Revenue management strongly relies on accurate forecasts. Thus, when extraordinary events cause outlier demand, revenue management systems need to recognise this and adapt both forecast and controls. Many passenger transport service providers, such as railways and airlines, control the sale of tickets through revenue management. State-of-the-art systems in these industries rely on analyst expertise to identify outlier demand both online (within the booking horizon) and offline (in hindsight). So far, little research focuses on automating and evaluating the detection of outlier demand in this context. To remedy this, we propose a novel approach, which detects outliers using functional data analysis in combination with time series extrapolation. We evaluate the approach in a simulation framework, which generates outliers by varying the demand model. The results show that functional outlier detection yields better detection rates than alternative approaches for both online and offline analyses. Depending on the category of outliers, extrapolation further increases online detection performance. We also apply the procedure to a set of empirical data to demonstrate its practical implications. By evaluating the full feedback-driven system of forecast and optimisation, we generate insight on the asymmetric effects of positive and negative demand outliers. We show that identifying instances of outlier demand and adjusting the forecast in a timely fashion substantially increases revenue compared to what is earned when ignoring outliers.