Estimating deterministic trends with an integrated or stationary noise component

Pierre Perron, Tomoyoshi Yabu

Research output: Contribution to journalArticle

59 Citations (Scopus)

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 languageEnglish
Pages (from-to)56-69
Number of pages14
JournalJournal of Econometrics
Volume151
Issue number1
DOIs
Publication statusPublished - 2009 Jul

Fingerprint

Deterministic Trend
Normal distribution
Estimate
Slope
Statistics
Specifications
Standard Normal distribution
Serial Correlation
Generalized Least Squares
Economics
Autoregression
Unit Root
Econometrics
Test function
Least Square Method
Industry
Simulation
Specification
Imply
Unknown

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 journalArticle

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