A Bootstrap Test for the Existence of Moments for GARCH Processes

This paper studies the joint inference on conditional volatility parameters and the innovation moments by means of bootstrap to test for the existence of moments for GARCH(p,q) processes. We propose a residual bootstrap to mimic the joint distribution of the quasi-maximum likelihood estimators and the empirical moments of the residuals and also prove its validity. A bootstrap-based test for the existence of moments is proposed, which provides asymptotically correctly-sized tests without losing its consistency property. It is simple to implement and extends to other GARCH-type settings. A simulation study demonstrates the test's size and power properties in finite samples and an empirical application illustrates the testing approach.