Correlation impulse response functions

Volatility impulse response functions are a widely used tool for analyzing the temporal impact of shocks on (co-)volatilities of financial time series. This paper proposes an extension to correlation impulse response functions (CIRF), based on a multivariate GARCH modeling framework. As we show, CIRF and corresponding covariance impulse response functions can react quite differently to a given shock and even move in opposite directions. Due to the inherent nonlinearity, no analytical form is available for CIRF, but we propose a straightforward algorithm to estimate the CIRF numerically. In an empirical application we focus on the change of the consensus protocol of Ethereum in 2022 and its effect on the correlation with Bitcoin.

Automated summary

This paper proposes an extension to correlation impulse response functions (CIRF) based on a multivariate GARCH modeling framework. We find that CIRF and corresponding covariance impulse response functions can react differently and even move in opposite directions to a given shock. Due to nonlinearity, there is no analytical form available for CIRF, but we propose a straightforward algorithm to numerically estimate it. In an empirical application, we focus on the impact of the change in Ethereum's consensus protocol in 2022 on its correlation with Bitcoin.