Robust M tests using kernel-based estimators with bandwidth equal to sample size

Following Kiefer and Vogelsang [Kiefer, N.M. and Vogelsang, T.J., 2002b. Heteroskedasticity-autocorrelation robust testing using bandwidth equal to sample size. Econometric Theory 18 1350-1366], we propose two classes of robust M tests that extend those of Kuan and Lee [Kuan, C.-M. and Lee, W.-M., 2006. Robust M tests without consistent estimation of the asymptotic covariance matrix. Journal of the American Statistical Association 101 1264-1275] and apply them to testing serial correlations. It is found that, with a properly selected kernel function, the power improvement of the proposed tests over the existing robust tests is substantial.