Ujjwal Kumar

  • Chemistry & Climate Division, KNMI – Royal Netherlands Meteorological Institute, De-Bilt, The Netherlands

Received: March 19, 2014
Revised: July 2, 2014
Accepted: August 27, 2014
Download Citation: ||https://doi.org/10.4209/aaqr.2014.03.0046  

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Cite this article:
Kumar, U (2015). An Integrated SSA-ARIMA Approach to Make Multiple Day Ahead Forecasts for the Daily Maximum Ambient O3 Concentration. Aerosol Air Qual. Res. 15: 208-219. https://doi.org/10.4209/aaqr.2014.03.0046


  • SSA-ARIMA is introduced to forecast daily maximum ambient O3 concentration. 
  • Comparison of SSA-ARIMA with FFT-ARIMA forecasts at 6 European AIRBASE stations. 
  • The component extraction by SSA appears to be working superior to FFT. 
  • Forecast error analysis reveals that SSA-ARIMA consistently outperforms FFT-ARIMA.
  • The multiple days ahead forecasts have also clearly improved while using SSA-ARIMA. 



An integrated approach that combines a signal extraction method SSA (Singular Spectrum Analysis) with ARIMA (Autoregressive Integrated Moving Average) has been introduced to make multiple day ahead forecasts for daily maximum ambient O3 concentrations. The results are compared with the forecasts obtained by more commonly used signal extraction method FFT (Fast Fourier Transforms) in combination with ARIMA. The data from six different European AIRBASE stations have been analyzed to test their skills in one-day ahead to five-day ahead forecasts. In SSA-ARIMA, the SSA has been used to extract the different structural components of the time series. The first few principal components have been selected based on their dominance in the eigenvalues spectrum. Each component has been modelled separately and their sum is called SSA-component. The residuals of the “SSA-component subtracted from the actual data” exhibited stationarity and have been modeled using ARIMA process. In the second approach called by FFT-ARIMA, FFT has been used to model the periodicities exhibited by the time series. The first few predominant frequencies have been selected based on the power-spectrum characteristics of the time series. The residuals of the “FFT-component subtracted from the actual data” were modeled using ARIMA process. The performances of both the SSA-ARIMA and FFT-ARIMA were evaluated for 30 out of sample days for one to five day ahead forecasts. The statistical indicators RMSE (root mean square error) and MAE (mean absolute error) reveal that the SSA-ARIMA consistently outperforms FFT-ARIMA. Moreover, SSA-ARIMA has also been found to perform better especially for multiple day ahead forecasts. The results clearly indicate that the SSA-ARIMA approach can be a potential alternative to make short term air quality forecasting.

Keywords: Singular Spectrum Analysis (SSA); Fast Fourier Transform (FFT); Autoregressive Integrated Moving Average (ARIMA); Ambient O3; Forecasting

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