A Methodology to Increase the Accuracy of Particulate Matter Predictors Based on Time Decomposition

Abstract

Particulate matter (PM) is one of the most harmful air pollutants to human health studied worldwide. In this scenario, it is of paramount importance to monitor and predict PM concentration. Artificial neural networks (ANN) are commonly used to forecast air pollution levels due to their accuracy. The use of partition on prediction problems is well known because decomposition of time series allows the latent components of the original series to be revealed. It is a matter of extracting the “deterministic” component, which is easy to predict the random components. However, there is no evidence of its use in air pollution forecasting. In this work, we introduce a different approach consisting of the decomposition of the time series in contiguous monthly partitions, aiming to develop specialized predictors to solve the problem because air pollutant concentration has seasonal behavior. The goal is to reach prediction accuracy higher than those obtained by using the entire series. Experiments were performed for seven time series of daily particulate matter concentrations (PM_2.5 and PM₁₀–particles with diameter less than 2.5 and 10 micrometers, respectively) in Finland and Brazil, using four ANNs: multilayer perceptron, radial basis function, extreme learning machines, and echo state networks. The experimental results using three evaluation measures showed that the proposed methodology increased all models’ prediction capability, leading to higher accuracy compared to the traditional approach, even for extremely high air pollution events. Our study has an important contribution to air quality prediction studies. It can help governments take measures aiming air pollution reduction and preparing hospitals during extreme air pollution events, which is related to the following United Nations sustainable developments goals: SDG 3—good health and well-being and SDG 11—sustainable cities and communities.

1. Introduction

According to the World Health Organization [1], nine out of ten people are exposed to high air pollution levels. In this sense, particulate matter (PM) is considered one of the most harmful air pollutants, since it can be deposited in the lungs, reaching the alveoli and bloodstream [2]. It can also cause severe cardiopulmonary diseases, lung cancer, even death [3,4]. Many epidemiological studies have already shown the association between particulate matter concentration and cardiopulmonary diseases, or even mortality [3,4,5,6,7]. In recent years, approximately 7 million deaths were caused by fine particles, which present an aerodynamic diameter of less than 2.5 micrometers (PM_2.5) [1]. Monitoring and forecasting PM concentrations in the air are essential to the population, health institutions, and governments worldwide [1].

In this context, we highlight the forecasting systems based on artificial neural networks (ANNs), due to the excellent performances demonstrated in the literature [8,9,10,11,12,13,14,15]. These systems generally employ two data-driven approaches for ANN adjustment: the use of only previous (historical) data of PM concentration [12,13,16,17] or the use of the historical data of PM jointly with related features, such as temperature, relative humidity, wind speed and direction, and others [8,9,10,11,14,18,19,20,21].

Traditionally, systems based on ANN use only one forecasting model for the entire series [8,9,10,12,13,14,15,16]. However, some works [19,20,21,22,23,24,25,26,27,28] address a set of predictors for a specific part of the series. Based on the literature, the latter approach has not been employed to predict particulate matter time series [29,30,31,32]. The use of partition on prediction problems is well known because decomposition of time series reveals the latent components of the original series. It is a matter of extracting the “deterministic” component, making it easier to predict the random components. However, there is no evidence of its use to air pollution forecasting [33,34,35]. Yet, it has been used in other scenarios, such as hydrology [36], finance [22,23,25], energy [37], and natural phenomena [24].

This paper introduces a different time series forecasting approach, which consists of decomposing the series in contiguous (non-overlapping) partitions (time windows). The decomposition is performed for generating sub-series from the series under analysis, aiming to obtain a prediction accuracy higher than the one obtained with the conventional approach, using the entire series. This process is conducted to get an average coefficient of variation (CV) lower than the CV calculated in the whole series. This proposal is based on two premises: (i) PM concentration time series have specific patterns in different epochs of the year [38,39,40,41], and (ii) a set of predictors modeled for specific patterns present into time windows reaches better results of accuracy than a single forecasting model for the entire series [22,23,24,25,26].

We used seven time-series of daily PM levels comprising data from Helsinki–Finland, and São Paulo, Campinas, and Ipojuca–Brazil to assure the robustness of the proposed approach. Each series is decomposed into twelve sub-series, one for each month of the year. Subsequently, a forecasting method is specifically modeled for each case. In this paper, we employed four artificial neural network architectures: multilayer perceptron (MLP), radial basis function network (RBF), extreme learning machines (ELM), and echo state networks (ESN), considering the traditional and the monthly approach.

The rest of this paper is organized as follows: Section 2 introduces the proposed methodology; Section 3 depicts the case studies; Section 4 presents the computational results and critical analysis; and Section 5 shows the main conclusions.

2. Proposed Methodology

The methodology can be divided into two phases: training and testing. Figure 1 depicts the general framework of the first phase. In this case, the dataset is divided into n sub series (partitions), such that the partitions attend a given statistical condition. Then n prediction models are trained, one for each of the n partitions.

In the first step of Figure 1, a seasonality test is performed to determine the series’ seasonal period. In this work, we used Friedman’s test and Kruskal-Wallis test [42]. For example, suppose we assume that the PM time series presents similar patterns in a monthly fashion based on the statistic tests. In that case, a forecasting model is employed to perform daily predictions in a specific month. The objective is to build models specialized for each month, since similar patterns may be present in the same month. These models are selected based on the current prediction month.

A statistical test is adopted using the coefficient of variation (CV) analysis, which should answer the question: “Is the mean CV calculated from partitions smaller than the CV of the entire series?” We adopted this step, given the existence of a relationship between predictability and CV demonstrated by [43,44,45]. The purpose of employing a seasonality test is to find time series partitions with lower CV values than the entire time series.

Figure 2 depicts the framework of the testing phase. The first part consists of determining the partition used for the prediction purpose. For partition j, the system uses the F_j model, which was previously designed (in the training phase) precisely to predict the j-th sub series (in the j-th partition). The definition of the number of subseries is based on the seasonality tests above mentioned and the mean CV values, in which the value n = 12 achieved the best results. Furthermore, n = 12 also represents the seasonal component of the series. Thus, if the prediction is performed in March, then the F₃ model is used; if it is performed in December, the F₁₂ model is used.

Different scenarios used this monthly approach. Ballini et al. [46] used fuzzy inference systems for identifying two hydrological processes and their use in generating synthetic monthly inflow sequences. Luna and Ballini [37] addressed monthly electrical energy demand forecasting to an energy enterprise in Brazil’s Southeastern region. At the same time, Siqueira et al. [27,28] proposed a similar methodology for a seasonal streamflow series forecasting released to hydroelectric plants. In such studies, the lags (inputs) of the models were the previous month data. For example, to predict May 2010, the entries were April, March, and February samples from 2010. However, there are essential differences between the method introduced in this work and the approaches mentioned above:

• A seasonality test is conducted to find a suitable seasonal period for the series;
• The calculation of the CV is employed to determine which partitions present similar patterns;
• MLP, RBF, ESN, and ELM are used to assess the proposed methodology.

