In this paper, we introduce two new definitions of pair-wise and multi-wise similarity between short-run dynamics of inflation rates in terms of equality of forecast functions and show that in the context of invertible ARIMA processes the autoregressive metric introduced by Piccolo (1990) is a useful measure to evaluate such similarity. Then, we study the similarity of short-run inflation dynamics across European Union (EU)-25 Member States during the Euro period. Consistent with studies on inflation differentials and inflation persistence, our findings suggest that after seven years from the launch of the Euro the degree of similarity of short-run inflation dynamics across Euro area countries is still weak. By contrast, we find that EU countries not adopting the common currency, whether old EU or new accession Members, display a higher degree of inflation dynamics similarity both among each other and with Euro area countries.