Estimating deterministic trends with an integrated or stationary noise component

We propose a test for the slope of a trend function when it is a priori unknown whether the series is trend-stationary or contains an autoregressive unit root. The procedure is based on a Feasible Quasi Generalized Least Squares method from an AR(1) specification with parameter alpha, the sum of the autoregressive coefficients. The estimate of a is the OLS estimate obtained from an autoregression applied to detrended data and is truncated to take a value 1 whenever the estimate is in a T(-delta) neighborhood of 1. This makes the estimate "super-efficient" when alpha = 1 and implies that inference on the slope parameter can be performed using the standard Normal distribution whether alpha = I or vertical bar alpha vertical bar < 1. Theoretical arguments and simulation evidence show that delta = 1/2 is the appropriate choice. Simulations show that our procedure has better size and power properties than the tests proposed by [Bunzel, H., Vogelsang, T.J., 2005. Powerful trend function tests that are robust to strong serial correlation with an application to the Prebish-Singer hypothesis. journal of Business and Economic Statistics 23, 381-394] and [Harvey. D.I., Leybourne, S.J., Taylor, A.M.R., 2007. A simple, robust and powerful test of the trend hypothesis. Journal of Econometrics 141,1302-1330]. (c) 2009 Elsevier B.V. All rights reserved.