It is remarkable that in the traditional approach, a forecasting model needs to learn the statistical fluctuations of nonlinear mapping for all months of the year. In the proposed approach, despite having less data to adjust, it only needs to learn the month’s statistical fluctuations in evaluation.

2.1. Partition Creation and Calculation of the Coefficient of Variation

Figure 3 shows the partitioning scheme proposed in this work. The training set is composed of daily records of m full years. The 12 partitions are created by grouping the data of each month in a different setting. Thus, Partition₁ corresponds to the training data only of January from Year 1 to Year m, Partition₂ is the training data of February from Year 1 to Year m, and so on.

As each partition contains data specific to a particular month, it is expected that similar temporal patterns are clustered. Consequently, one expects a favorable scenario to present lower values of the CV in the partitions in comparison to the CV in the entire series. Since low/high values of the CV point to low/high data fluctuations, a correspondingly high/low predictability is expected, some works in the literature, e.g., [43,44,45,47,48,49], used this measure in different forecasting applications.

Kahn [44] addressed the CV as a measure of predictability in the sales support and operations planning process. Fatichi et al. [49] used it to investigate the inter-annual variability of precipitation on a global scale. Bahra [48] used a market’s implied risk-neutral density (RND) function measure based on the CV as a volatility forecasting tool.

2.2. Forecasting Models Used in the Proposed Approach

The ANNs have been widely used in time series forecasting, including air pollution prediction and control [50,51,52,53]. In this work, we used four different neural models in the framework depicted in Figure 1: multilayer perceptron (MLP), radial basis function network (RBF), extreme learning machines (ELM), and echo state networks. These models were selected due to their extensive use in time series forecasting [8,9,10,11,12,13,14,15,16,28,46,54,55,56]. These ANN architectures can approximate any nonlinear, continuous, limited, and differentiable function, being universal approximators [57].

2.2.1. Multilayer Perceptron

The MLP is a feedforward artificial neural network (ANN) with multiple layers of artificial neurons (nodes) [27]. The artificial neurons of layer i are entirely connected to the subsequent layer’s nodes (i + 1).

This architecture can have three or more layers [57]:

• Input layer: transmits the input signal to the hidden layers;
• Hidden (intermediate) layers: these set of neurons performs a nonlinear transformation, mapping the input signal to another space;
• Output layer: this layer receives the signal from the hidden layers and generates a combination to form the network’s output. Often this process is based on linear combinations.

In this work, we addressed MLP with just one hidden layer. Let u be the vector containing the inputs, b the bias vector, $w_{kn}^i$ the intermediate layer weights. The variable n = 1, …, N is the index of each input, k = 1, …, K is related to each neuron, and $w_{1n}^0$ are the weights of the output neuron. The output response of the network is given by Equation (1):

$$y=f_s\left[{\displaystyle \sum _{k=1}^K{w}_{1k}^0\left(f\hspace{0.17em}\left({\displaystyle \sum _{n=1}^N{w}_{k\hspace{0.17em}n}^i\hspace{0.17em}{u}_n}+b\right)\right)}\right],$$

(1)

in which f is the activation function of the hidden neurons and f_s a linear activation function of the output layer.

The training process of an ANN is defined as the steps to find its best set of weights to solve the task. In an MLP, the most usual way to adjust the network is to use an iterative process, resorting the solution of an unrestricted nonlinear optimization algorithm. The MLP architecture used in this work has three layers, and the training process is based on the modified scaled conjugate gradient, a second-order method [27].

2.2.2. Radial Basis Function Network

The radial basis function network (RBF) is also a widely known ANN framework, with two neuron layers: hidden and output layers. The first performs an input-output mapping, based on kernel (activation) functions of radial basis. In the hidden layer, each neuron presents two free parameters, a center, and a dispersion. The most used function is the Gaussian, given by Equation (2):

$$\phi \left(u\right)=e^{-\frac{{\left(u-c\right)}^2}{2{\sigma }^2}},$$

(2)

where c is the center of the Gaussian function, and σ² is its variance.

The second layer conducts a combination of the previous layer’s outputs, in many cases, using a linear approach [57].

The training step of an RBF is performed following two stages. Initially, the weights of the hidden layer are adjusted, calculating their centers and dispersions. This task is performed using non-supervised clustering methods, like the K-Medoids. The second step is accomplished tuning the weights of the output layer. One can use a linear procedure to combine the outputs of the hidden layer. In this work, we address the Moore-Penrose pseudoinverse [58]. This operation ensures the minimum mean squared error (MSE) in the output. This solution is present in Equation (3):

$$W^{out}={\left(X_{hid}^T{X}_{hid}\right)}^{-1}\hspace{0.17em}\hspace{0.17em}{X}_{hid}^{T}d,$$

(3)

where X_hid is the matrix containing the outputs of the hidden layer for the training set, W^out the weights of the output layer, and d the desired output.

2.2.3. Extreme Learning Machines

Extreme learning machines (ELM) [55] are single layer feedforward neural networks, with high similarity with the traditional MLP. The main difference between them is the training since, in this case, the hidden layers are not adjusted during the training process [28]. In this phase, just the output layer is tuned [27]. Therefore, its training processes require less computational effort than the previous. As the MLP, the ELM is a universal approximator.

Consider u the vector of inputs and b the bias. The output of the hidden layer is given by Equation (4):

$$x^h=f^h\left(W^h\hspace{0.17em}u+b\right),$$

(4)

where W^h is the matrix containing the hidden layer weights and f^h(.) is the matrix of the activation functions of these neurons.

The output of the network is given by Equation (5):

$$y=W^{out}{x}_n^h,$$

(5)

in which W^out is matrix with the weights of the output layer.

The training process is summarized in finding the weights of the output layer, while W is randomly chosen. The most usual way to solve this task is applying the same Moore-Penrose pseudoinverse operator depicted in the RBF case.

2.2.4. Echo State Networks

Echo state networks (ESN) are recurrent ANN, since they present feedback loops of information in the hidden layer, named dynamic reservoir here [56]. This characteristic can be an advantage, especially in problems with temporal dependence between the samples. As the ELM, the training process of an ESN just adjusts the output layer.

Jaeger [56] proved the possibility of settting in advance the weights of the neurons in the reservoir, and kept unchanged during the training, under specific conditions [27,28].

The output of the reservoir x_n+1 is given by Equation (6):

$$x_{n+1}=f\left(W^{in}\hspace{0.17em}{u}_{n+1}+W\hspace{0.17em}{x}_n\right),$$

(6)

being u_n+1 the input signal, Wⁱⁿ the matrix containing the weights of the input layer, W the weights of the reservoir that presents the feedback connections’ synaptic weights and f(.) the respective activation functions.

The output y of the network is as in Equation (7):

$$y_{n+1}=W^{out}\hspace{0.17em}{x}_{n+1},$$

(7)

where W^out contains the weights of the output layer.

There are some manners to generate the weights of the reservoir. In this work, we address the proposal from Jaeger [56], presented in Equation (8):

$$W=\{\begin{array}{c}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0.4 \mathrm{with} \mathrm{probability} 0.025\\ \begin{array}{l}\hspace{0.17em}-0.4 \mathrm{with} \mathrm{probability} 0.025\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}0.0 \mathrm{with} \mathrm{probability} 0.950\end{array}\end{array}.$$

(8)

Once again, we use the Moore-Penrose pseudoinverse operator to train the network [59,60,61].

