Estimating deterministic trends with an integrated or stationary noise component

Pierre Perron () and Tomoyoshi Yabu ()

Journal of Econometrics, 2009, vol. 151, issue 1, pages 56-69

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].

Keywords: Linear; trend; Unit; root; Median-unbiased; estimates; GLS; procedure; Super; efficient; estimates (search for similar items in EconPapers)
Date: 2009
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Related works:
Working Paper: Estimating Deterministic Trend with an Integrated or Stationary Noise Component (2007)
Working Paper: Estimating Deterministric Trends with an Integrated or Stationary Noise Component (2005)
Working Paper: Estimating Deterministic Trends with an Integrated or Stationary Noise Component (2006)
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Persistent link: http://EconPapers.repec.org/RePEc:eee:econom:v:151:y:2009:i:1:p:56-69

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