The CUSUMSQ test of homoskedasticity is shown in the autoregression model to be consistent against a broad range of nonstationary volatility specification recently studied in the literature. The limit distribution is derived, and numerical examples are presented to illustrate the theoretical...

We show that the CUSUM and LM tests for structural change in the volatility process enjoy monotonic power. The framework is general including many recently proposed non-stationary GARCH-type models. The result is in contrast to the well-known issue of non-monotonic power for the CUSUM-based...