3. Case Studies

Aiming to analyze if the proposed methodology brings gains to any studied location, we chose databases from two countries with specific climate and emission sources (Brazil and Finland). The case studies consist of predicting PM₁₀ and PM_2.5 to four different areas, with distinct characteristics. Helsinki (Kallio station—PM₁₀ and PM_2.5, and Vallila station—PM₁₀), São Paulo city (Tietê station—PM₁₀ and PM_2.5), Campinas city (PM₁₀) (São Paulo State, Brazil), and Ipojuca city, Pernambuco State, Brazil (Ipojuca station—PM₁₀).

São Paulo and Campinas cities are in Southeast Brazil. São Paulo city is the capital of São Paulo state and the most populous city in Brazil, with 12,252,023 inhabitants, 969.32 km² urban area, out of the total area—1521.11 km²—and demographic density of 7398.26 inhabitants per km² [62]. It is the leading business and commercial, the financial center of South America with a Human Development Index of 0.805 [59,63]. Campinas city is the third most populous municipality in São Paulo state, Brazil, occupying 797.6 km², with an urban area of 238.2 km², and 1,194,094 inhabitants, demographic density of 1359.60 inhabitants per km² [62]. Campinas and São Paulo have similar climates, with hot and rainy long summers and shorter winters with mild temperatures. The temperature ranges from 13 °C to 29 °C, rarely reaching values below 9 °C and above 33 °C [64].

Ipojuca city, Pernambuco state, Brazil, is located in the Brazilian Northeast, metropolitan region of Pernambuco state capital—Recife. It is a coastal city with 96,204 inhabitants and a demographic density of 152.98 inhabitants per km² [62]. With a hot and windy climate, the temperature ranges from 22 °C to 32 °C, rarely reaching values below 21 °C and above 34 °C [64].

Helsinki is the capital and the most populous city of Finland, with 655,276 inhabitants and an urban area of 1,268,296 km² [62]. It is the most important center of Finland for politics, education, finance, culture, and research in Finland. Helsinki weather differs significantly from the other studied cities, with temperature ranging from −8 °C to 21 °C, rarely reaching values below −19 °C and above 26 °C [64].

The demographic, business, and meteorological characteristics of each studied city are distinct and will ensure the proposed methodology is relevant to any location. Additionally, they present variable emission sources.

Figure 4 and Figure 5 show each station’s location from Brazil and Finland, respectively. São Paulo and Campinas are mainly affected by vehicular emissions. São Paulo station is near a ring road, being influenced mainly by heavy-duty emissions. In contrast, Campinas station is located near one of the city’s main avenues (urban area) with predominantly light-duty emissions. Ipojuca station is near a petrol refinery (industrial area) and port of Suape, a different emission pattern than Campinas and São Paulo. Beyond the demographic, business, and meteorological differences from Helsinki to Brazil, Kallio station is an urban background, and Vallila is in the city downtown, with high traffic [13,16,21]. We highlight the data from Finland were addressed in important investigations about air pollution forecasting [13,16,21].

Table 1. Number of samples, data range and considered pollutant to each studied station.

Station	Number of Samples	Time Range	Data Source
Kallio–PM10	1090	Jan 1st 2001 to Dec 31st 2003	[66]
Kallio–PM2.5	1095	Jan 1st 2001 to Dec 31st 2003	[66]
Vallila–PM10	1092	Jan 1st 2001 to Dec 31st 2003	[66]
São Paulo–PM10	1095	Jan 1st 2017 to Dec 31st 2019	[67]
São Paulo–PM2.5	1095	Jan 1st 2017 to Dec 31st 2019	[67]
Campinas–PM10	731	Jan 1st 2007 to Dec 31st 2008	[67]
Ipojuca–PM10	632	Jul 17th 2015 to Apr 9th 2017	[68]

shows the number of samples and studied period for each station considered in this work. Additionally, we present the data source for each one. It is relevant to highlight the time range for Ipojuca station, leaving some months (May and June) with data for a year only. The time range is variable for each station, to comprise a different database and analyze the robustness of the proposed approach. The Kallio and Vallila time series were used, even with the old-time range, as the literature’s remarkable works [10,14,65] used it.

Table 2. Mean, standard deviation, maximum and minimum values for each studied station.

Pollutant	Station	Mean	S. Deviation	Max	Min
PM10 [µg/m3]	Kallio	16.7	9.91	80.0	2.9
	Vallila	20.3	12.69	138.0	3.1
	São Paulo	32.1	17.30	102.4	5.5
	Campinas	38.0	15.25	128.7	12.2
	Ipojuca	35.8	11.13	78.7	2.8
PM2.5 [µg/m3]	Kallio	8.8	5.48	56.8	1.8
	São Paulo	19.7	11.37	64.1	3.4

shows the mean, standard deviation, maximum and minimum values of PM₁₀ and PM_2.5 concentrations for each station. There is high variability between databases. With maximum PM₁₀ levels ranging from 78.7 to 138 µg/m³, and the means varying from 16.7 to 38 µg/m³. We have only two PM_2.5 available databases, but with distinct values. São Paulo station has higher levels of PM_2.5 than Kallio. This information shows the diversity of our data that is important to test the proposed methodology’s robustness. Figure A1, Figure A2, Figure A3, Figure A4, Figure A5, Figure A6 and Figure A7 in Appendix A show each station and pollutant concentrations during the studied period to illustrate the databases’ temporal variability.

4. Computational Simulations

Before applying the methodology, the database is divided into three sets:

• Test set, for performance evaluation: it is composed of the last 10 samples of each month (for example, in January, we used the data from 22nd to 31st);
• Validation set, to avoid the excessive adjustment (only to the MLP): formed by the last 10 samples of the remainders of each month, excepting the test (in January, we used the data from 12nd to 21st);
• Training, to adjust the free parameters of the neural models: the remainder samples.

We standardized the test set to all months in 10 samples, since for Ipojuca series, there are two cases in which just one month of daily data (April and May 2016) is available. In this sense, we have 30 samples to adjust and evaluate the predictor’s performances to the decomposed series.

For all experiments, we normalized the dataset in the interval [−1, +1]. It is mandatory for neural models due to the saturation provided by the hyperbolic tangent activation functions [57].

