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Time reversal invariance in finance

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  • Gilles Zumbach

Abstract

Time reversal invariance can be summarized as follows: no difference can be measured if a sequence of events is run forward or backward in time. Because price time series are dominated by a randomness that hides possible structures and orders, the existence of time reversal invariance requires care to be investigated. Different statistics are constructed with the property to be zero for time series which are time reversal invariant; they all show that high-frequency empirical foreign exchange prices are not invariant. The same statistics are applied to mathematical processes that should mimic empirical prices. Monte Carlo simulations show that only some ARCH processes with a multi-timescales structure can reproduce the empirical findings. A GARCH(1,1) process can only reproduce some asymmetry. On the other hand, all the stochastic volatility type processes are time reversal invariant. This clear difference related to the process structures gives some strong selection criterion for processes.

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  • Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.
    • Handle: RePEc:arx:papers:0708.4022
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    References listed on IDEAS

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    Cited by:

    1. Vitor H. Carvalho & Raquel M. Gaspar, 2021. "Relativistically into Finance," Working Papers REM 2021/0175, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    2. Rubina Zadourian, 2024. "Model-based and empirical analyses of stochastic fluctuations in economy and finance," Papers 2408.16010, arXiv.org.
    3. Vitor H. Carvalho & Raquel M. Gaspar, 2021. "Relativistic Option Pricing," IJFS, MDPI, vol. 9(2), pages 1-24, June.

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