Copula Processes

TL;DR

This paper introduces copula processes to model dependencies among multiple variables independently of their marginals, and develops a stochastic volatility model called GCPV that outperforms GARCH in certain scenarios.

Contribution

The paper proposes a novel copula process framework and a Gaussian Copula Process Volatility model, enabling flexible dependency modeling and improved volatility prediction.

Findings

GCPV can outperform GARCH on simulated and financial data.

Both Bayesian inference methods (Laplace and MCMC) yield comparable results.

GCPV handles missing data and covariates more easily than GARCH.

Abstract

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find both methods comparable. We also find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.