The models’ performance was determined based on five measurements, depicted in Equations (9)–(13) [69,70]:

• Mean squared error (MSE):

  $$MSE=\frac{1}{N_s}{\displaystyle \sum _{t=1}^{N_s}{\left(x_t-{\widehat{x}}_t\right)}^2}$$

  (9)

  where $x_t$ is the observed sample in time t, ${\widehat{x}}_t$ is the prediction, and N_s the number of predicted samples.
• Mean absolute error (MAE):

  $$MAE=\frac{1}{N_s}{\displaystyle \sum _{t=1}^{N_s}\left|x_t-{\widehat{x}}_t\right|}$$

  (10)
• Mean absolute percentage error (MAPE):

  $$MAPE=100\times \frac{1}{N_s}{\displaystyle \sum _{t=1}^{N_s}\left|\frac{x_t-{\widehat{x}}_t}{x_t}\right|}$$

  (11)
• Root mean squared error (RMSE):

  $$RMSE=\sqrt{\left(\frac{1}{N_s}{\displaystyle \sum _{t=1}^{N_s}{\left(x_t-{\widehat{x}}_t\right)}^2}\right)}$$

  (12)
• Index of agreement (IA):

  $$IA=1-\left(\frac{{\displaystyle \sum _{t=1}^{N_s}{\left(x_t-{\widehat{x}}_t\right)}^2}}{{\displaystyle \sum _{t=1}^{N_s}{\left(\left|{\widehat{x}}_t-\overline{x}\right|+\left|x_t-\overline{x}\right|\right)}^2}}\right)$$

  (13)

  in which $\overline{x}$ is the average of the observed series.

For the MSE and MAPE measures, the lower their values, the more accurate the model was. The IA varies in the range of [0, 1], and the higher its value, the better is the accuracy.

We performed 30 simulations for each PM series. The best configuration was selected based on the highest MSE value in the validation set. For all experiments, the models were evaluated in the one-step-ahead forecasting from the testing set. We highlight that the number of inputs, corresponding to time lags of the time series [71], is established from the wrapper method [72], considering the MSE as the evaluation function [73]. We considered up to 10 lags.

Table 3. Coefficient of variation (CV) for particulate matter (PM) concentration time series.

	Partition	Coefficient of Variation (CV)												Mean CV
Kallio PM10	Without Partition (whole series)	0.60												0.60
	Annual Partition	0.55				0.68				0.54				0.59
	Monthly Partition	0.44	0.69	0.49	0.53	0.40	0.36	0.48	0.57	0.68	0.56	0.39	0.54	0.51
Kallio PM2.5	Without Partition (whole series)	0.62												0.62
	Annual Partition	0.54				0.69				0.60				0.61
	Monthly Partition	0.52	0.64	0.71	0.48	0.48	0.37	0.39	0.74	0.60	0.57	0.48	0.80	0.57
Vallila PM10	Without Partition (whole series)	0.63												0.63
	Annual Partition	0.52				0.71				0.58				0.60
	Monthly Partition	0.43	0.65	0.53	0.60	0.40	0.35	0.32	0.59	0.55	0.71	0.46	0.57	0.51
S Paulo PM10	Without Partition (whole series)	0.52												0.52
	Annual Partition	0.54				0.56				0.51				0.53
	Monthly Partition	0.33	0.4	0.37	0.45	0.46	0.44	0.46	0.59	0.50	0.42	0.36	0.37	0.43
S Paulo PM2.5	Without Partition (whole series)	0.57												0.57
	Annual Partition	0.56				0.60				0.56				0.57
	Monthly Partition	0.34	0.38	0.39	0.45	0.47	0.48	0.47	0.59	0.52	0.42	0.37	0.35	0.44
Campinas PM10	Without Partition (whole series)	0.41												0.41
	Annual Partition	0.41						0.37						0.39
	Monthly Partition	0.28	0.22	0.30	0.27	0.35	0.38	0.35	0.32	0.44	0.35	0.24	0.26	0.31
Ipojuca PM10	Without Partition (whole series)	0.31												0.31
	Annual Partition	0.28				0.32				0.27				0.29
	Monthly Partition	0.32	0.31	0.31	0.24	0.48	0.24	0.35	0.30	0.23	0.21	0.18	0.22	0.28

shows the calculation of the coefficient of variation (CV) for all series regarding different scenarios: without a partition (whole series), with an annual partition (separated by year), and monthly partition. The values in bold indicate the months in which the CV is smaller than the CV of the series without partition or annual partition. Note that Campinas series presents just two years.

The CV (Table 3) has a reduction tendency when using the monthly partition. Comparing the CV of monthly partition to annual and without partition, we can observe that it showed lower values from 6 to 11 months. Additionally, the mean coefficient of variation (right column of Table 3) decreased when we employed the monthly partition to all studied time series, which means our approach may lead to better forecasting performances.

4.1. Results

Table 4. MSE for Kallio PM₁₀. The best values by month are highlighted in bold.

Method	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	33.79	54.96	53.72	27.25	38.33	10.82	29.72	7.69	5.20	54.47	8.24	15.19
RBFPP	21.41	35.13	38.06	24.47	30.08	9.08	31.14	4.65	4.73	34.21	6.83	15.68
ELMPP	29.42	79.28	59.10	31.86	39.42	15.09	46.66	14.10	9.09	42.57	7.58	20.39
ESNPP	23.59	56.50	45.52	32.84	27.31	8.88	37.14	7.57	5.24	36.39	7.48	16.81
ARPP	24.37	33.48	76.04	30.05	34.31	11.86	37.25	11.61	8.16	41.06	7.27	20.95
MLPTR	36.37	75.82	53.34	25.55	44.51	13.80	35.55	10.85	10.26	52.37	11.11	25.56
RBFTR	38.82	78.13	46.95	22.37	47.54	15.40	32.90	12.90	12.28	57.20	13.45	26.61
ELMTR	31.62	74.93	39.17	16.79	38.90	14.18	35.60	9.09	7.50	52.72	9.94	22.00
ESNTR	31.48	76.61	49.01	22.46	51.36	14.15	33.70	11.19	7.93	54.40	10.39	22.07
ARTR	103.18	116.57	173.42	107.56	113.79	33.00	51.40	23.00	20.84	83.75	32.82	27.27
PERS	34.87	57.26	78.32	32.15	44.92	16.43	36.32	15.54	16.74	72.91	15.24	32.72

,

Table 5. MSE for Kallio PM_2.5. The best values by month are highlighted in bold.

Method	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	6.41	13.51	29.91	12.90	7.03	1.76	14.24	1.32	2.55	32.71	0.99	14.01
RBFPP	6.43	17.22	29.86	10.82	4.84	2.23	16.10	1.40	6.27	8.17	1.49	9.18
ELMPP	5.06	25.50	27.43	18.22	6.95	3.63	12.08	3.41	7.69	33.36	1.94	16.64
ESNPP	8.45	15.02	24.61	11.34	6.75	2.20	4.82	2.99	5.50	28.27	1.95	12.93
ARPP	11.39	16.73	56.51	22.50	7.17	2.73	11.29	2.16	7.28	30.48	1.85	14.34
MLPTR	9.35	36.07	43.18	20.21	7.58	4.09	20.30	2.58	9.59	37.35	2.12	20.92
RBFTR	39.13	46.18	46.49	52.77	20.02	6.78	22.89	3.73	26.26	31.27	10.69	36.23
ELMTR	4.95	31.75	42.73	17.92	7.33	3.56	12.72	2.23	8.06	34.14	2.15	18.79
ESNTR	11.86	25.83	40.35	21.53	7.98	4.15	11.88	3.51	9.16	35.85	1.84	21.25
ARTR	58.30	188.61	217.16	92.71	30.99	17.01	79.73	7.10	60.99	106.93	10.98	34.32
PERS	16.40	22.77	67.26	29.09	9.08	4.76	16.15	3.02	14.46	44.13	2.47	33.33

,

Table 6. MSE for Vallila PM₁₀. The best values by month are highlighted in bold.

