Asymptotic normality of wavelet covariances and of multivariate wavelet Whittle estimators

Irène Gannaz (1, 2)

1 PSPM - Probabilités, statistique, physique mathématique
2 ICJ - Institut Camille Jordan

Multivariate processes with long-range memory properties can be encountered in many applications fields. Two fundamentals characteristics in such frameworks are the long-memory parameters and the correlation between time series. We consider multivariate linear processes, not necessarily Gaussian, presenting long-memory dependence. We show that the covariances between the wavelet coefficients in this setting are asymptotically Gaussian. We also study the asymptotic distributions of the estimators of the long-memory parameter and of the long-run covariance by a wavelet-based Whittle procedure. We prove the asymptotic normality of the estimators and we give an explicit expression for the asymptotic covariances. An empirical illustration of this result is proposed on a real dataset of a rat brain connectivity.

Mots clés: Multivariate processes; long-range memory; covariance; wavelets; asymptotic normality; cerebral connectivity; Multivariate processes

Domaines: Statistiques [math.ST]

Irène Gannaz. Asymptotic normality of wavelet covariances and of multivariate wavelet Whittle estimators. 2020. ⟨hal-03068460v1⟩