Superposed epoch analysis using time-normalization: A Python tool for statistical event analysis - Walton, Samuel D.; Murphy, Kyle R. (Frontiers in Astronomy and Space Sciences, 2022)
A superposed epoch analysis (SEA) is a simple, yet powerful statistical analysis technique, used to identify patterns in the temporal evolution of observed quantities relative to defined epochs. In some cases, the event duration and time between epochs (epoch length) can be highly variable. If the measured response scales with the event duration or epoch length, then the underlying temporal patterns can be suppressed when analyzed in absolute time. In this article, we describe an adaptation of the traditional SEA, where we apply time-normalization to each event and present a Python package sea_norm which implements the time-normalized SEA. Rather than defining a singular epoch time, a start, epoch, and end time are defined for each event, separating each event into two intervals. For every event, the duration of both intervals is normalized to a common time axis, essentially stretching or compressing each interval, such that each respective epoch interval is the same length for all events. This technique has the advantage of identifying temporal patterns not observed in a traditional SEA. Given a time series, a list of event start, epoch, and end times, and specified binning dimensions the Python package sea_norm returns a time-normalized SEA analysis of the time-series. This technique is widely applicable across the Space Physics field, where events have defined start and end times, and where the response to those events may scale proportionally with event length. We provide examples demonstrating how the SEA code works with one-dimensional and two-dimensional time series, and how users can specify their own statistics to use in the superposed analysis (e.g., percentiles).