Multi-Fractional Brownian Motion: Estimating the Hurst Exponent via Variational Smoothing with Applications in Finance

Beginning with the basics of Wiener process, we consider limitations characterizing “Brownian approach” in analyzing real phenomena. This leads us to first fractional Brownian motion (fBm)—also discussing Wood–Chan fast algorithm generate sample paths—to then focus on multi-fBm and methods its trajectories. is heavily linked Hurst exponent study, which link data, firstly considering an absolute moment method, allowing obtain raw estimates, variational calculus approaches smooth it. The latter smoothing tool was tested accuracy synthetic comparing it exponential moving average method. Previous analyses results were exploited develop a forecasting procedure applied data foreign exchange rates from Forex market.