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We propose a novel approach to modelling and forecasting high-frequency trading volumes. In order to provide a parsimonious representation of the rich dependence structure of high frequency trading volumes, our model is based on a component structure featuring an intra-day periodic, a short-term non periodic and a smoothly varying long term component. The proposed model generalizes the Component Multiplicative Error Model of Brownlees et al. (2011) by considering a more flexible specification of the long-run component which is based on a Heterogeneous MIDAS polynomial structure. This uses an additive cascade of MIDAS polynomial filters moving at different frequencies in order to reproduce the changing long-run level and the persistent autocorrelation structure of high frequency trading volumes. On the theoretical ground, the statistical properties of the model are investigated and, namely, its stationarity conditions are derived.  On the empirical ground, the merits of the proposed approach are illustrated by means of an application to a set of stocks traded on the XETRA market characterised by different degrees of liquidity.