Ding et al. (1993) [Ding, Z., Granger, C.W.J., Engle, R.F., 1993. A long memory property of stock market returns and a new model. Journal of Empirical Finance 1, 83-106] suggested a model which extends the ARCH family of models for analyzing a wider class of power transformations than simply taking the absolute value or squaring the data as in the conventional conditional heteroscedastic models. This paper analyzes the applicability of these power ARCH (PARCH) models to national stock market returns for 10 countries plus a world index. We find the PARCH model to be generally applicable once GARCH and leverage effects are taken into consideration. In addition, we also find that the optimal power transformation is remarkably similar across countries.