In this study, monthly particulate matter (PM_2.5) of Paris for the period between January 2000 and December 2019 is investigated by utilizing a periodogram-based time series methodology. The main contribution of the study is modeling the PM_2.5 of Paris by extracting the information purely from the examined time series data, where proposed model implicitly captures the effects of other factors, as all their periodic and seasonal effects reside in the air pollution data. Periodicity can be defined as the patterns embedded in the data other than seasonality, and it is crucial to understand the underlying periodic dynamics of air pollutants to better fight pollution. The method we use successfully captures and accounts for the periodicities, which could otherwise be mixed with seasonality under an alternative methodology. Upon the unit root test based on periodograms, it is revealed that the investigated data has periodicities of 1 year and 20 years, so harmonic regression is utilized as an alternative to Box-Jenkins methodology. As the harmonic regression displayed a better performance both in and out-of-sample forecasts, it can be considered as a powerful alternative to model and forecast time series with a periodic structure.

在这项研究中，利用基于周期图的时间序列方法研究了巴黎 2000 年 1 月至 2019 年 12 月期间的每月颗粒物 (PM _2.5 )。该研究的主要贡献是模拟 PM _2.5巴黎通过纯粹从检查的时间序列数据中提取信息，其中提出的模型隐含地捕捉了其他因素的影响，因为它们的所有周期性和季节性影响都存在于空气污染数据中。周期性可以定义为嵌入在数据中而不是季节性的模式，了解空气污染物的潜在周期性动态以更好地对抗污染至关重要。我们使用的方法成功捕获并说明了周期性，否则在替代方法下可能会与季节性混合。基于周期图的单位根检验表明，调查数据具有 1 年和 20 年的周期性，因此使用谐波回归作为 Box-Jenkins 方法的替代方法。