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Mathematics > Statistics Theory

arXiv:2012.09436 (math)
[Submitted on 17 Dec 2020 (v1), last revised 6 Apr 2022 (this version, v2)]

Title:Asymptotic normality of wavelet covariances and of multivariate wavelet Whittle estimators

Authors:Irène Gannaz (PSPM, ICJ)
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Abstract:Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time series. We consider multivariate long-range dependent linear processes, not necessarily Gaussian. 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-range dependence parameter and the long-run covariance by a wavelet-based Whittle procedure. We prove the asymptotic normality of the estimators, and we provide an explicit expression for the asymptotic covariances. An empirical illustration of this result is proposed on a real dataset of rat brain connectivity.
Subjects: Statistics Theory (math.ST)
Cite as: arXiv:2012.09436 [math.ST]
  (or arXiv:2012.09436v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2012.09436

Submission history

From: Irene Gannaz [view email] [via CCSD proxy]
[v1] Thu, 17 Dec 2020 08:12:47 UTC (34 KB)
[v2] Wed, 6 Apr 2022 06:40:19 UTC (62 KB)
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