Method	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	42.06	76.13	75.64	30.58	27.42	23.16	17.79	6.40	74.74	73.58	16.43	22.69
RBFPP	18.75	59.08	80.90	45.65	22.84	23.91	14.08	4.33	37.84	35.48	12.67	17.96
ELMPP	47.77	86.75	180.87	68.37	20.55	25.88	21.18	11.39	75.77	75.67	7.85	27.25
ESNPP	34.15	31.77	176.27	83.43	25.28	13.41	9.92	7.13	59.59	34.95	14.92	17.91
ARPP	48.33	74.74	199.81	58.92	31.84	44.52	10.63	8.01	84.54	84.54	15.19	26.91
MLPTR	60.01	107.66	260.43	38.51	34.04	40.02	26.00	7.54	75.85	75.85	9.72	21.69
RBFTR	58.16	84.31	242.66	59.80	23.17	56.10	30.12	8.30	90.22	90.22	12.79	21.92
ELMTR	59.38	102.80	228.67	42.17	36.35	36.13	24.36	8.16	84.25	84.25	9.53	22.17
ESNTR	71.34	115.27	239.23	50.10	44.84	49.51	25.52	8.67	98.79	98.79	11.26	20.20
ARTR	340.26	390.36	1562.82	223.77	170.67	176.45	126.24	29.43	158.63	158.63	36.32	43.24
PERS	73.55	105.38	332.57	56.22	46.08	58.54	23.38	10.83	135.86	135.86	13.34	29.02

,

Table 7. MSE for São Paulo PM₁₀. The best values by month are highlighted in bold.

Method	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	83.18	25.43	35.11	40.66	88.37	86.17	96.45	75.08	226.37	19.76	55.82	18.78
RBFPP	99.12	7.27	34.05	43.42	78.31	98.97	39.80	61.14	370.70	25.03	38.71	9.96
ELMPP	88.20	16.73	34.62	62.27	107.28	93.21	101.08	135.57	241.65	27.67	51.69	16.74
ESNPP	73.61	9.31	21.02	68.25	87.18	96.13	71.79	39.88	260.88	48.37	35.96	15.69
ARPP	75.76	13.27	25.09	81.89	95.36	131.43	126.04	103.74	304.84	46.40	39.04	17.09
MLPTR	115.94	27.97	31.68	139.21	125.65	136.33	231.53	170.03	284.37	120.30	100.27	17.80
RBFTR	133.41	26.47	70.20	119.44	192.56	225.62	256.58	180.61	316.18	98.14	103.74	16.50
ELMTR	124.15	28.85	32.10	135.68	118.77	125.79	207.64	151.44	266.64	110.73	92.64	14.38
ESNTR	102.98	13.89	28.01	136.71	150.38	171.41	220.79	172.95	270.97	74.31	103.01	15.37
ARTR	138.64	52.17	55.57	191.96	221.42	306.05	496.17	408.73	562.43	189.19	174.39	26.71
PERS	131.44	32.44	60.26	148.14	215.47	183.56	231.51	127.88	435.96	138.17	119.08	21.86

,

Table 8. MSE for São Paulo PM_2.5. The best values by month are highlighted in bold.

Method	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	10.30	2.75	7.99	2.46	43.76	36.35	49.64	49.46	65.77	20.48	10.34	6.13
RBFPP	27.55	3.16	10.34	8.82	34.71	21.27	46.34	47.50	96.53	13.56	17.09	4.80
ELMPP	15.71	4.26	9.18	20.40	59.60	53.02	40.52	54.93	36.99	21.25	18.95	6.26
ESNPP	26.91	2.58	10.56	18.69	30.11	36.65	34.22	39.47	67.48	16.16	15.20	7.35
ARPP	26.65	2.82	12.17	18.55	45.33	52.59	58.11	61.25	100.75	19.41	16.53	6.99
MLPTR	39.48	5.36	14.21	38.17	61.94	70.72	131.36	78.94	108.48	30.30	40.51	10.96
RBFTR	39.14	6.52	19.48	31.39	83.84	55.69	107.52	67.57	100.25	38.46	46.33	9.52
ELMTR	33.93	5.48	13.55	39.54	45.88	54.51	109.71	64.24	104.51	33.89	40.00	10.29
ESNTR	27.69	5.54	13.17	40.31	59.88	90.64	116.58	76.05	95.36	35.81	41.80	11.45
ARTR	33.36	6.75	19.42	58.86	89.82	97.71	291.64	153.85	241.77	74.66	79.37	16.97
PERS	30.93	8.21	22.38	42.97	100.33	79.20	127.24	75.87	146.63	48.68	56.56	11.55

,

Table 9. MSE for Campinas PM₁₀. The best values by month are highlighted in bold.

Method	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	14.87	11.50	64.03	33.67	91.46	59.00	76.03	302.27	42.71	37.54	32.52	43.23
RBFPP	7.84	9.42	31.84	28.78	104.30	74.89	44.87	276.74	94.13	33.39	32.20	67.83
ELMPP	10.61	9.48	47.14	36.83	88.62	97.08	43.59	359.92	38.84	59.05	29.68	47.04
ESNPP	16.19	14.89	43.80	20.99	46.39	107.17	38.97	238.39	39.71	40.45	17.74	36.03
ARPP	14.82	12.04	79.41	21.58	71.48	118.86	56.20	384.12	79.95	60.59	27.02	45.84
MLPTR	12.00	12.01	75.01	36.68	122.75	91.17	56.64	354.30	51.96	72.35	26.60	39.30
RBFTR	13.47	16.47	94.06	48.51	265.75	71.91	68.07	320.24	63.64	82.74	28.48	41.46
ELMTR	13.85	13.33	75.25	36.34	105.96	80.75	51.02	212.47	48.42	63.18	27.62	38.44
ESNTR	8.75	17.38	57.54	35.75	78.01	49.80	52.17	380.44	39.54	63.29	21.21	48.57
ARTR	47.70	30.00	200.80	188.40	340.38	219.91	127.13	993.01	119.35	269.66	85.60	103.41
PERS	14.13	20.62	116.89	42.52	96.52	85.77	76.56	578.28	74.19	105.49	40.91	60.30

and

Table 10. MSE for Ipojuca PM₁₀. The best values by month are highlighted in bold.

