We study ARCH/GARCH effects under possible deviation from normality. Since skewness is the principal cause for deviations from normality in many practical applications, e.g. finance, we study in particular skewness. We propose robust tests for normality both for NoVaS and modified NoVaS transformed and original data. Such an approach is not applicable for EGARCH, but applicable for GARCH-GJR models. A novel test procedure is proposed for the skewness in autoregressive conditional volatility models. The power of the tests is investigated with various underlying models. Applications with financial data show the applicability and the capabilities of the proposed testing procedure.