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].
| Original language | English |
|---|---|
| Pages (from-to) | 56-69 |
| Number of pages | 14 |
| Journal | Journal of Econometrics |
| Volume | 151 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2009 Jul |
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Keywords
- GLS procedure
- Linear trend
- Median-unbiased estimates
- Super efficient estimates
- Unit root
ASJC Scopus subject areas
- Economics and Econometrics
- Applied Mathematics
- History and Philosophy of Science
Cite this
Estimating deterministic trends with an integrated or stationary noise component. / Perron, Pierre; Yabu, Tomoyoshi.
In: Journal of Econometrics, Vol. 151, No. 1, 07.2009, p. 56-69.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Estimating deterministic trends with an integrated or stationary noise component
AU - Perron, Pierre
AU - Yabu, Tomoyoshi
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
UR - http://www.scopus.com/inward/record.url?scp=67349132415&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=67349132415&partnerID=8YFLogxK
U2 - 10.1016/j.jeconom.2009.03.011
DO - 10.1016/j.jeconom.2009.03.011
M3 - Article
AN - SCOPUS:67349132415
VL - 151
SP - 56
EP - 69
JO - Journal of Econometrics
JF - Journal of Econometrics
SN - 0304-4076
IS - 1
ER -