We propose a local adaptive multiplicative error model (MEM) accommodating time‐varying parameters. MEM parameters are adaptively estimated based on a sequential testing procedure. A data‐driven optimal length of local windows is selected, yielding adaptive forecasts at each point in time. Analysing 1‐minute cumulative trading volumes of five large NASDAQ stocks in 2008, we show that local windows of approximately 3 to 4 hours are reasonable to capture parameter variations while balancing modelling bias and estimation (in)efficiency. In forecasting, the proposed adaptive approach significantly outperforms a MEM where local estimation windows are fixed on an ad hoc basis. Copyright © 2014 John Wiley & Sons, Ltd.