Simultaneous Detection of Structural Breaks and Outliers in Time Series
提出用分段自回归过程建模含异常值的非平稳时间序列，通过最小描述长度准则和遗传算法同时确定分段数、段长、自回归阶数及异常值类型与位置，模拟和实际数据表现良好。
ABSTRACT This article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive (AR) processes in the presence of outliers. The number and locations of the piecewise AR segments, as well as the orders of the respective AR processes, are assumed to be unknown. In addition, each piece may contain an unknown number of innovational and/or additive outliers. The minimum description length (MDL) principle is applied to compare various segmented AR fits to the data. The goal is to find the “best” combination of the number of segments, the lengths of the segments, the orders of the piecewise AR processes, and the number and type of outliers. Such a “best” combination is implicitly defined as the optimizer of an MDL criterion. Since the optimization is carried over a large number of configurations of segments and positions of outliers, a genetic algorithm is used to find optimal or near‐optimal solutions. Numerical results from simulation experiments and real data analyses show that the procedure enjoys excellent empirical properties.