Detecção de pontos de mudança em séries temporais com base no algoritmo Pruned Exact Linear Time (PELT)

Abstract

Time series analysis is a statistical technique aimed at studying observations collected over time, which naturally exhibit interdependence. This type of analysis plays an important role in understanding the behavior of data over time, especially when there are indications that this behavior has undergone some modification. These changes, known as change points, represent significant alterations in series characteristics such as mean, variance, or trend, and are generally associated with events of major impact in the context of the data, such as economic crises, political shocks, or pandemics. With computational advancements and, consequently, the availability of longer time series, there arises a need to develop and study methods capable of detecting these change points in extensive data without having a very high computational complexity, that is, methods that are both accurate and efficient. In this context, this work aims to identify change points in a real financial series, using the Pruned Exact Linear Time (PELT) algorithm, which achieves good accuracy in identifying the points and also has low computational complexity, as it combines the minimization of a cost function with a pruning method.