Investigating the Degree of Persistence, Trend and the Best Time Series Forecasting Models for Particulate Matter (PM10) Pollutant Across Malaysia


  • Lawan Adamu Isma'il School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
  • Norhashidah Awang School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
  • Ibrahim Lawal Kane Department of Mathematics and Statistics, Umaru Musa Yar’adua University, 2218 Katsina State, Nigeria



Particulate Matter, Long memory, ARIMA, Mann-Kendall Trend, Forecasting


Particulate matter is the most common atmospheric pollutant with some negative consequences on human health, environment, and the ambient air quality. In this study, the concentration of particulate matter in sixty-five air quality monitoring stations across Malaysia during January to December 2018 is analyzed. We investigated the degree of persistence and trend of the particulate matter series and developed a forecasting model using both the autoregressive integrated moving average (ARIMA) and the autoregressive fractionally integrated moving average (ARFIMA) time series methods for each monitoring station separately. Mean absolute deviation (MAD), mean absolute percentage error (MAPE) and root mean square error (RMSE) are used to determine the best fitted model for forecasting each monitoring station. Ljung-Box test of uncorrelated residuals confirmed the adequacy of each of the model. The results confirmed the evidence of transitory form of persistence in the level of particulate matter pollutant at sixty-four monitoring stations while trend increases in seventeen monitoring stations. Forecast error analysis indicates that ARFIMA models performed better than ARIMA models by producing smaller RMSE values in forty-two of the sixty-five monitoring stations. However, the overall result indicates that none of the model could be regarded as universal in forecasting particulate matter concentration, and their performance is independent of the category or location of a given monitoring station.


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