Estimating deterministic trends with an integrated or stationary noise component |
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Authors: | Pierre Perron Tomoyoshi Yabu |
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Affiliation: | 1. Department of Economics, Boston University, 270 Bay State Road, Boston, MA, 02215, United States;2. Faculty of Business and Commerce, Keio University, Tokyo, 108-8345, Japan |
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Abstract: | 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 α, the sum of the autoregressive coefficients. The estimate of α 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−δ neighborhood of 1. This makes the estimate “super-efficient” when α=1 and implies that inference on the slope parameter can be performed using the standard Normal distribution whether α=1 or |α|<1. Theoretical arguments and simulation evidence show that δ=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]. |
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Keywords: | C22 |
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