Semiparametric, parametric, and possibly sparse models for multivariate long-range dependence

Several available formulations, parametric models and sparsity settings for multivariate long-range dependence (MLRD) are discussed. Furthermore, a new parametric identifiable model for a general formulation of MLRD is introduced in any dimension, and another sparsity setting is identified of potential interest in MLRD modeling. Estimation approaches for MLRD are also reviewed, including some recent progress and open questions about estimation in higher dimensions and sparse settings.

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