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Testing for Trend in the Presence of Autoregressive Error: A Comment

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  • Pierre Perron
  • Tomoyoshi Yabu

Abstract

Roy, Falk and Fuller (2004) presented a procedure aimed at providing a test for the value of the slope of a trend function that has (nearly) controlled size in autoregressive models whether the noise component is stationary or has a unit root. In this note, we document errors in both their theoretical results and the simulations they reported. Once these are corrected for, their procedure delivers a test that has very liberal size in the case with a unit root so that the stated goal is not achieved. Interestingly, the mistakes in the code used to generate the simulated results (which is the basis for the evidence about the reliability of the method) are such that what they report is essentially equivalent to the size and power of the test proposed by Perron and Yabu (2009), which was shown to have the standard Normal distribution whether the noise is stationary or has a unit root.
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  • Pierre Perron & Tomoyoshi Yabu, 2012. "Testing for Trend in the Presence of Autoregressive Error: A Comment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 844-844, June.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:844-844
    DOI: 10.1080/01621459.2012.668638
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    1. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    2. Anindya Roy & Barry Falk & Wayne A. Fuller, 2004. "Testing for Trend in the Presence of Autoregressive Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1082-1091, December.
    3. Roy, Anindya & Fuller, Wayne A, 2001. "Estimation for Autoregressive Time Series with a Root Near 1," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 482-493, October.
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    1. Josep Lluís Carrion‐i‐Silvestre & María Dolores Gadea & Antonio Montañés, 2021. "Nearly Unbiased Estimation of Autoregressive Models for Bounded Near‐Integrated Stochastic Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(1), pages 273-297, February.
    2. Pierre Perron & Mototsugu Shintaniz & Tomoyoshi Yabu, 2020. "Trigonometric Trend Regressions of Unknown Frequencies with Stationary or Integrated Noise," Boston University - Department of Economics - Working Papers Series WP2020-012, Boston University - Department of Economics.
    3. Pierre Perron & Mototsugu Shintani & Tomoyoshi Yabu, 2017. "Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(5), pages 822-850, October.
    4. Jiawen Xu & Pierre Perron, 2013. "Robust testing of time trend and mean with unknown integration order errors Frequency (and Other) Contaminations," Boston University - Department of Economics - Working Papers Series 2013-006, Boston University - Department of Economics.

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