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Consideration of Trends in Time Series

Author

Listed:
  • White Halbert

    (University of California, San Diego)

  • Granger Clive W.J.

    (University of California, San Diego)

Abstract

Even though the trend components of economic time series were among the first to be distinguished, even today the trend remains relatively little understood. As Phillips (2005) notes, no one understands trends, but everyone sees them in the data. Economists and econometricians can give plenty of examples of trends, such as straight lines, exponentials or polynomials in time, and also forms of random walks, but these are merely examples. Individuals or groups do have their own personal definitions, but these diverse approaches illustrate the lack of a generally accepted definition of a trend. They also suggest a richness of alternatives to consider, both individually and jointly. Here, we make a variety of observations about trends, and based on these, we offer working definitions of various kinds of trends. We emphasize that these are working definitions, as our purpose here is to invite discussion, not to settle matters once and for all. Our hope is that our discussion here may facilitate development of increasingly better methods for prediction, estimation and hypothesis testing for non-stationary time-series data, and ultimately may enable decision makers to make more informed decisions.

Suggested Citation

  • White Halbert & Granger Clive W.J., 2011. "Consideration of Trends in Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-40, February.
  • Handle: RePEc:bpj:jtsmet:v:3:y:2011:i:1:n:2
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    References listed on IDEAS

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    1. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-469, December.
    2. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, pages 401-416.
    3. Hiroshi Yamada, 2005. "Nonlinear co-trending and the Fisher relationship in Japan: a note," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 1(5), pages 285-287, September.
    4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    5. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2006. "Forecasting Time Series Subject to Multiple Structural Breaks," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1057-1084.
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    8. Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
    9. Phillips, Peter C.B. & Magdalinos, Tassos, 2008. "Limit Theory For Explosively Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 24(04), pages 865-887, August.
    10. Hui Liu & Gabriel Rodriguez, 2003. "Human Activities and Global Warming: A Cointegration Analysis," Working Papers 0307E, University of Ottawa, Department of Economics.
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    Citations

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    Cited by:

    1. Gonzalo, Jesús & Gadea Rivas, María Dolores, 2017. "Trends in distributional characteristics : Existence of global warming," UC3M Working papers. Economics 24121, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    3. repec:eee:econom:v:200:y:2017:i:1:p:118-134 is not listed on IDEAS
    4. repec:rdg:wpaper:em-dp2013-03 is not listed on IDEAS
    5. Yonghui Zhang & Liangjun Su & Peter C. B. Phillips, 2012. "Testing for common trends in semi‐parametric panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 56-100, February.
    6. Terence Mills & Kerry Patterson, 2013. "Modelling the Trend: The Historical Origins of Some Modern Methods and Ideas," Economics & Management Discussion Papers em-dp2013-03, Henley Business School, Reading University.
    7. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60 Edward Elgar Publishing.
    8. Wulfrano Gómez & Leovardo Mata & Montserrat Reyna, 2013. "Hodrick-Prescott Filter: An Extreme-Sport Testing," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 7(1), pages 1-13.
    9. repec:eee:eneeco:v:65:y:2017:i:c:p:424-433 is not listed on IDEAS
    10. Yamada, Hiroshi & Yoon, Gawon, 2014. "When Grilli and Yang meet Prebisch and Singer: Piecewise linear trends in primary commodity prices," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 193-207.

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