A Fractional Process with Jumps for Modeling Karstic Spring Discharge Data

Fractal dimensions for the daily discharge data series of several karstic springs in northeast Hungary have recently been computed and analyzed. We model four of those series with similar fractal dimensions using a superposition of a fractional Ornstein–Uhlenbeck process and a jump process of renewal–reward type. Beyond some usual goodness-of-fit measures, simulations of the model show an visually appealing good fit. When the fractal dimension is not taken into account in the modeling, the simulated accumulated discharges tend to significantly exceed realistic values.