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

27 Pages Posted: 5 Mar 2014

See all articles by Ke-Li Xu

Ke-Li Xu

Indiana University Bloomington

Jui-Chung Yang

Texas A&M University

Date Written: February 23, 2014

Abstract

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.

Keywords: Cochrane-Orcutt estimator; Deterministic trend; Efficiency gain; Nearly-integrated process; Nonstationary volatility; Semiparametric model

JEL Classification: C22

Suggested Citation

Xu, Ke-Li and Yang, Jui-Chung, Towards Uniformly Efficient Trend Estimation Under Weak/Strong Correlation and Nonstationary Volatility (February 23, 2014). Available at SSRN: https://ssrn.com/abstract=2403314 or http://dx.doi.org/10.2139/ssrn.2403314

Ke-Li Xu (Contact Author)

Indiana University Bloomington ( email )

100 S. Woodlawn Ave.
Department of Economics, Wylie Hall
Bloomington, IN 47405-7104
United States

HOME PAGE: http://sites.google.com/view/kelixu

Jui-Chung Yang

Texas A&M University ( email )

Langford Building A
798 Ross St.
College Station, TX 77843-3137
United States

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