Projected Dynamic Conditional Correlations

Likelihood Geometry of Correlation Models

“…The unrestricted model corresponds to the case when L = S n 0 in (2). The equicorrelation model consists of correlation matrices for which Σ i j = ρ for all i ≠ j.…”

“…The unique correlation matrix that satisfies K i j = W i j for i ≠ j can be found using a simple numerical scheme in R n . We describe this procedure in detail because it provides a computationally efficient alternative to the algorithm developed in [2], which may be of interest for applications.…”

“…More specifically, we focus on the problem of estimating a correlation, that is, a positive definite matrix Σ such that the diagonal entries are 1. This problem appeared in statistics in many different contexts [2,5,7,9,11,12].…”

“…In the first, the data are represented by a symmetric positive semidefinite (PSD) matrix and the goal is to estimate the correlation matrix Σ by finding a suitable projection of the sample covariance matrix S (or other similar matrix) on the space of correlation matrices; see e.g. [2,15]. In the second problem, each entry of Σ can be estimated from a different sample and, in consequence, the data is represented by a symmetric but not necessarily PSD matrix [5].…”

“…However, they also lead to pseudolikelihood estimators for a wide range of non-gaussian scenarios. Minimizing the Stein's loss in the correlation model was recently considered by [2].…”