Nowadays, modelling long-term money demand is largely unambiguous. There is a vast amount of empirical evidence concerning a cointegrating relationship between money demand, some kind of interest rate and income. In contrast to this, short-run dynamics are still opaque. In the existing literature, the return to steady state is modelled quite differently. Simple error correction models have failed in some cases to explain short-run dynamics adequately. Partial-adjustment models allow for a smooth return to equilibrium as costs for adjusting real money balances lead to a sticky behaviour of actual money. Other authors model the return to steady state in a non-linear error correction form, instead. All these models consider disequilibria by the gap between money demand and its steady state of only the last period, disregarding disequilibria in periods before. Ignoring deviations from steady state occurred further in the past miss to account for money stockpiling activities of economic agents. I use a model where weights for cumulating are geometrically decreasing the more they are located in the past. According to Koyck (1954) such models possess an ARMA (1,1) representation. The combination of the Koyck-model with the error correction approach leads to an ARMAX model which is shown to be capable in some cases to track money demand short-run dynamics better and more parsimony than partial-adjustment models.