Abstract
We study on speculative financial bubbles whose characteristic can be modeled by Log Periodic Power Law (LPPL) which is represented by Anders Johansen, Olivier Ledoit and Didier Sornette. The most probable time of the crash is estimated by a parameter in the equation. All parameters used in the equation, are forecasted by optimization through a genetic algorithm. Analysis of a time series by S&P 500 from 1987 shows the signals of the LPPL before the financial crisis of October 1987. In addition to the speculative bubbles, we also present and investigate antibubbles. They, likewise speculative bubbles, also follow log-periodic power law but, of course, with decelerating oscillations and, generally, in a bearish way inclined instead of a bullish way. We also introduce an alternative method which approaches the bubble concept geometrically and benefits from the advantages of optimization and machine learning.
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Acknowledgements
This research has been supported by TUBITAK (The Scientific and Technological Research Council of Turkey) under the grant number 112T744.
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Kürüm, E., Weber, GW., İyigün, C. (2014). Financial Bubbles. In: Pinto, A., Zilberman, D. (eds) Modeling, Dynamics, Optimization and Bioeconomics I. Springer Proceedings in Mathematics & Statistics, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-04849-9_26
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DOI: https://doi.org/10.1007/978-3-319-04849-9_26
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