Co-movement, fractal behaviour and forecasting of exchange rates

In this paper we analyse the fractal behaviour and correlations of exchange rates and develop a new approach to obtain better forecast results with small errors. Multifractal de-trended fluctuation analysis (MFDFA) is used to get fractal time series and their Hurst Exponents in specific time period and based on these results. We established Vector Autoregressive Fractionally Integrated Moving Average (VARFIMA) models of exchange rates on certain dates. Hurst Exponents allows us to detect small fluctuations (persistent characteristic) of time series and their multifractal behaviour. We consider, USD/CAD, USD/GBP, USD/EUR and USD/CHF exchange rates prices are as time series. Our theory is to show that if a time series has the highest multifractal degree then it has the most succesfull prediction results for the time interval which four time series have highest co-movement. We use Wavelet coherence analysis to understand co-movement of the exchange rates. The findings of Wavelet Coherence showed correlation between these exchange rates, the relationships among the two and four rates (with multiple wavelet coherence-MWC) and how these connections differ in the space of frequency-time. These relations and MFDFA results authorize us to construct VARFIMA models of exchange rate data which produce effective forecast outcomes with small errors.