Parameter estimation for pair-copula constructions

TL;DR

This paper evaluates various estimators for pair-copula constructions, highlighting the stepwise semiparametric estimator's efficiency, computational advantages, and suitability for high-dimensional data and model selection.

Contribution

It introduces the asymptotic properties and estimation algorithm for SSP, demonstrating its practical benefits over traditional methods in high-dimensional settings.

Findings

SSP is generally less efficient than maximum likelihood but with low efficiency loss.

SSP is semiparametrically efficient for Gaussian copulas.

SSP is computationally feasible in high dimensions and useful for model selection.

Abstract

We explore various estimators for the parameters of a pair-copula construction (PCC), among those the stepwise semiparametric (SSP) estimator, designed for this dependence structure. We present its asymptotic properties, as well as the estimation algorithm for the two most common types of PCCs. Compared to the considered alternatives, that is, maximum likelihood, inference functions for margins and semiparametric estimation, SSP is in general asymptotically less efficient. As we show in a few examples, this loss of efficiency may however be rather low. Furthermore, SSP is semiparametrically efficient for the Gaussian copula. More importantly, it is computationally tractable even in high dimensions, as opposed to its competitors. In any case, SSP may provide start values, required by the other estimators. It is also well suited for selecting the pair-copulae of a PCC for a given data set.