TY - JOUR
T1 - Estimating deterministic trends with an integrated or stationary noise component
AU - Perron, Pierre
AU - Yabu, Tomoyoshi
N1 - Funding Information:
Pierre Perron acknowledges financial support from the National Science Foundation under Grant SES-0078492. We also wish to thank Eiji Kurozumi, Adam McCloskey and two referees for comments.
PY - 2009/7
Y1 - 2009/7
N2 - 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].
AB - 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].
KW - GLS procedure
KW - Linear trend
KW - Median-unbiased estimates
KW - Super efficient estimates
KW - Unit root
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U2 - 10.1016/j.jeconom.2009.03.011
DO - 10.1016/j.jeconom.2009.03.011
M3 - Article
AN - SCOPUS:67349132415
SN - 0304-4076
VL - 151
SP - 56
EP - 69
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 1
ER -