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Stochastic modelling of non-stationary financial assets

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  • Joana Estevens
  • Paulo Rocha
  • Joao Boto
  • Pedro Lind

Abstract

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of values. Having the evolution equations of the log-normal parameters, we reconstruct the statistics of the first moments of volume-price distributions which fit well the empirical data. Finally, the proposed framework is general enough to study other non-stationary stochastic variables in other research fields, namely biology, medicine and geology.

Suggested Citation

  • Joana Estevens & Paulo Rocha & Joao Boto & Pedro Lind, 2017. "Stochastic modelling of non-stationary financial assets," Papers 1705.01145, arXiv.org.
  • Handle: RePEc:arx:papers:1705.01145
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    File URL: http://arxiv.org/pdf/1705.01145
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    Cited by:

    1. So-Kumneth Sim & Philipp Maass & Pedro G. Lind, 2018. "Wind Speed Modeling by Nested ARIMA Processes," Energies, MDPI, vol. 12(1), pages 1-18, December.

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