Abstract
If a financial time series is presented backward in time, is it possible to see differences? For example, a simple constant volatility random walk is invariant under time reversal. Because financial data are dominated by randomness, the differences, if they exist, are small. Three estimators are presented which are sensitive to the direction of time. When applied to empirical data, they show unambiguously that financial time series are not invariant. The same tests applied to theoretical processes become a powerful selection criterion. The multiscale ARCH structure is able to reproduce the observed asymmetries, whereas the stochastic volatility processes cannot (regardless of the parameter values).
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Notes
- 1.
An even function is such that f(−r)=f(r), an odd function such that f(−r)=−f(r).
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Zumbach, G. (2013). Time-Reversal Asymmetry. In: Discrete Time Series, Processes, and Applications in Finance. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31742-2_11
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DOI: https://doi.org/10.1007/978-3-642-31742-2_11
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