Fractional lower-order covariance-based measures for cyclostationary time series with heavy-tailed distributions: application to dependence testing and model order identification
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重尾循环平稳时间序列的分数低阶协方差度量：依赖检验与模型阶数识别
- 研究问题
- 当循环平稳时间序列具有重尾分布甚至无限方差、传统自协方差无法使用时，如何度量周期性依赖并识别模型阶数？
- 方法与思路
- 作者以分数低阶协方差构造周期分数低阶自相关与偏自相关函数，用于总体依赖检验以及周期自回归、移动平均模型定阶。
- 材料陈述的贡献
- 摘要提出替代传统周期相关函数的依赖度量及两类应用，并通过模拟与空气污染数据展示无限方差过程中的分析潜力。
- 阅读关注点
- 核对低阶矩的存在条件、相关与偏相关度量的定义、检验参考分布，以及周期结构和重尾程度对定阶表现的影响。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收均未核验；摘要未给出具体矩条件、检验有效性条件或效率比较数值。
原文摘要
This article introduces new methods for the analysis of cyclostationary time series with infinite variance. Traditional cyclostationary analysis, based on periodically correlated (PC) processes, relies on the autocovariance function (ACVF). However, the ACVF is not suitable for data exhibiting a heavy-tailed distribution, particularly with infinite variance. Thus, we propose a novel framework for the analysis of cyclostationary time series with heavy-tailed distribution, utilizing the fractional lower-order covariance (FLOC) as an alternative to covariance. This leads to the introduction of two new autodependence measures: the periodic fractional lower-order autocorrelation function (peFLOACF) and the periodic fractional lower-order partial autocorrelation function (peFLOPACF). These measures generalize the classical periodic autocorrelation function (peACF) and periodic partial autocorrelation function (pePACF), offering robust tools for analyzing infinite-variance processes. Two practical applications of the proposed measures are explored: a portmanteau test for testing dependence in cyclostationary series and a method for order identification in periodic autoregressive (PAR) and periodic moving average (PMA) models with infinite variance. Both applications demonstrate the potential of new tools, with simulations validating their efficiency. The methodology is further illustrated through the analysis of real-world air pollution data, which showcases its practical utility. The results indicate that the proposed measures based on FLOC provide reliable and efficient techniques for analyzing cyclostationary processes with heavy-tailed distributions.