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Rational bubbles: Too many to be true?

Author

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  • Caravello, Tomas E.
  • Psaradakis, Zacharias
  • Sola, Martin
Abstract
Issues that arise in the practical implementation of the Phillips et al. (2011) and Phillips et al. (2015a) recursive procedures for identifying and dating explosive episodes in time series are considered. It is argued that the use of critical values for right-tailed unit-root tests obtained under the assumption of a drift whose magnitude depends on the sample size and becomes negligible in large samples results in over-rejection of the unit-root hypothesis when, as in many financial time series, the deterministic drift effect is non-negligible relatively to the stochastic trend. In addition, the standard practice of using conventional levels of significance for critical values involved in the algorithms that locate the origination and termination dates of explosive episodes lead to false discoveries of explosiveness with high probability. The magnitude of these difficulties is quantified via simulations using artificial data whose properties reflect closely those of real-world time series such as stock prices and dividends. The findings offer a potential explanation for the relatively large number of apparent explosive episodes that are often reported in applied work. Ways of overcoming the aforementioned difficulties by using bootstrap-based calibration techniques are considered. An empirical example focusing on monthly U.S. data on real stock prices and real dividends is also discussed.

Suggested Citation

  • Caravello, Tomas E. & Psaradakis, Zacharias & Sola, Martin, 2023. "Rational bubbles: Too many to be true?," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:dyncon:v:151:y:2023:i:c:s0165188923000726
    DOI: 10.1016/j.jedc.2023.104666
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    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(4), pages 1043-1078, November.
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    16. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1043-1078, November.
    17. Bouri, Elie & Shahzad, Syed Jawad Hussain & Roubaud, David, 2019. "Co-explosivity in the cryptocurrency market," Finance Research Letters, Elsevier, vol. 29(C), pages 178-183.
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    2. Nicolas Cofre & Magdalena Mosionek-Schweda, 2023. "A simulated electronic market with speculative behaviour and bubble formation," Papers 2311.12247, arXiv.org.

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    More about this item

    Keywords

    Bootstrap; Bubbles; Date-stamping; Explosive behavior; Unit-root test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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