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Peaks, Gaps, and Time Reversibility of Economic Time Series

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Abstract

Locating the running maxima and minima of a time series, and measuring the current deviation from them, generates processes that are analytically relevant for the analysis of the business cycle and for characterizing bull and bear phases in financial markets. The measurement of the time distance from the running peak originates a first order Markov chain, whose characteristics can be used for testing time reversibility of economic dynamics and specific types of asymmetries in financial markets. The paper derives the time series properties of the gap process and other related processes that arise from the same measurement context, and proposes new nonparametric tests of time reversibility. Empirical examples illustrate their uses for characterizing the depth of a recession and the duration of bull and a bear market.

Suggested Citation

  • Tommaso Proietti, 2020. "Peaks, Gaps, and Time Reversibility of Economic Time Series," CEIS Research Paper 492, Tor Vergata University, CEIS, revised 17 Jun 2020.
    • Handle: RePEc:rtv:ceisrp:492
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    Cited by:

    1. Giancaterini, Francesco & Hecq, Alain, 2025. "Inference in mixed causal and noncausal models with generalized Student’s t-distributions," Econometrics and Statistics, Elsevier, vol. 33(C), pages 1-12.
    2. Tommaso Proietti, 2024. "Ups and (Draw)Downs," CEIS Research Paper 576, Tor Vergata University, CEIS, revised 03 May 2024.
    3. Francesco Giancaterini & Alain Hecq & Claudio Morana, 2022. "Is Climate Change Time-Reversible?," Econometrics, MDPI, vol. 10(4), pages 1-18, December.
    4. Demetrescu, Matei & Kruse-Becher, Robinson, 2025. "Is U.S. real output growth non-normal? A tale of time-varying location and scale," Journal of Economic Dynamics and Control, Elsevier, vol. 171(C).
    5. Gianluca Cubadda & Francesco Giancaterini & Stefano Grassi, 2025. "Sequential Monte Carlo for Noncausal Processes," Papers 2501.03945, arXiv.org.

    More about this item

    Keywords

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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