Method	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	41.26	81.25	19.32	20.55	176.04	72.43	53.04	21.50	19.38	43.25	20.11	6.56
RBFPP	97.72	38.99	22.46	21.20	137.01	62.80	33.18	79.39	9.88	53.88	31.14	11.34
ELMPP	102.74	33.55	33.03	24.10	176.59	58.18	34.86	49.75	21.46	44.68	11.47	8.12
ESNPP	23.09	16.03	26.33	16.35	108.81	46.49	40.17	73.25	11.57	30.73	19.35	7.63
ARPP	21.98	20.80	26.80	15.74	87.27	48.01	45.54	127.38	20.42	52.57	23.03	3.80
MLPTR	34.84	44.61	38.83	15.46	147.92	100.06	57.74	89.10	13.78	72.92	14.47	8.24
RBFTR	31.00	147.25	37.94	19.70	126.84	89.11	63.83	173.77	11.00	75.68	15.58	11.54
ELMTR	33.24	61.78	32.99	14.70	126.62	104.05	59.12	41.04	15.78	78.06	13.62	8.44
ESNTR	23.10	43.11	31.63	9.11	121.14	86.48	39.17	135.14	17.35	62.38	13.20	8.51
ARTR	45.91	46.49	79.73	61.37	563.32	238.31	102.43	248.19	34.55	99.80	29.17	21.24
PERS	37.05	49.25	46.55	19.90	227.81	141.80	66.80	213.59	18.60	84.85	16.96	16.98

show the results achieved in terms of MSE for the seven previously mentioned stations, separated by month. The subscript “PP” means the results of the proposed partition–monthly decomposition (12 predictors), while “TR” represents the traditional approach (only one predictor to the whole series). For the sake of comparison, we also performed the linear autoregressive model (AR), from the box and Jenkins family, and a simple Naive persistent method (“PERS”) [74]. The best performances by month are highlighted in bold. The decomposition was used for all three sets (training, validation, and test). Also,

Table A1. Evaluation measures to the Kallio PM₁₀. The best values by month are highlighted in bold.

	Metric	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	MSE	33.79	54.96	53.72	27.25	38.33	10.82	29.72	7.69	5.20	54.47	8.24	15.19
	MAE	4.10	6.10	5.81	4.04	4.90	2.35	4.39	2.20	1.38	3.51	2.08	3.01
	MAPE	27.72	17.70	48.69	37.98	28.64	16.00	16.52	30.19	13.31	17.89	25.94	27.18
	RMSE	5.81	7.41	7.33	5.22	6.19	3.29	5.45	2.77	2.28	7.38	2.87	3.90
	IA	0.78	0.91	0.72	0.94	0.63	0.79	0.82	0.96	0.82	0.70	0.59	0.78
RBFPP	MSE	21.41	35.13	38.06	24.47	30.08	9.08	31.14	4.65	4.73	34.21	6.83	15.68
	MAE	3.44	5.49	4.60	3.94	4.03	2.30	4.28	1.90	1.82	3.65	2.11	3.46
	MAPE	20.86	18.45	24.54	35.91	23.76	17.03	18.69	21.11	14.08	18.57	22.68	39.49
	RMSE	4.63	5.93	6.17	4.95	5.48	3.01	5.58	2.16	2.18	5.85	2.61	3.96
	IA	0.86	0.96	0.88	0.94	0.73	0.83	0.88	0.98	0.89	0.87	0.79	0.74
ELMPP	MSE	29.42	79.28	59.10	31.86	39.42	15.09	46.66	14.10	9.09	42.57	7.58	20.39
	MAE	4.16	7.70	6.30	4.70	5.03	2.81	5.94	3.02	2.81	2.98	1.92	3.58
	MAPE	23.70	23.62	51.07	44.61	30.57	19.99	25.82	46.80	23.86	12.10	25.34	43.85
	RMSE	5.42	8.90	7.69	5.64	6.28	3.89	6.83	3.75	3.01	6.52	2.75	4.52
	IA	0.70	0.86	0.69	0.92	0.60	0.70	0.59	0.90	0.62	0.75	0.63	0.60
ESNPP	MSE	23.59	56.50	45.52	32.84	27.31	8.88	37.14	7.57	5.24	36.39	7.48	16.81
	MAE	3.87	6.50	5.42	4.89	4.40	2.36	4.61	2.18	1.60	2.85	1.95	3.24
	MAPE	25.60	19.90	49.98	41.49	23.37	17.60	23.06	32.30	14.20	15.61	24.98	39.44
	RMSE	4.86	7.52	6.75	5.73	5.23	2.98	6.09	2.75	2.29	6.03	2.74	4.10
	IA	0.78	0.92	0.78	0.93	0.78	0.81	0.81	0.96	0.85	0.81	0.65	0.69
ARPP	MSE	24.37	33.48	76.04	30.05	34.31	11.86	37.25	11.61	8.16	41.06	7.27	20.95
	MAE	3.60	4.98	6.98	4.59	5.09	2.64	4.54	2.61	2.29	4.33	1.88	3.73
	MAPE	26.18	15.20	67.26	36.45	33.53	22.09	27.20	35.93	20.58	32.84	23.64	43.16
	RMSE	4.94	5.79	8.72	5.48	5.86	3.44	6.10	3.41	2.86	6.41	2.70	4.58
	IA	0.80	0.96	0.58	0.95	0.73	0.78	0.85	0.94	0.78	0.79	0.71	0.57
MLPTR	MSE	36.37	75.82	53.34	25.55	44.51	13.80	35.55	10.85	10.26	52.37	11.11	25.56
	MAE	4.96	7.38	6.57	4.26	5.23	2.67	5.30	2.51	2.77	3.71	3.05	4.14
	MAPE	29.19	22.18	44.70	38.42	28.59	18.02	25.83	37.12	23.93	19.71	30.29	41.97
	RMSE	6.03	8.71	7.30	5.05	6.67	3.71	5.96	3.29	3.20	7.24	3.33	5.06
	IA	0.63	0.87	0.73	0.95	0.59	0.75	0.79	0.94	0.59	0.68	0.72	0.59
RBFTR	MSE	38.82	78.13	46.95	22.37	47.54	15.40	32.90	12.90	12.28	57.20	13.45	26.61
	MAE	5.03	7.49	6.45	4.00	5.03	2.86	4.81	2.83	3.12	3.83	3.37	4.29
	MAPE	29.45	22.51	41.27	35.57	27.14	20.14	23.87	42.50	26.45	19.06	32.94	44.71
	RMSE	6.23	8.84	6.85	4.73	6.89	3.92	5.74	3.59	3.50	7.56	3.67	5.16
	IA	0.62	0.86	0.79	0.95	0.55	0.72	0.82	0.92	0.53	0.68	0.67	0.51
ELMTR	MSE	31.62	74.93	39.17	16.79	38.90	14.18	35.60	9.09	7.50	52.72	9.94	22.00
	MAE	4.33	7.25	5.61	3.51	4.67	2.72	5.07	2.21	2.14	3.37	2.68	3.75
	MAPE	23.73	21.80	34.52	29.79	25.59	18.57	23.09	36.00	18.20	17.14	27.52	38.47
	RMSE	5.62	8.66	6.26	4.10	6.24	3.77	5.97	3.01	2.74	7.26	3.15	4.69
	IA	0.69	0.87	0.83	0.97	0.63	0.75	0.78	0.94	0.73	0.71	0.73	0.61
ESNTR	MSE	31.48	76.61	49.01	22.46	51.36	14.15	33.70	11.19	7.93	54.40	10.39	22.07
	MAE	4.19	7.51	6.39	3.84	5.87	2.61	4.82	2.70	2.60	4.04	2.66	3.77
	MAPE	26.05	22.73	39.04	35.03	31.75	17.53	23.21	40.63	21.91	21.78	26.34	42.46
	RMSE	5.61	8.75	7.00	4.74	7.17	3.76	5.81	3.35	2.82	7.38	3.22	4.70
	IA	0.75	0.87	0.81	0.95	0.59	0.77	0.81	0.93	0.69	0.68	0.73	0.62
ARTR	MSE	103.18	116.57	173.42	107.56	113.79	33.00	51.40	23.00	20.84	83.75	32.82	27.27
	MAE	8.24	9.50	11.50	8.56	8.84	4.27	6.02	3.63	4.02	5.03	4.74	4.34
	MAPE	37.94	25.70	57.66	52.68	32.98	22.49	30.27	56.51	36.02	24.16	29.04	46.94
	RMSE	10.16	10.80	13.17	10.37	10.67	5.74	7.17	4.80	4.57	9.15	5.73	5.22
	IA	0.83	0.90	0.88	0.58	0.86	0.88	0.83	0.84	0.51	0.72	0.87	0.65
PERS	MSE	34.87	57.26	78.32	32.15	44.92	16.43	36.32	15.54	16.74	72.91	15.24	32.72
	MAE	4.19	6.64	6.88	4.97	5.59	3.56	5.09	3.40	3.45	5.57	3.41	4.70
	MAPE	27.95	21.59	41.53	38.95	33.02	25.18	26.46	45.94	28.12	30.32	35.67	40.43
	RMSE	5.90	7.57	8.85	5.67	6.70	4.05	6.03	3.94	4.09	8.54	3.90	5.72
	IA	0.76	0.92	0.76	0.94	0.68	0.79	0.85	0.92	0.54	0.73	0.57	0.62

