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<p>Multiple seasonalities often appear in high-frequency data such as hourly measurements of air pollutants. These multiple seasonalities are due to human activities, with daily and weekly cycles, and climatic conditions, with daily and annual cycles. Multiple seasonal components were in the past often modelled in a deterministic way by trigonometric functions or dummy variables. Since pollution seasonalities vary over time, the deterministic assumption is very strict and a more flexible model is needed. We propose to allow seasonality to slowly change as a seasonal autoregressive integrated moving average (ARIMA) model, where the seasonality is modelled as a stochastic process (combining different seasonal ARIMA models). We apply the proposed methodology to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="477_2025_2958_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {NO}_2\)</EquationSource> </InlineEquation> hourly measurements of pollutants in Madrid with daily, weekly, and annual seasonalities, and demonstrate the usefulness of our approach by comparing it with other methodological approaches proposed for this type of data. In an extensive exercise involving 15-year hourly forecasts, we show that the proposed procedure performs very well in predicting hourly pollution over a 24-h horizon and improves on deep neural network procedures. Unlike most papers on pollution forecasting, we incorporate a clear exploratory analysis of Madrid’s <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="477_2025_2958_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {NO}_2\)</EquationSource> </InlineEquation> pollution levels based on a deep understanding of the underlying meteorological phenomena. Additionally, the impact on the predictions of covariates such as wind speed, temperature, and festivities was evaluated.</p>

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Modelling time series with multiple seasonalities: an application to hourly NO\({_2}\) pollution levels

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月11日

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  • M. L. Avila,
  • A. M. Alonso,
  • D. Peña

摘要

Multiple seasonalities often appear in high-frequency data such as hourly measurements of air pollutants. These multiple seasonalities are due to human activities, with daily and weekly cycles, and climatic conditions, with daily and annual cycles. Multiple seasonal components were in the past often modelled in a deterministic way by trigonometric functions or dummy variables. Since pollution seasonalities vary over time, the deterministic assumption is very strict and a more flexible model is needed. We propose to allow seasonality to slowly change as a seasonal autoregressive integrated moving average (ARIMA) model, where the seasonality is modelled as a stochastic process (combining different seasonal ARIMA models). We apply the proposed methodology to \(\text {NO}_2\) hourly measurements of pollutants in Madrid with daily, weekly, and annual seasonalities, and demonstrate the usefulness of our approach by comparing it with other methodological approaches proposed for this type of data. In an extensive exercise involving 15-year hourly forecasts, we show that the proposed procedure performs very well in predicting hourly pollution over a 24-h horizon and improves on deep neural network procedures. Unlike most papers on pollution forecasting, we incorporate a clear exploratory analysis of Madrid’s \(\text {NO}_2\) pollution levels based on a deep understanding of the underlying meteorological phenomena. Additionally, the impact on the predictions of covariates such as wind speed, temperature, and festivities was evaluated.