Composite pseudo-likelihood estimation for pair-tractable copulas such as Archimedean, Archimax and related hierarchical extensions

Abstract

The pairwise pseudo-likelihood estimator (PPLE) is introduced for estimating the parameters of pair-tractable copulas, so copulas with analytically or numerically tractable pairwise margins, such as Archimedean, hierarchical Archimedean, Archimax and hierarchical Archimax copulas. In cases where feasible, the PPLE is compared, by simulation, to the standard maximum pseudo-likelihood estimator (MPLE) in terms of bias, root mean squared error (RMSE) and run time. The PPLE is also compared to the aggregated MPLE (AMPLE) for hierarchical Archimedean copulas. The simulation results indicate that the PPLE has a bias and RMSE comparable to the MPLE for those Archimedean copulas where the latter is available. For hierarchical Archimedean and hierarchical Archimax copulas for which the MPLE is not easily available, the PPLE mostly outperforms the AMPLE in bias and RMSE, with a clear advantage in terms of run time.

KEYWORDS:

• Maximum pseudo-likelihood estimator
• aggregated maximum pseudo-likelihood estimator
• bivariate margins
• probability density function
• Archimedean and Archimax copulas
• hierarchical copulas

MSC CLASSIFICATIONS:

• 62H12
• 62F10
• 62H99
• 65C60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author thanks the Czech Science Foundation (GAČR) for financial support for this work through grant [21-03085S].