The Theory and Taxonomy of Spike Anomalies in Time Series Data: A Short Glance

A spike is an excursion of a process away from its current level. This short note develops the formal theory of spikes and their first differences on a uniform sampling distribution: a full taxonomy, the symmetry–antisymmetry theorem is then introduced which links the shape of a spike to the shape of its difference signal, the slope-ratio identity that recovers rise/decay asymmetry from the difference amplitudes and the two artefacts of discrete sampling – aliasing and the at the end-of-day time series lag – that make the detected day of a spike convention-dependent. The note contributes to classical foundations of spike analysis and developments in spike and anomaly detection.