Portmanteau 拟合优度检验在简单、混合和多重季节性自相关存在下的应用

中文摘要 AI 辅助

评估线性模型拟合优度的标准诊断程序包括检验残差无自相关的零假设与线性依赖的备择假设。文献中提出了几种针对 SARMA 模型残差自相关的 portmanteau 检验，主要关注两种情况：短期自相关和单季节性自相关。由于许多时间序列表现出多种季节性模式，其周期分量可能相互影响，因此需要多季节性框架下的残差自相关诊断检验。然而，文献中仍缺乏专门针对多重季节性自相关的 portmanteau 检验。本文通过将经典 portmanteau 检验扩展到具有多重季节性的设置来填补这一空白。此外，所提出的方法同时检验短期和多重季节性残差自相关。定义了检验统计量及其渐近分布。然后，使用蒙特卡罗模拟评估检验的性能，并通过统计检验评估与预期结果的一致性。结果表明，所提出的扩展可以作为 mSARIMA 模型类有用的拟合优度诊断工具。还提供了对道路交通数据的应用。

英文摘要

Standard diagnostic procedures for assessing the goodness of fit of linear models include tests of the null hypothesis of no residual autocorrelation against the alternative of linear dependence. The literature proposes several portmanteau tests for residual autocorrelation in SARMA models, mainly focusing on two cases: short-term and single-seasonal autocorrelation. Since many time series exhibit multiple seasonal patterns, whose periodic components may interact with one another, diagnostic tests for residual autocorrelation in a multi-seasonal framework are needed. However, the literature still lacks portmanteau tests specifically designed for multiple seasonal autocorrelation. This paper addresses this gap by extending classical portmanteau tests to settings with multiple seasonalities. In addition, the proposed approach jointly tests for both short-term and multiple seasonal residual autocorrelation. Test statistics and their asymptotic distributions are defined. Then, Monte Carlo simulations are used to evaluate the performance of the tests and the consistency with the expected results is assessed using statistical tests. The results suggest that the proposed extension can serve as a useful goodness-of-fit diagnostic tool for the class of mSARIMA models. An application to road traffic data is also provided.

发表机构

• University of Padua（帕多瓦大学）

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