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On a Definition of Trend

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  • Silva Lopes, Artur

Abstract

Several reasons explain the absence of a precise, complete and widely accepted definition of trend for economic time series, and the existence of two major disparate models is one of the most important. A recent operational proposal tried to overcome this difficulty resorting to a statistical test with good asymptotic properties against both those alternatives. However, this proposal may be criticized because it rests on a tool for inductive, not deductive, inference. Besides criticizing this recent definition, drawing heavily on previous ones, the paper provides a new proposal, more complete, containing several necessary but no sufficient condition(s).

Suggested Citation

  • Silva Lopes, Artur, 2025. "On a Definition of Trend," MPRA Paper 125073, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:125073
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    File URL: https://mpra.ub.uni-muenchen.de/125073/1/MPRA_paper_125073.pdf
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    References listed on IDEAS

    as
    1. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    2. Gadea Rivas, María Dolores & Gonzalo, Jesús, 2020. "Trends in distributional characteristics: Existence of global warming," Journal of Econometrics, Elsevier, vol. 214(1), pages 153-174.
    3. Peter C. B. Phillips, 2010. "The Mysteries of Trend," Cowles Foundation Discussion Papers 1771, Cowles Foundation for Research in Economics, Yale University.
    4. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    5. James D. Hamilton, 2018. "Why You Should Never Use the Hodrick-Prescott Filter," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 831-843, December.
    6. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    7. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
    8. Seater, John J, 1993. "World Temperature-Trend Uncertainties and Their Implications for Economic Policy," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 265-277, July.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • 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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