What is the standard test for checking against potential structural breaks in log return data and realized variance that is used for GARCH modeling?
There appears to be a range of different CUSUM and LM tests available but I cannot seem to figure out which ones are the most commonly used? Or is there perhaps some other test that should be used instead? Is there an R package for this test?
Would a test for structural breaks in this setting have to be done on both the mean and the realized variance or just either of them? Or possibly even on the residuals?