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Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity
Journal of Statistical Computation and Simulation (2011)
  • Douglas G Steigerwald, University of California, Santa Barbara
  • Jack Erb
We study the finite-sample performance of test statistics in linear regression models where the error dependence is of unknown form. With an unknown dependence structure there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the amount of heterogeneity in the process. When allowing for heterogeneity, through conditional heteroskedasticity, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags we study test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. To improve the accuracy of the test statistics, we employ the second-order asymptotic refinement in Rothenberg (1988) to determine critical values. The simulation results of this paper suggest that when sample sizes are small, modeling the heterogeneity of a process is secondary to accounting for dependence. We find that a conditionally homoskedastic covariance matrix estimator (when used in conjunction with Rothenberg's second-order critical value adjustment) improves test size with only a minimal loss in test power, even when the data manifest significant amounts of heteroskedasticity. In some specifications, the size inflation was cut by nearly 40% over the traditional HAC test. Finally, we note that the proposed test statistics do not require that the researcher specify the bandwidth or the kernel.
  • autocorrelation,
  • confidence interval,
  • heteroskedasticity,
  • robust test,
  • test size
Publication Date
Citation Information
Douglas G Steigerwald and Jack Erb. "Accurately Sized Test Statistics with Misspecified Conditional Homoskedasticity" Journal of Statistical Computation and Simulation Vol. 3 Iss. 4 (2011)
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