Impulse Response Function for Conditional Volatility in GARCH Models

Abstract

This article defines and analyzes the impulse response function for conditional volatility in generalized autoregressive conditional heteroscedasticity (GARCH) models. It first derives the function from a vector autoregressive and moving average representation of the GARCH models and obtains the corresponding standard errors from the first-order derivatives of the function and the covariance matrix of the estimated parameters. Then this article employs a Monte Carlo study to assess the finite-sample properties of the standard errors and provides an empirical example of the dependence of exchange-rate volatility to demonstrate its use in empirical applications.