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Estimating deterministic trends with an integrated or stationary noise component

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Author Info
Perron, Pierre
Yabu, Tomoyoshi

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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 [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]<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].

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

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    Other versions:
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Mohitosh Kejriwal & Pierre Perron, 2009. "A Sequential Procedure to Determine the Number of Breaks in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series wp2009-005, Boston University - Department of Economics. [Downloadable!]
    Other versions:
  2. Travaglini, Guido, 2008. "Dynamic GMM Estimation With Structural Breaks. An Application to Global Warming and its Causes," MPRA Paper 7108, University Library of Munich, Germany. [Downloadable!]
  3. Pierre Perron & Tomoyoshi Yabu, 2007. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2007-025, Boston University - Department of Economics. [Downloadable!]
    Other versions:
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