Change point detection using $L_2$ loss statistic

초록

The goal of this paper is to detect a single change point in sequential data. To achieve this, we introduce the Add-one-in L${}_2$ Loss (ADO-IL) statistic, which is based on sequential means calculated by adding one data point at a time. The mathematical expectation of the ADO-IL statistic provides crucial insights for conducting this detection. When a dataset has one change point, the ADO-IL statistic should be mathematically constant before the change point and be increasing after it. Our detection methodology utilizes the ADO-IL-based algorithm to address various change point scenarios, including changes in mean, variance, and both mean and variance, under relaxed data distribution assumptions. The key strength of the algorithm is its solid mathematical foundation, which allows it to be effective regardless of the type of change point. In a simulation study, the ADO-IL algorithm demonstrates its advantage by delivering consistent performance across different locations and types of changes, overcoming the limitations of the PELT algorithm, which is highly dependent on matching a loss function to a specific type of change. Additionally, using USD/KRW exchange rate data, we show that the performance of the ADO-IL-based algorithm is comparable to or surpasses that of the existing PELT algorithm in real-world applications.

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