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INAR模型的多变点探测
Multiple Change Point Detection for INAR Model

DOI: 10.12677/hjdm.2024.142009, PP. 102-115

Keywords: INAR模型,变点探测,似然比扫描方法
INAR Model
, Change Point Detection, Likelihood Ratio Scanning Method

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Abstract:

本文考虑了分段平稳的整数值自回归模型的多变点问题。借助最小描述长度函数得到似然比扫描方法,并将似然比扫描方法运用到分段平稳的整数值自回归模型中。此外,还研究了当模型系数之和趋于1时的情况,此时针对似然比扫描方法中的最小描述长度函数进行了调整,以提高变点探测的准确性。然后通过大量的数值模拟,验证了似然比扫描方法在不同的模型参数设置下的有效性,最后并将其运用于一组精神分裂症患者在知觉速度测试中的日常观察得分数据的实证分析之中。
This paper considers the multiple change-points problem in piecewise stationary integer-valued autoregressive model. Using the Minimum Description Length function, the likelihood ratio scanning method is obtained and applied to the piecewise stationary integer-value autoregressive model. In addition, when the sum of the model coefficients tends to 1, the Minimum Description Length function in the likelihood ratio scanning method is adjusted to improve the accuracy of the change point detection. Then, through many numerical simulations, the effectiveness of the likelihood ratio scanning method in different model parameter settings was verified. Finally, it was applied to the empirical analysis of the daily observations of the score achieved by a schizophrenic patient on a test of perceptual speed.

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