Eye tracking methods are usually focused on obtaining the highest spatial precision as possible, locating the centre of the pupil and the point of gaze for a series of frames. However, for the analysis of eye movements such as saccades or fixations, the temporal precision needs to be optimised as well. The results should not only be precise, but also stable. Eye tracking using low-cost hardware such as webcams brings a new series of challenges that have to be specifically taken into account. Noise, low resolution and low frame rates are some of these challenges, which in the end are the cause of temporal instabilities that negatively affect the results. This paper proposes a measure for temporal stability of pupil detection algorithms, applied on video streams obtained from webcams. The aim of this metric is to compare and evaluate the temporal stability of different algorithms (following a multi-layered approach for pupil detection), in order to identify which one is more adequate to its use for movement detection using low-cost hardware. The obtained results show how the temporal stability of different algorithms is affected by several factors.