Multiple Changepoint Detection for Non‐Gaussian Time Series
本文结合现有技术，提出一种检测非高斯自相关时间序列中多个变点的方法，通过变换将高斯序列转为非高斯序列，并用惩罚似然法处理，在棒球击球比例和热带气旋计数数据上验证了有效性。
ABSTRACT This article combines methods from existing techniques to identify multiple changepoints in non‐Gaussian autocorrelated time series. A transformation is used to convert a Gaussian series into a non‐Gaussian series, enabling penalized likelihood methods to handle non‐Gaussian scenarios. When the marginal distribution of the data is continuous, the methods essentially reduce to the change of variables formula for probability densities. When the marginal distribution is count‐oriented, Hermite expansions and particle filtering techniques are used to quantify the scenario. Simulations demonstrating the efficacy of the methods are given and two data sets are analyzed: 1) the proportion of home runs hit by Major League Baseball batters from 1920 to 2023 and 2) a six‐dimensional series of tropical cyclone counts from the Earth's basins of generation from 1980 to 2023. In the first series, beta marginal distributions are used to describe the proportions; in the second, Poisson marginal distributions seem appropriate.