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

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  • Pierre Perron
  • Mototsugu Shintani
  • Tomoyoshi Yabu

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.
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  • 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.
    • Handle: RePEc:bla:obuest:v:79:y:2017:i:5:p:822-850
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    File URL: http://hdl.handle.net/10.1111/obes.12169
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    16. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
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    Cited by:

    1. Claudio, Morana & Giacomo, Sbrana, 2017. "Temperature anomalies, radiative forcing and ENSO," Working Papers 361, University of Milano-Bicocca, Department of Economics, revised 10 Feb 2017.
    2. Jamal G. HUSEIN & S. Murat KARA, 2023. "Are Shocks To Electricity Consumption Permanent Or Transitory? Evidence From A Panel Stationarity Test With Gradual Structural Breaks For 25 Oecd Countries," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 23(1), pages 57-76.
    3. Claudio, Morana & Giacomo, Sbrana, 2017. "Some Financial Implications of Global Warming: An Empirical Assessment," Working Papers 377, University of Milano-Bicocca, Department of Economics, revised 25 Dec 2017.
    4. Yeonwoo Rho & Yun Liu & Hie Joo Ahn, 2020. "Revealing Cluster Structures Based on Mixed Sampling Frequencies," Papers 2004.09770, arXiv.org, revised Feb 2021.
    5. 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.
    6. Atanu Ghoshray & Madhavi Pundit, 2021. "Economic growth in China and its impact on international commodity prices," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2776-2789, April.
    7. Razvan Pascalau & Junsoo Lee & Saban Nazlioglu & Yan (Olivia) Lu, 2022. "Johansen‐type cointegration tests with a Fourier function," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 828-852, September.
    8. Erhua Zhang & Xiaojun Song & Jilin Wu, 2022. "A non‐parametric test for multi‐variate trend functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 856-871, November.
    9. Husein, Jamal, 2020. "Current account sustainability for 21 African economies: Evidence based on nonlinear flexible Fourier stationarity and unit-root tests," MPRA Paper 100410, University Library of Munich, Germany.
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    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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