Gaussian and Student's $t$ mixture vector autoregressive model with application to the effects of the Euro area monetary policy shock

TL;DR

This paper introduces a novel mixture vector autoregressive model combining Gaussian and Student's t distributions, capturing heteroskedasticity and regime shifts, with applications to Euro area monetary policy shocks.

Contribution

The paper develops a new mixture VAR model with Gaussian and Student's t components, providing theoretical properties and an empirical application to monetary policy shocks.

Findings

Stronger effects on inflation before the Financial crisis

Model captures regime-dependent dynamics

Implemented in R package gmvarkit

Abstract

A new mixture vector autoregressive model based on Gaussian and Student's $t$ distributions is introduced. As its mixture components, our model incorporates conditionally homoskedastic linear Gaussian vector autoregressions and conditionally heteroskedastic linear Student's $t$ vector autoregressions. For a $p$th order model, the mixing weights depend on the full distribution of the preceding $p$ observations, which leads to attractive practical and theoretical properties such as ergodicity and full knowledge of the stationary distribution of $p+1$ consecutive observations. A structural version of the model with statistically identified shocks is also proposed. The empirical application studies the effects of the Euro area monetary policy shock. We fit a two-regime model to the data and find the effects, particularly on inflation, stronger in the regime that mainly prevails before the Financial crisis than in the regime that mainly dominates after it. The introduced methods are implemented in the accompanying R package gmvarkit.