Portmanteau Goodness-of-Fit Tests in the Presence of Simple, Mixed, and Multiple Seasonal Autocorrelation
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AI 根据所提供的论文材料归类：摘要直接研究多季节时间序列模型的残差自相关检验，涉及 SARMA 与 mSARIMA 的拟合诊断。
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简单、混合与多重季节自相关下的综合拟合优度检验
- 研究问题
- 当时间序列存在多个可能相互作用的季节周期时，如何诊断模型残差中的短期及多重季节自相关，评估模型拟合？
- 方法与思路
- 作者将经典综合自相关检验扩展至多季节情形，联合检验短期与多个季节滞后的残差相关，并给出统计量及渐近分布。
- 材料陈述的贡献
- 摘要称，该扩展填补针对多重季节自相关的诊断缺口；模拟支持其作为 mSARIMA 模型拟合工具，并提供道路交通应用。
- 阅读关注点
- 应核对季节滞后及其交互项的选取、参数估计对零分布的影响，以及重叠周期下的尺寸、功效与自由度计算。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未列明渐近条件、具体检验形式或模拟性能数值。
原文摘要
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.