The classification of volatility of financial time series has recently received a lot of contributions: in particular using model based clustering algorithms. Recent works have evidenced how volatility structure can vary along time, with gradual or abrupt changes in the coefficients of the model. We wonder if these changes can affect the classification of series in terms of similar volatility structure. We propose to classify the level of the unconditional volatility obtained from Multiplicative Er- ror Models with the possibility of changes in the parameters of the model in terms of regime switching or time varying smoothed coefficients. They provide different unconditional volatility structures with a proper interpretation, useful to represent different situations of interest. The different methodologies are coherent with each other and provide a common synthetic pattern. The procedure is experimented on fifteen stock indices volatilities.