Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Nonstationary Volatility

In this paper we consider the deterministic trend model where the error process is allowed to be weakly or strongly correlated and subject to nonstationary volatility. Extant estimators of the trend coefficient are analyzed. We find that under heteroskedasticity the Cochrane-Orcutt-type estimator (with some initial condition) could be less efficient than OLS when the process is highly persistent, while it is asymptotically equivalent to OLS when the process is less persistent. An efficient nonparametrically weighted Cochrane-Orcutt-type estimator is then proposed. The efficiency is uniform over weak or strong serial correlation and non-stationary volatility of unknown form. The feasible estimator relies on nonparametric estimation of the volatility function, and the asymptotic theory is provided. We use the data-dependent smoothing bandwidth that can automatically adjust for the strength of nonstationarity in volatilities. The implementation does not require pretesting persistence of the process or specification of nonstationary volatility. Finite-sample evaluation via simulations and an empirical application demonstrates the good performance of proposed estimators