Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices

A new class of HAC covariance matrix estimators is proposed based on the notion of a flat-top kernel as in Politis and Romano (1995)and Politis (2001). The new estimators are shown to be higher-order accurate when higher-order accuracy is possible, and a discussion on kernel choice is given. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semi-definite property. Nevertheless, we show how a modified flat-top estimator is positive semi-definite while maintaining its higher-order accuracy. In addition, an automatic and consistent procedure for optimal bandwidth choice for flat-top kernel HAC estimators is given. The general problem of spectral matrix estimation is also treated.