Measuring non-linearity, long memory and self-similarity in high-frequency European exchange rates

This paper combines analysis of deterministic non-linear dynamics and stochastic models of long memory volatility processes. Measures of non-linear dependency, due to Savit and Green, and originally used in the physical sciences, are applied to high-frequency foreign exchange rate returns. The analysis is applied before and after long memory characteristics are removed from the volatility process of returns, with the standard errors of the procedure being bootstrapped. The study finds that high-frequency currency returns volatility is well represented by a FIGARCH model. The estimates of the long memory parameter are remarkably consistent across time aggregations and currencies and are suggestive of self-similarity. While there is some evidence of a small remaining amount of non-linear temporal dependence; it is found to be too weak to be exploitable for forecasting purposes.