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Peaks, gaps, and time‐reversibility of economic time series

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  • Tommaso Proietti

Abstract

By locating the running maxima and minima of a time series, and measuring the current deviation from them, it is possible to generate processes that are relevant for the analysis of the business cycle and for characterizing bull and bear phases in financial markets. First, 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. Second, the gap processes can be combined to provide a non‐parametric measure of the growth cycle. The article derives the time series properties of the gap process and other related processes that arise from the same measurement context, and proposes new non‐parametric tests of time‐reversibility and new measures of the output gap.

Suggested Citation

  • Tommaso Proietti, 2023. "Peaks, gaps, and time‐reversibility of economic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 43-68, January.
    • Handle: RePEc:bla:jtsera:v:44:y:2023:i:1:p:43-68
    DOI: 10.1111/jtsa.12649
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    1. Francesco Giancaterini & Alain Hecq & Claudio Morana, 2022. "Is Climate Change Time-Reversible?," Econometrics, MDPI, vol. 10(4), pages 1-18, December.
    2. 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).
    3. 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.
    4. Gianluca Cubadda & Francesco Giancaterini & Stefano Grassi, 2025. "Sequential Monte Carlo for Noncausal Processes," Papers 2501.03945, arXiv.org.
    5. Tommaso Proietti, 2024. "Ups and (Draw)Downs," CEIS Research Paper 576, Tor Vergata University, CEIS, revised 03 May 2024.

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    More about this item

    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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