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Estimating deterministic trends with an integrated or stationary noise component

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  • Perron, Pierre
  • Yabu, Tomoyoshi

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 [alpha], the sum of the autoregressive coefficients. The estimate of [alpha] 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]=1 or [alpha]

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 151 (2009)
Issue (Month): 1 (July)
Pages: 56-69

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Handle: RePEc:eee:econom:v:151:y:2009:i:1:p:56-69

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Linear trend Unit root Median-unbiased estimates GLS procedure Super efficient estimates;

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