Copula--based Specification of vector MEMs

TL;DR

This paper introduces a copula-based approach to extend the vector MEM model, enabling flexible modeling of correlated nonnegative processes like volatility and trading activity, resulting in improved forecast accuracy.

Contribution

It proposes a novel copula-based method for estimating multivariate MEMs, addressing the lack of flexible density functions for innovations.

Findings

Copula approach effectively models correlations in multivariate MEMs.

Enhanced volatility forecasts when including trading activity indicators.

Demonstrates the importance of contemporaneous correlations in financial modeling.

Abstract

The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows for the innovations to be contemporaneously correlated. We overcome the lack of sufficiently flexible probability density functions for such processes by suggesting a copula function approach to estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate this vector MEM with an application to the interactions between realized volatility, volume and the number of trades. We show that significantly superior realized volatility forecasts are delivered in the presence of other trading activity indicators and contemporaneous correlations.