A Mixed Copula-Based Vector Autoregressive Model for Econometric Analysis

Abstract

In many practical applications, the dynamics of different quantities is reasonably well described by linear equations. In economics, such linear dynamical models are known as vector autoregressive (VAR) models. These linear models are, however, only approximate. The deviations of the actual value of each quantity from the predictions of the linear model are usually well described by normal or Student-t distributions. To complete the description of the joint distribution of all these deviations, we need to supplement these marginal distributions with the information about the corresponding copula. To describe this dependence, in the past, researchers followed the usual idea of trying copulas from several standard families: Gaussian, Student, Clayton, Frank, Gumbel, and Joe families. To get a better description, we propose to also use convex combinations of copulas from different families; such convex combinations are known as mixed copulas. On the example of the dynamics of US macroeconomic data, including GDP, unemployment, consumer price index, and the real effective exchange rate, we show that mixed copulas indeed lead to a better description of the actual data. Specifically, it turns out that the best description is obtained if we use a convex combination of Student and Frank copulas.

Structural and predictive analyses with a mixed copula‐based vector autoregression model

“…The mixed Copula is a combination of different copula families, and it can capture both symmetric and asymmetric and other complicated dependence structures. To our knowledge, the copula-based VAR model has already been proposed by Brechmann and Czado (2015) and Yamaka and Thongkairat (2020); however, the estimation and computation aspects of mixed copula-based VAR has never been proposed yet. 1 For this reason, this study attempts to fill the gap of knowledge by applying various combinations of mixed Copula to allow better flexibility of capturing almost all possible dependence structures between error terms in the VAR framework.…”