The Trigonometric Box-Cox ARMA Trend Seasonal (TBATS) model has been designed to estimate complex cyclical patterns (e.g., weeks within years) in time series data. This paper seeks to evaluate its applicability to educational data, daily school attendance in particular. Attendance rates in four high schools are analyzed over a ten year period using TBATS to illustrate the presence of both weekly and annual patterns in three of the schools and only weekly patterns in the fourth. The model features are explicated and it is shown how the estimation of weekly and annual cycles enhances the description of the data and improves our understanding of how the assessment of endogenous variability contributes to our understanding of daily high school attendance behavior. R script is provided in an appendix.

中文翻译：

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使用时间序列分析来估计日常高中出勤的复杂规律周期

三角 Box-Cox ARMA 季节性趋势 (TBATS) 模型旨在估计时间序列数据中的复杂周期性模式（例如，几年内的几周）。本文旨在评估其对教育数据的适用性，特别是日常学校出勤率。使用 TBATS 分析了 10 年期间四所高中的出勤率，以说明其中三所学校存在每周和年度模式，而第四所学校只有每周模式。解释了模型特征，并显示了每周和每年周期的估计如何增强数据的描述并提高我们对内生变异性评估如何有助于我们理解日常高中出勤行为的理解。R 脚本在附录中提供。