Do Sentiment and Exchange Rate Share Memories? An Application of Multifractional Process Modeling

We use the notion of local Holder regularity to investigate the roughness of the pattern of EUR/USD exchange rate process as well as the corresponding investor sentiment dynamic process. Specifically, we use the pointwise Holder exponent to measure the local Holder regularity of a multifractional process. This application extends the increment ratio method to estimate the pointwise Holder exponent of multifractional Brownian motion function. Our testing and comparison results show that both the exchange rate and the sentiment proxy's local Holder regularities are time-varying and are more homogeneous during crises periods. More importantly, in contrast to the optimistic sentiment, the roughness of the pessimistic sentiment dynamic process displays only slightly higher similarity to that of EUR/USD exchange rate. These results suggest that the EUR/USD exchange rate process and the pessimistic sentiment dynamic process share a common pattern of smoothness, which implies that they share a similar "memory" pattern