Improving the bandwidth-free inference methods by prewhitening

• More intuition and motivation for prewhitening are added to aid understanding for practitioners in the second paragraph on page 2.
• Theoretical intuition for prewhitening is also added in the last paragraph of Section 4.
• Examples, for which assumptions K1 and K2 hold, are added right after introducing them on page 4.
• Other minor adjustments were made, such as fixing inconsistent notations or paper mistakes.

In this paper we consider inference of parameters in time series regression models. In the traditional inference approach, the heteroskedasticity and autocorrelation consistent (HAC) estimation is often involved to consistently estimate the asymptotic covariance matrix of regression parameter estimator. Since the bandwidth parameter in the HAC estimation is difficult to choose in practice, there has been a recent surge of interest in developing bandwidth-free inference methods. However, existing simulation studies show that these new methods suffer from severe size distortion in the presence of strong temporal dependence for a medium sample size. To remedy the problem, we propose to apply the prewhitening to the inconsistent long-run variance estimator in these methods to reduce the size distortion. The asymptotic distribution of the prewhitened Wald statistic is obtained and the general effectiveness of prewhitening is shown through simulations.