## 3 Proposed Methods
### Feature Selection  
The selection of effective features for forecasting PM\({}_{2.5}\) concentration depends on spatiotemporal meteorological patterns and local geographical terrains. This phenomenon manifests in the discrepancy among the chosen features in the literature for studies conducted at different places [7; 15; 16; 20; 29]. It resembles the selection of appropriate functional components in the software design life cycle (SDLC) of a software project. In light of this,  
Figure 1: Architecture of our multi-model framework. we adopt the _spiral model_ broadly used in the SDLC field to determine the features which will be employed in our forecasting framework. The spiral model [10; 11; 33; 34] as shown in Figure 2 repeats spiral iterations of four phases: planning, design, conduct, and evaluation. In the planning phase, system and unit specifications are acquired. Design phase starts with the software design according to the specifications. In the construct phase, the code implementation of the system prototype is fulfilled. In the evaluation phase, the users' feedback with the prototype is collected for system evaluation and risk analysis. Then the software development process enters into the next spiral iteration to enhance the feedback evaluation and resolve the risk until the system evaluation and incurred risk are acceptable. The planning and design in the SDLC depend on the system requirement and unit specifications which are not complete enough in the early SDLC phases, so the spiral model allows the software development to incrementally converge to the ideal system. Analogously, the design of effective features for forecasting PM\({}_{2.5}\) depends on the geographical places where the investigation is conducted because the formation of PM\({}_{2.5}\) concentrations are highly related to local anthropogenic and meteorological patterns. Therefore, we adapt the spiral model to a feasible feature selection model for prediction of PM\({}_{2.5}\) concentration. We start with an initial set of diverse features which are determined by the literature review and our own invention, such as the temporal periodical features and compound features. Then, in each spiral iteration, we respectively remove each feature from the current set to conduct the production of respective new system prototypes with the same training set. The resulting risk (prediction RMSE as will be defined) of each system prototype is evaluated from system simulation over the validation set. Based on the evaluation, the feature whose test removal has resulted in the remaining feature set having the minimum risk in terms of RMSE with the validation set is actually removed from the current feature set. Then the spiral feature validation process enters into the next spiral iteration until the current feature set contains only one feature. Finally, the best set of features can be determined by comparing the risk variations of generated prototypes along the spiral iterations. In the following, we describe our feature engineering process in detail. Table 2 shows the initial set of features with which we start the spiral validation process for feature selection. The initial set contains 20 features determined by our own invention (the periodic features and short-term compound features as will be noted) and the literature review (the meteorological and autoregression features). These features are classified in four categories. (1) _Periodic variables_. We preliminarily examined our dataset and found a commonly observed situation in Puli Township that the daily low PM\({}_{2.5}\) appears in early afternoon, and the daily high PM\({}_{2.5}\) is usually observed around midnight. Figure 3a shows a typical example of daily periods observed within 1 February 2011 and 8 February 2011. We anticipate that this salient daily period would be a useful  
Figure 2: The spiral model of software development life cycle. indicator for adjusting the prediction for PM\({}_{2.5}\) concentration.