Asset returns have a very complicated dynamic pattern. Yet they display regularity across different assets and periods. We consider a new family of volatility models which account for such patterns, focussing in particular on the long memory nature of asset returns volatility. We propose an estimation procedure for such models based on a Gaussian pseudo maximum likelihood estimator, for which we establish the relevant asymptotic theory. An empirical application based on forex and stock return indexes suggests the potential of these models to capture the dynamic features of the data.