Time Reversal Invariance in Finance

23 Pages Posted: 10 Aug 2007

See all articles by Gilles O. Zumbach

Gilles O. Zumbach

Edgelab; Consulting in Financial Engineering

Date Written: January 2007


Time reversal invariance can be sumarised 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-time scales 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.

Keywords: Time reversal symmetry, ARCH processes, stochastic volatility processes

JEL Classification: C10, C22, C15, C51, C52

Suggested Citation

Zumbach, Gilles, Time Reversal Invariance in Finance (January 2007). Available at SSRN: https://ssrn.com/abstract=1004992 or http://dx.doi.org/10.2139/ssrn.1004992

Gilles Zumbach (Contact Author)

Edgelab ( email )

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Lausanne, 1006
+41764351267 (Phone)

Consulting in Financial Engineering ( email )

Ch. Charles Baudouin 8
Saconnex d'Arve, 1228
+41 76 4351267 (Phone)

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