Higher-order approximations for frequency domain time series regression

Second-order expansions and mean squared error approximations are given for efficient frequency domain regression estimators. While bandwidth choices do not figure in first order asymptotics for these estimators, they do influence second-order terms and it is shown how suitable choices will enhance second-order efficiency. Data-based bandwidth selection rules are given for practical implementation of these procedures. Two commonly used and asymptotically equivalent spectral regression estimators are studied and shown to differ in their second-order asymptotic behavior. Some Monte Carlo evidence is reported.