Abstract
The statistical regularities observed for most financial time series are known as the “stylized facts”. The most prominent ones are the heteroscedasticity and the fat-tailed distributions. This chapter contains a systematic empirical analysis of the stylized facts for FX time series, often using a multiscale analysis in order to extract at best the deviations from a simple random walk. The analysis includes probability density functions, scaling for the moments, excess kurtosis, lagged correlations, correlations between historical and realized volatilities, and the trend and leverage effects. In particular, the cross-correlation between volatilities at different time horizons gives a characteristic signature of the heteroscedasticity, which emphasizes the (non)invariance with respect to the reversal of the time direction.
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Zumbach, G. (2013). Stylized Facts. In: Discrete Time Series, Processes, and Applications in Finance. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31742-2_3
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