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Estimating Deterministic Trends with an Integrated or Stationary Noise Component

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  • Pierre Perron

    ()
    (Department of Economics, Boston University)

  • Tomoyoshi Yabu

    (Department of Economics, Boston University)

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

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2006-012.

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Length: 39 pages
Date of creation:
Date of revision: Feb 2006
Handle: RePEc:bos:wpaper:wp2006-012

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Keywords: linear trend; unit root; median-unbiased estimates; GLS procedure; super efficient estimates;

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References

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