Application of Functional Time Series Model in Forecasting Monthly Diurnal Maximum API Curves: A Comparison between Multi-Step Ahead and Iterative One-Step Ahead Approach

In Malaysia, Air Pollution Index (API) is used to assess the status of background air quality. The computation of API involved six major air pollutants including PM10, PM2.5, O-3, CO, SO2 and NOx. Due to the harmful effect of air pollution, forecasting API is important. Exposure and risk assessment play important role to measure the impact of air pollution towards humans health for controlling and mitigation purposes. Information based on continuous diurnal level of air pollution is more fruitful compared to daily average point data in the assessment process. This requires the needs for analyzing and predicting continuous diurnal level of API in the form of curves. To enable the analysis to be conducted, this paper introduces the application of Functional Time Series (FTS) model in forecasting monthly diurnal maximum API curves at two selected sites in Peninsular Malaysia; namely Shah Alam Selangor and Pasir Gudang Johor. Two FTS models were compared which include Multi-Step ahead and Iterative One-Step ahead approach. The results show that the Multi-Step ahead model has produced better performance giving the lowest error measures; FMSE, FRMSE and FMAPE compared to Iterative One-Step ahead. This study has shown that FTS model has the advantage because it enables the prediction of continuous API levels within a defined continuum time, which in this study was the interval time within 24 hours. Functional descriptive mean shows a bimodal pattern with a peak at 3.00 pm and the average levels are at a healthy level. Functional mean of API exhibits an increasing pattern after sunrise towards 10.00 am at both sites, which inform that, this is the time with a higher contribution of vehicles emission while the standard deviation differs in the pattern. The model is recommended as an alternative model to be used by the government and environmentalists in providing input for guiding pollution control and protecting public health at the early stage. Furthermore, as for the private sector and industries, this study might provide a predictive analytic tool for forecasting daily API curves instead of a single daily average API value.