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Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component

Pierre Perron, Mototsugu Shintani and Tomoyoshi Yabu

No wp2015-018, Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics

Abstract: This paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on the work of Perron and Yabu (2009a) and is based on a Feasible Generalized Least Squares procedure that uses a superefficient estimator of the sum of the autoregressive coe¢ cients when = 1. The resulting Wald test statistic asymptotically follows chi-square distribution in both the I(0) and I(1) cases. To improve the finite sample properties of the test, we use a bias corrected version of the OLS estimator of proposed by Roy and Fuller (2001). We show that our procedure is substantially more powerful than currently available alternatives. We illustrate the usefulness of our method via an application to modeling the trend of global and hemispheric temperatures.

Keywords: Fourier approximation; median-unbiased estimator; nonlinear trends; super-efficient estimator; unit root (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Date: 2015-01, Revised 2015-11
New Economics Papers: this item is included in nep-ets and nep-ore
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Related works:
Journal Article: Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component (2017) Downloads
Working Paper: Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component (2015) Downloads
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