Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series

TL;DR

This paper introduces a fast variational Bayes estimator for high-dimensional copula models with discrete or mixed margins, enabling efficient modeling of complex multivariate time series data.

Contribution

It presents a novel variational Bayes approach for estimating large-scale copula models with discrete margins, outperforming previous likelihood-based methods in speed and scalability.

Findings

Successfully estimated copulas with up to 792 dimensions and 60 parameters.

Demonstrated flexibility of time series copula models with real data examples.

Showed the method's efficiency in handling heteroskedasticity and features like zero inflation.

Abstract

We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension $rT$, where $T$ is the number of observations and $r$ is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a feature of most ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes and under- or over-dispersion. Using six example series, we illustrate both the flexibility of the time series copula models, and the efficacy of the variational Bayes estimator for copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods.