# A copula approach for dependence modeling in multivariate nonparametric time series

## TL;DR

This paper introduces a copula-based method for modeling dependence in multivariate nonparametric time series, accounting for covariates affecting mean and variance but assuming stable innovation distributions.

## Contribution

It develops nonparametric and semiparametric estimators for the copula of innovations, demonstrating their asymptotic equivalence to unobserved innovation-based estimators.

## Key findings

- Copula estimators are asymptotically consistent.
- Method performs well in simulations.
- Application to real data illustrates practical utility.

## Abstract

This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences only the conditional mean and the conditional variance of each of the time series but the distribution of the standardized innovations is not influenced by the covariate and is stable in time. The joint distribution of the time series is then determined by the conditional means, the conditional variances and the marginal distributions of the innovations, which we estimate nonparametrically, and the copula of the innovations, which represents the dependency structure. We consider a nonparametric as well as a semiparametric estimator based on the estimated residuals. We show that under suitable assumptions these copula estimators are asymptotically equivalent to estimators that would be based on the unobserved innovations. The theoretical results are illustrated by simulations and a real data example.