Etude expérimentale de l'influence d'un échantillonnage irrégulier dans l'estimation du paramètre de Hurst
Résumé
In this article, we propose to study an estimator of the Hurst parameter for irregularly sampled Fractional Brownian trajectories. Trajectories are simulated by means of Cholesky algorithm, and the Hurst parameter is estimated by maximising likelihood. Both techniques are time consuming, but prove to be well suited to this type of data. We present various tables containing the estimates of the self-similarity measure, according to several sampling procedures with several sizes of trajectories. The study of these tables is based on a series of statistical tests (Student, Fisher), making it possible to compare and analyse the differences between the sampling processes on hand. The more erratic the sampling, the greater the discrepancy between the results and those expected for a regular sampling. This discrepancy tends to decrease when the size of the signals increases. Results from random samplings are closer to those from a regular deterministic sampling when the random sampling model is uniform.
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