,

Table A2. Evaluation measures to the Kallio PM_2.5. The best values by month are highlighted in bold.

	Metric	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	MSE	6.41	13.51	29.91	12.90	7.03	1.76	14.24	1.32	2.55	32.71	0.99	14.01
	MAE	1.75	2.99	4.23	2.22	2.17	1.08	3.28	0.91	1.32	3.28	0.84	3.21
	MAPE	21.69	17.09	46.94	19.36	30.25	19.27	20.73	19.70	19.68	44.55	13.94	81.17
	RMSE	2.53	3.68	5.47	3.59	2.65	1.33	3.77	1.15	1.60	5.72	0.99	3.74
	IA	0.91	0.95	0.47	0.81	0.56	0.85	0.78	0.98	0.87	0.70	0.86	0.49
RBFPP	MSE	6.43	17.22	29.86	10.82	4.84	2.23	16.10	1.40	6.27	8.17	1.49	9.18
	MAE	2.18	3.23	3.98	2.73	1.85	1.29	3.16	1.01	2.23	2.22	0.98	2.29
	MAPE	26.76	17.26	40.83	30.80	24.95	21.94	19.61	21.70	35.53	45.83	14.32	60.88
	RMSE	2.54	4.15	5.46	3.29	2.20	1.49	4.01	1.18	2.50	2.86	1.22	3.03
	IA	0.84	0.93	0.62	0.81	0.77	0.79	0.72	0.98	0.41	0.95	0.83	0.73
ELMPP	MSE	5.06	25.50	27.43	18.22	6.95	3.63	12.08	3.41	7.69	33.36	1.94	16.64
	MAE	1.95	4.17	3.83	3.31	2.26	1.51	2.97	1.39	2.13	3.13	1.11	3.56
	MAPE	25.47	27.13	45.15	32.67	30.41	28.04	18.33	34.90	32.29	45.73	18.97	87.76
	RMSE	2.25	5.05	5.24	4.27	2.64	1.90	3.48	1.85	2.77	5.78	1.39	4.08
	IA	0.90	0.90	0.44	0.65	0.61	0.57	0.85	0.94	0.50	0.70	0.65	0.42
ESNPP	MSE	8.45	15.02	24.61	11.34	6.75	2.20	4.82	2.99	5.50	28.27	1.95	12.93
	MAE	2.44	3.16	3.62	2.38	2.07	1.12	1.72	1.24	1.74	3.25	1.27	2.96
	MAPE	32.46	22.20	39.22	23.44	27.79	18.75	10.75	29.01	30.70	44.02	21.27	71.69
	RMSE	2.91	3.88	4.96	3.37	2.60	1.48	2.20	1.73	2.35	5.32	1.40	3.60
	IA	0.83	0.95	0.51	0.83	0.76	0.81	0.95	0.96	0.62	0.79	0.71	0.66
ARPP	MSE	11.39	16.73	56.51	22.50	7.17	2.73	11.29	2.16	7.28	30.48	1.85	14.34
	MAE	2.70	2.87	5.48	3.47	2.10	1.42	2.80	1.17	2.19	3.42	1.14	3.29
	MAPE	37.10	21.83	66.79	35.85	30.48	24.19	17.56	28.11	34.59	58.32	20.12	70.35
	RMSE	3.38	4.09	7.52	4.74	2.68	1.65	3.36	1.47	2.70	5.52	1.36	3.79
	IA	0.78	0.94	0.37	0.70	0.73	0.73	0.85	0.97	0.48	0.75	0.64	0.62
MLPTR	MSE	9.35	36.07	43.18	20.21	7.58	4.09	20.30	2.58	9.59	37.35	2.12	20.92
	MAE	2.35	5.20	4.58	3.37	2.04	1.73	3.44	1.27	2.41	3.44	0.90	4.13
	MAPE	26.07	31.45	53.36	32.38	23.56	27.21	20.62	31.77	34.39	46.31	12.54	94.29
	RMSE	3.06	6.01	6.57	4.50	2.75	2.02	4.51	1.61	3.10	6.11	1.45	4.57
	IA	0.80	0.83	0.42	0.65	0.54	0.73	0.68	0.95	0.44	0.68	0.77	0.42
RBFTR	MSE	11.22	227.99	162.36	379.87	9748.12	3.76	29977.90	3.25	17.72	45.03	3.37	23.05
	MAE	2.56	11.06	7.61	9.99	32.88	1.48	81.32	1.36	3.33	4.08	1.43	4.39
	MAPE	27.34	86.81	108.48	109.85	405.43	22.21	564.63	34.17	49.45	54.56	20.62	102.25
	RMSE	3.35	15.10	12.74	19.49	98.73	1.94	173.14	1.80	4.21	6.71	1.83	4.80
	IA	0.73	0.24	0.16	0.27	0.01	0.77	0.00	0.94	0.51	0.50	0.71	0.35
ELMTR	MSE	4.95	31.75	42.73	17.92	7.33	3.56	12.72	2.23	8.06	34.14	2.15	18.79
	MAE	1.95	4.72	4.63	2.87	2.03	1.58	3.00	1.16	2.27	3.10	0.96	3.86
	MAPE	21.98	29.21	53.01	25.83	23.95	24.33	19.16	29.37	33.43	45.43	13.52	89.46
	RMSE	2.23	5.64	6.54	4.23	2.71	1.89	3.57	1.50	2.84	5.84	1.47	4.34
	IA	0.88	0.88	0.41	0.68	0.66	0.76	0.83	0.96	0.49	0.71	0.81	0.47
ESNTR	MSE	11.86	25.83	40.35	21.53	7.98	4.15	11.88	3.51	9.16	35.85	1.84	21.25
	MAE	2.59	4.01	4.27	3.49	2.25	1.63	2.79	1.51	2.46	3.29	0.77	3.96
	MAPE	33.95	27.46	49.92	33.25	27.98	23.93	18.58	38.15	37.56	47.22	10.83	93.57
	RMSE	3.44	5.08	6.35	4.64	2.82	2.04	3.45	1.87	3.03	5.99	1.36	4.61
	IA	0.81	0.91	0.41	0.67	0.70	0.76	0.87	0.93	0.43	0.71	0.84	0.44
ARTR	MSE	58.30	188.61	217.16	92.71	30.99	17.01	79.73	7.10	60.99	106.93	10.98	34.32
	MAE	5.91	10.89	10.48	7.38	5.17	3.45	7.52	2.14	6.02	5.94	2.61	5.06
	MAPE	47.51	30.60	122.91	47.20	41.33	34.82	22.86	69.88	62.43	78.85	24.03	333.31
	RMSE	7.64	13.73	14.74	9.63	5.57	4.12	8.93	2.67	7.81	10.34	3.31	5.86
	IA	0.87	0.95	0.11	0.79	0.89	0.78	0.96	0.88	0.75	0.78	0.93	0.62
PERS	MSE	16.40	22.77	67.26	29.09	9.08	4.76	16.15	3.02	14.46	44.13	2.47	33.33
	MAE	2.73	3.90	6.05	4.00	2.54	1.72	3.31	1.48	2.98	4.57	1.18	4.87
	MAPE	32.16	28.30	75.79	41.74	33.83	28.28	22.63	33.82	48.57	66.59	18.14	93.74
	RMSE	4.05	4.77	8.20	5.39	3.01	2.18	4.02	1.74	3.80	6.64	1.57	5.77
	IA	0.78	0.93	0.33	0.63	0.62	0.66	0.83	0.96	0.43	0.75	0.72	0.43

