Comparison of Daily Ozone Curve Forecasting Between Multi-Step and Iterative One-Step Ahead Methods with Different Basis Functions

Abstract

Ground-level Ozone pollution causes several potential environmental and human health issues. Forecasting the concentration levels helps to mitigate the problem. This study compared two functional time-series (FTS) forecasting methods, Multistep-ahead and Iterative One-step ahead, for forecasting daily Ozone curves. Beyond comparing the relative performance of the two methods, this study investigates the impact of different basis functions (B-spline, Fourier, and Polygonal) on the forecasting performance. Hourly recorded Ozone data obtained from the Department of Environment (DOE) Malaysia, involving Shah Alam, Batu Muda and Klang air quality monitoring stations were utilized. The methodology began by transforming real observed hourly Ozone data from January 1 to November 6, 2019, to daily Ozone curves using the basis expansion method, followed by FTS modelling. The models’ forecasting performance was evaluated using error measures including Mean Squared Error (MSE), Mean Absolute Error (MAE), Integrated Squared Error (ISE), and the coefficient of determination (R²). The analysis results indicate that variations in the types of basis functions influence forecasting performance across stations; however, no significant differences are observed within the same station. Overall R² of Multi-step ahead method is found to be higher than the Iterative One-step ahead method in forecasting daily Ozone curves at the study locations, with (0.8017, 0.8214, 0.629) and (0.7831, 0.8208, 0.6154), respectively. The findings suggest that, while the Multi-step ahead approach offers a somewhat improved functional representation of diurnal Ozone dynamics, its predictive performance remains comparable to that of the Iterative one-step ahead approach, indicating only a modest superiority rather than absolute.