Time reversal invariance in finance
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Paul Lynch & Gilles Zumbach, 2003. "Market heterogeneities and the causal structure of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 320-331.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Gilles Zumbach & Paul Lynch, 2001. "Heterogeneous volatility cascade in financial markets," Papers cond-mat/0105162, arXiv.org.
- Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006.
"Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets,"
Science & Finance (CFM) working paper archive
500067, Science & Finance, Capital Fund Management.
- Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006. "Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets," Papers physics/0603084, arXiv.org, revised Mar 2007.
- Ramsey, James B & Rothman, Philip, 1996.
"Time Irreversibility and Business Cycle Asymmetry,"
Journal of Money, Credit and Banking,
Blackwell Publishing, vol. 28(1), pages 1-21, February.
- Zumbach, Gilles & Lynch, Paul, 2001. "Heterogeneous volatility cascade in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 521-529.
- Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
- Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:0708.4022. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.