Bootstrap-Based Method of Structural Breaks Detection in GARCH Models

In this work, we study a method for detecting a structural break in GARCH(1, 1) models, based on the application of the bootstrap scheme to series of standardized independent errors. Using numerical experiments consisting of 1000 tests each, this bootstrap-based method is compared with the classic CUSUM method. The methods are compared for parameters inherent to the logarithmic stock returns of large American companies, and type I errors for both methods are comparable. Despite the fact that both tests show good results asymptotically - at N = 2000 the power of the test is close to 1, in the case of small number of observations the power of the bootstrap method was significantly lower than the power of the classical CUSUM test. Thus, the performed numerical experiments indicate that the CUSUM method is more preferable than the bootstrap method in the case of small samples.