Change-point detection in GARCH models: asymptotic and bootstrap tests

Two classes of tests designed to detect changes in volatility are proposed. Procedures based on squared model residuals and on the likelihood ratio are considered. The tests are applicable to parametric nonlinear models like GARCH. Both asymptotic and bootstrap tests are investigated by means of a simulation study and applied to returns data. The tests based onthe likelihood ratio are shown to be generally preferable. A wavelet based estimator of long memory is applied to returns data to shed light on the interplay of change points and long memory.