Kim Byungsoo, Lee Sangyeol
Department of Statistics, Yeungnam University, Gyeongsan 38541, Korea.
Department of Statistics, Seoul National University, Seoul 08826, Korea.
Entropy (Basel). 2020 Apr 24;22(4):493. doi: 10.3390/e22040493.
In this study, we consider the problem of testing for a parameter change in general integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family when the data are contaminated by outliers. In particular, we use a robust change point test based on density power divergence (DPD) as the objective function of the minimum density power divergence estimator (MDPDE). The results show that under regularity conditions, the limiting null distribution of the DPD-based test is a function of a Brownian bridge. Monte Carlo simulations are conducted to evaluate the performance of the proposed test and show that the test inherits the robust properties of the MDPDE and DPD. Lastly, we demonstrate the proposed test using a real data analysis of the return times of extreme events related to Goldman Sachs Group stock.
在本研究中，我们考虑在数据受到异常值污染时，对条件分布属于单参数指数族的一般整数值时间序列模型中的参数变化进行检验的问题。具体而言，我们使用基于密度幂散度（DPD）的稳健变化点检验作为最小密度幂散度估计器（MDPDE）的目标函数。结果表明，在正则条件下，基于DPD的检验的极限零分布是布朗桥的函数。进行了蒙特卡罗模拟以评估所提出检验的性能，结果表明该检验继承了MDPDE和DPD的稳健特性。最后，我们通过对与高盛集团股票相关的极端事件的回报时间进行实际数据分析，展示了所提出的检验。
