Abnormal behaviour may indicate important objects and situations in e.g. surveillance applications. This paper is concerned with algorithms for automated anomaly detection in trajectory data. Based on the theory of Conformal prediction, we propose the Similarity based Nearest Neighbour Conformal Anomaly Detector (SNN-CAD) which is a parameter-light algorithm for on-line learning and anomaly detection with wellcalibrated false alarm rate. The only design parameter in SNN-CAD is the dissimilarity measure. We propose two parameterfree dissimilarity measures based on Hausdorff distance for comparing multi-dimensional trajectories of arbitrary length. One of these measures is appropriate for sequential anomaly detection in incomplete trajectories. The proposed algorithms are evaluated using two public data sets. Results show that high sensitivity to labelled anomalies and low false alarm rate can be achieved without any parameter tuning.