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Prediction of linear fractional stable motions using codifference

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  • Matthieu Garcin
  • Karl Sawaya
  • Thomas Valade

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

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  • Matthieu Garcin & Karl Sawaya & Thomas Valade, 2025. "Prediction of linear fractional stable motions using codifference," Papers 2507.15437, arXiv.org.
    • Handle: RePEc:arx:papers:2507.15437
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    File URL: http://arxiv.org/pdf/2507.15437
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