Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance

Abstract EN

In order to estimate the memory parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR).

Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with other methods.

In this paper we present a rigorous study of the MAVAR log-regression estimator.

In particular, under the assumption that the signal process is a fractional Brownian motion, we prove that it is consistent and asymptotically normally distributed.

Finally, we discuss its connection with the wavelets estimators.