What does fractional Brownian motion include that standard Brownian motion does not?

Fractional Brownian motion is a generalization of standard Brownian motion that introduces the concept of long-range dependence, which standard Brownian motion does not exhibit. In fractional Brownian motion, the paths can have varying degrees of roughness, characterized by the Hurst parameter. This allows for modeling phenomena that display persistent trends or mean-reverting behavior over time, unlike standard Brownian motion, which has independent increments and does not account for long-range dependence.

In addition to paths having varying degrees of smoothness, fractional Brownian motion can capture the intricate structures seen in financial time series, making it more suitable for applications in financial modeling where such dependencies and roughness characteristics are significant. In contrast, the other options do not pertain to the unique features of fractional Brownian motion. For instance, standard methods for predicting stock prices, aspects of volatility, or the influence of economic shocks do not distinguish fractional Brownian motion from standard Brownian motion in the same fundamental way.