Mean-Structure and Autocorrelation Consistent Covariance Matrix Estimation

We consider estimation of the asymptotic covariance matrix in nonstationary time series. A nonparametric estimator that is robust against unknown forms of trends and possibly a divergent number of change points (CPs) is proposed. It is algorithmically fast because neither a search for CPs, estimation of trends, nor cross-validation is required. Together with our proposed automatic optimal bandwidth selector, the resulting estimator is both statistically and computationally efficient. It is, therefore, useful in many statistical procedures, for example, CPs detection and construction of simultaneous confidence bands of trends. Empirical studies on four stock market indices are also discussed.