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We analyze the generalized $k$-variations for the solution to the waveequation driven by an additive Gaussian noise which behaves as a fractionalBrownian with Hurst parameter $H>\frac{1}{2}$ in time and which is white inspace. The $k$-variations are defined along {\it filters} of any order $p\geq1$ and of any length. We show that the sequence of generalized $k$-variationsatisfies a Central Limit Theorem when $p> H+\frac{1}{4}$ and we estimate therate of convergence for it via the Stein-Malliavin calculus. The results areapplied to the estimation of the Hurst index. We construct several consistentestimators for $H$ and these estimators are analyzed theoretically andnumerically.

Generalized $k$-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus