, 2093–2095.CrossRefGoogle Scholar
Kiefer, N.M. & Vogelsang, T.J. (2002b) Heteroskedasticity-autocorrelation robust testing using bandwidth equal to sample size. Econometric Theory 18, 1350–1366.CrossRefGoogle Scholar
Kiefer, N.M. & Vogelsang, T.J. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 1130–1164.CrossRefGoogle Scholar
Kiefer, N.M., Vogelsang, T.J., & Bunzel, H. (2000) Simple robust testing of regression hypotheses. Econometrica 68, 695–714.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1994) Automatic lag selection in covariance estimation. Review of Economic Studies 61, 631–654.CrossRefGoogle Scholar
Phillips, P.C.B. (1993) Operational algebra and regression t-tests. In Phillips, Peter C.B. (ed.), Models, Methods, and Applications of Econometrics. Basil Blackwell.Google Scholar
Phillips, P.C.B. (2005a) Automated discovery in econometrics. Econometric Theory 21, 3–20.CrossRefGoogle Scholar
Phillips, P.C.B. (2005b) HAC estimation by automated regression. Econometric Theory 21, 116–142.CrossRefGoogle Scholar
Phillips, P.C.B., Sun, Y., & Jin, S. (2006) Spectral density estimation and robust hypothesis testing using steep origin kernels without truncation. International Economic Review 21, 837–894.CrossRefGoogle Scholar
Phillips, P.C.B., Sun, Y., & Jin, S. (2007) Long-run variance estimation and robust regression using sharp origin kernels with no truncation. Journal of Statistical Planning and Inference 137, 985–1023.CrossRefGoogle Scholar
Ray, S. & Savin, N.E. (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 23, 91–109.CrossRefGoogle Scholar
Ray, S., Savin, N.E., & Tiwari, I.A. (2009) Testing the CAPM revisited. Journal of Empirical Finance 16, 721–733.CrossRefGoogle Scholar
Sul, D., Phillips, P.C.B., & Choi, C-Y. (2005) Prewhitening bias in HAC estimation. Oxford Bulletin of Economics and Statistics 67, 517–546.CrossRefGoogle Scholar
Sun, Y. (2004) Estimation of the long-run average relationship in nonstationary panel time series. Econometric Theory 20, 1227–1260CrossRefGoogle Scholar
Sun, Y. (2009) Robust Trend Inference with Series Variance Estimator and Testing-Optimal Smoothing Parameter. Working paper, UC San Diego.CrossRefGoogle Scholar
Sun, Y., Phillips, P.C.B., & Jin, S. (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Econometrica 76, 175–194.CrossRefGoogle Scholar
Velasco, C. & Robinson, P.M. (2001) Edgeworth expansions for spectral density estimates and studentized sample mean. Econometric Theory 17, 497–539.CrossRefGoogle Scholar
Vogelsang, T.J. (2003) Testing in GMM models without truncation. In Fomby, T.B. & Hill, R.C. (eds.), Advances in Econometrics, vol. 17, Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later. pp. 199–233. Elsevier Science.Google Scholar