Estimating deterministic trends with an integrated or stationary noise component

Pierre Perron, Tomoyoshi Yabu

Research output: Contribution to journalArticlepeer-review

84 Citations (Scopus)


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 languageEnglish
Pages (from-to)56-69
Number of pages14
JournalJournal of Econometrics
Issue number1
Publication statusPublished - 2009 Jul


  • GLS procedure
  • Linear trend
  • Median-unbiased estimates
  • Super efficient estimates
  • Unit root

ASJC Scopus subject areas

  • Economics and Econometrics


Dive into the research topics of 'Estimating deterministic trends with an integrated or stationary noise component'. Together they form a unique fingerprint.

Cite this