Semi-Parametric Copula-Based Models Under Non-Stationarity

38 Pages Posted: 17 Oct 2018

See all articles by Bouchra R. Nasri

Bouchra R. Nasri

Department of Mathematics and Statistics, McGill University

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Taoufik Bouezmarni

HEC Montreal

Date Written: September 26, 2018

Abstract

In this paper, we consider non-stationary response variables and covariates, where the marginal distributions and the associated copula may be time-dependent. We propose estimators for the unknown parameters and we establish the limiting distribution of the estimators of the copula and the conditional copula, together with a parametric bootstrap method for constructing confidence bands around the estimator and for testing the adequacy of the model.

We also consider three examples of functionals of the copula-based model under non-stationarity: conditional quantiles, conditional mean, and conditional expected shortfall. The asymptotic distribution of the estimation errors is shown to be Gaussian, and bootstrapping methods are proposed to estimate their asymptotic variances.

The finite sample performance of our estimators is investigated through Monte Carlo experiments, and we show three examples of implementation of the proposed methodology.

Keywords: copula; covariates; non-stationarity; conditional distribution

Suggested Citation

Nasri, Bouchra R. and Remillard, Bruno and Bouezmarni, Taoufik, Semi-Parametric Copula-Based Models Under Non-Stationarity (September 26, 2018). Available at SSRN: https://ssrn.com/abstract=3255918 or http://dx.doi.org/10.2139/ssrn.3255918

Bouchra R. Nasri (Contact Author)

Department of Mathematics and Statistics, McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

Bruno Remillard

Department of Decision Sciences, HEC Montreal ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada
514-340-6794 (Phone)

Taoufik Bouezmarni

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada

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