Title: Wavelet eigenvalue regression for $n$-variate operator fractional Brownian motion,
Abstract: In this contribution, we extend the methodology proposed in Abry and Didier
(2017) to obtain the first joint estimator of the real parts of the Hurst
eigenvalues of $n$-variate OFBM. The procedure consists of a wavelet regression
on the log-eigenvalues of the sample wavelet spectrum. The estimator is shown
to be consistent for any time reversible OFBM and, under stronger assumptions,
also asymptotically normal starting from either continuous or discrete time
measurements. Simulation studies establish the finite sample effectiveness of
the methodology and illustrate its benefits compared to univariate-like
(entrywise) analysis. As an application, we revisit the well-known self-similar
character of Internet traffic by applying the proposed methodology to 4-variate
time series of modern, high quality Internet traffic data. The analysis reveals
the presence of a rich multivariate self-similarity structure.