Prediction of linear fractional stable motions using codifference

Matthieu Garcin, Karl Sawaya and Thomas Valade

Papers from arXiv.org

Abstract: The linear fractional stable motion (LFSM) extends the fractional Brownian motion (fBm) by considering $\alpha$-stable increments. We propose a method to forecast future increments of the LFSM from past discrete-time observations, using the conditional expectation when $\alpha>1$ or a semimetric projection otherwise. It relies on the codifference, which describes the serial dependence of the process, instead of the covariance. Indeed, covariance is commonly used for predicting an fBm but it is infinite when $\alpha

Date: 2025-07
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