Empirical study of periodic autoregressive models with additive noise -- estimation and testing
带加性噪声的周期自回归模型：估计与检验的实证研究AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究周期自回归时间序列的加性噪声、参数估计和模型检验。
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带加性噪声的周期自回归模型：估计与检验的实证研究
- 研究问题
- 当有限方差的周期自回归信号受到测量噪声或其他加性干扰时，如何估计模型，并检验数据是否包含相应的信息成分？
- 方法与思路
- 作者基于自协方差函数和 Yule–Walker 方程提出四种估计技术，并构造模型检验，以模拟及空气颗粒物浓度序列评估表现。
- 材料陈述的贡献
- 摘要称，方法适用于有限方差加性噪声；模拟展示了包括高斯噪声叠加异常值情形下的有效性，并考察检验功效。
- 阅读关注点
- 应核对信号与噪声的关系假设、四种技术的识别与数值差异、异常值设定，以及检验统计量、临界值和功效比较方式。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及接收状态未核实；摘要未列噪声依赖条件或具体模拟结果，不能外推至无限方差噪声。
原文摘要
Periodic autoregressive (PAR) time series with finite variance is considered as one of the most common models of second-order cyclostationary processes. However, in the real applications, the signals with periodic characteristics may be disturbed by additional noise related to measurement device disturbances or to other external sources. Thus, the known estimation techniques dedicated for PAR models may be inefficient for such cases. When the variance of the additive noise is relatively small, it can be ignored and the classical estimation techniques can be applied. However, for extreme cases, the additive noise can have a significant influence on the estimation results. In this paper, we propose four estimation techniques for the noise-corrupted PAR models with finite variance distributions. The methodology is based on Yule-Walker equations utilizing the autocovariance function. It can be used for any type of the finite variance additive noise. The presented simulation study clearly indicates the efficiency of the proposed techniques, also for extreme case, when the additive noise is a sum of the Gaussian additive noise and additive outliers. The proposed estimation techniques are also applied for testing if the data corresponds to noise-corrupted PAR model. This issue is strongly related to the identification of informative component in the data in case when the model is disturbed by additive non-informative noise. The power of the test is studied for simulated data. Finally, the testing procedure is applied for two real time series describing particulate matter concentration in the air.