Can portmanteau nonlinearity tests serve as general mis-specification tests?

A number of recent papers have employed the BDS test as a general test for mis-specification for linear and nonlinear models. We show that for a particular class of conditionally heteroscedastic models, the BDS test is unable to detect a common mis-specification. Our results also demonstrate that specific rather than portmanteau diagnostics are required to detect neglected asymmetry in volatility. However for both classes of tests reasonable power is only obtained using very large sample sizes.