## 2 Related Work and Contributions
### Research Trends and Contributions of This Paper  
Depending on the applications, the time unit for PM\({}_{2.5}\) forecasting varies significantly. For short-term forecasting, the PM\({}_{2.5}\) concentration is estimated for the next immediate hour or in the next 6 h, 12 h, or 24 h [8; 9; 17; 22; 27; 29]. For middle-term forecast, the daily and weekly PM\({}_{2.5}\) concentration are predicted in [7; 15; 16; 18; 19; 20; 21; 23; 26; 28; 30]. Relatively few works [18; 23] have contemplated the long-term prediction such as seasonal and yearly PM\({}_{2.5}\). For the country of the studied area, most existing works chose the cities in China as their investigation fields because these cities are among those which have the most serious PM\({}_{2.5}\) pollution in the world. Some other studies have been conducted in the rest of Asia (e.g., Taiwan, Iran, and India) and America (USA, Chile). From our literature review, we observe three research trends as follows. (1) The regression techniques and the machine learning (including ANN) models constitute the two main classes of approaches used in the literature for PM\({}_{2.5}\) forecasting. (2) Both parametric (which requires explanatory variables) and non-parametric (which requires no explanatory variables) models are widely adopted in the literature, and there are no significant performance advantages of one over the other. Various phenomena reveal that the relationship between PM\({}_{2.5}\) concentrations and the explanatory variables is too complex to be described by a parametric model. The PM\({}_{2.5}\) time series itself manifests some salient trends and the usage of non-parametric model is desired to realize the temporal trends. (3) Different lengths of training time span have been considered in the literature. It ranges from a week [8], a month [28; 29], to multiple years [7; 15]. Nevertheless, none of the approaches in the literature has fused both the short-term and long-term learning. This is the promising direction that will be explored in this paper. (4) An increasing number of recent work has developed hybrid approaches which combine multiple models in a single framework to exploit the strengths and weaknesses of individual models. In particular, regression has been hybridized with ANN [9] and SVM [8]. The characteristics of existing literature can be compared according to the following three aspects: forecasting approaches, time unit of forecasting, and the country of studied area, as listed in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline [PERSON] and [PERSON], 2015 & & & & & day & China \\ [PERSON] et al., 2015 & & & & & \(\bullet\) & day & Taiwan \\ [PERSON] et al., 2016 & & & & & & day & China \\ [PERSON] and [PERSON], 2016 & & & & & & day & Iran \\ [PERSON] et al., 2016 \({}^{*}\) & & & & & \(\bullet\) & day & USA \\ [PERSON] et al., 2016 & & & & & & hour & China \\ [PERSON] et al., 2017 & & & & & hour/day & China \\ [PERSON] et al., 2017 & & & & & day & China \\ [PERSON] et al., 2017 \({}^{*}\) & & & & & hour & China \\ [PERSON] and [PERSON], 2017 & & & & & day & China \\ [PERSON] et al., 2017 & & & & & hour & China \\ [PERSON] et al., 2017 & & & & & \(\bullet\) & hour & India \\ [PERSON] et al., 2017 & & & & & day & China \\ [PERSON] et al., 2018 & & & & & hour & Chile \\ [PERSON] et al., 2019 \({}^{*}\) & & & & & hour & China \\ [PERSON] et al., 2019 & & & & day/season/year & USA \\ [PERSON] et al., 2019 & & & & & hour & China \\ [PERSON] et al., 2020 & & & & week/season/year & China \\ [PERSON] et al., 2020 & & & & day & China \\ [PERSON] et al., 2020 \({}^{*}\) & & & & hour & India \\ \hline \end{tabular} \({}^{*}\) hybrid approaches.  
\end{table} 
Table 1: Comparison of recent works on PM\({}_{2.5}\) forecasting. In light of these trends, this paper proposes (1) a multi-model ensemble framework for the next 24-h PM\({}_{2.5}\) concentration forecast in Puli, Taiwan. The multiple models complement one another from different learning perspectives and they collaborate to maximize the overall performance.