,

Table A3. Evaluation measures for Vallila PM₁₀. The best values by month are highlighted in bold.

	Metric	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	MSE	42.06	76.13	75.64	30.58	27.42	23.16	17.79	6.40	74.74	73.58	16.43	22.69
	MAE	5.05	6.36	6.55	4.70	4.39	3.68	3.37	1.93	6.03	6.09	3.39	4.21
	MAPE	28.39	30.44	15.77	28.15	38.05	29.09	14.31	23.03	52.15	57.99	36.69	37.35
	RMSE	6.49	8.73	8.70	5.53	5.24	4.81	4.22	2.53	8.65	8.58	4.05	4.76
	IA	0.58	0.78	0.90	0.96	0.77	0.61	0.78	0.98	0.69	0.62	0.75	0.83
RBFPP	MSE	18.75	59.08	80.90	45.65	22.84	23.91	14.08	4.33	37.84	35.48	12.67	17.96
	MAE	3.21	5.15	6.60	5.42	4.02	4.06	3.28	1.79	4.71	5.17	2.88	3.50
	MAPE	17.96	28.04	15.92	30.75	31.83	31.63	13.99	23.34	31.36	45.27	25.87	39.08
	RMSE	4.33	7.69	8.99	6.76	4.78	4.89	3.75	2.08	6.15	5.96	3.56	4.24
	IA	0.88	0.89	0.88	0.94	0.81	0.72	0.83	0.98	0.84	0.87	0.87	0.82
ELMPP	MSE	47.77	86.75	180.87	68.37	20.55	25.88	21.18	11.39	75.77	75.67	7.85	27.25
	MAE	5.45	6.73	8.84	6.69	3.68	4.14	3.46	2.20	5.62	5.54	2.57	4.35
	MAPE	31.24	32.82	22.98	39.09	28.37	35.37	14.47	31.01	51.98	52.45	24.10	49.00
	RMSE	6.91	9.31	13.45	8.27	4.53	5.09	4.60	3.38	8.70	8.70	2.80	5.22
	IA	0.53	0.78	0.62	0.90	0.86	0.58	0.80	0.95	0.69	0.68	0.92	0.70
ESNPP	MSE	34.15	31.77	176.27	83.43	25.28	13.41	9.92	7.13	59.59	34.95	14.92	17.91
	MAE	4.21	4.52	10.58	7.54	4.06	2.98	2.55	1.99	5.45	4.83	2.95	3.45
	MAPE	29.16	17.82	28.85	46.04	30.34	22.84	11.30	25.34	48.74	43.30	32.54	38.72
	RMSE	5.84	5.64	13.28	9.13	5.03	3.66	3.15	2.67	7.72	5.91	3.86	4.23
	IA	0.80	0.95	0.75	0.87	0.81	0.81	0.91	0.97	0.72	0.82	0.78	0.82
ARPP	MSE	48.33	74.74	199.81	58.92	31.84	44.52	10.63	8.01	84.54	84.54	15.19	26.91
	MAE	5.41	6.18	10.70	5.59	4.37	5.39	2.66	2.14	6.66	6.66	3.22	4.10
	MAPE	34.39	30.93	32.54	26.61	35.15	40.44	12.53	27.62	73.17	73.17	32.47	43.21
	RMSE	6.95	8.65	14.14	7.68	5.64	6.67	3.26	2.83	9.19	9.19	3.90	5.19
	IA	0.61	0.84	0.68	0.94	0.70	0.47	0.91	0.97	0.53	0.53	0.80	0.73
MLPTR	MSE	60.01	107.66	260.43	38.51	34.04	40.02	26.00	7.54	75.85	75.85	9.72	21.69
	MAE	5.45	7.82	11.27	4.98	4.95	5.12	4.28	1.81	5.59	5.59	2.15	4.01
	MAPE	30.03	34.39	27.31	29.65	31.94	33.95	18.00	24.54	55.45	55.45	18.04	39.34
	RMSE	7.75	10.38	16.14	6.21	5.83	6.33	5.10	2.75	8.71	8.71	3.12	4.66
	IA	0.53	0.68	0.45	0.95	0.80	0.60	0.69	0.97	0.62	0.62	0.93	0.80
RBFTR	MSE	58.16	84.31	242.66	59.80	23.17	56.10	30.12	8.30	90.22	90.22	12.79	21.92
	MAE	5.45	6.63	9.74	5.97	3.96	6.00	4.40	1.87	6.50	6.50	2.71	4.04
	MAPE	29.81	29.83	21.02	33.69	27.49	39.76	17.58	25.62	62.21	62.21	23.07	41.10
	RMSE	7.63	9.18	15.58	7.73	4.81	7.49	5.49	2.88	9.50	9.50	3.58	4.68
	IA	0.56	0.77	0.41	0.92	0.85	0.46	0.59	0.96	0.62	0.62	0.90	0.79
ELMTR	MSE	138.81	77.37	1208.77	35.64	98.83	78.60	143.61	7.13	88.22	88.22	15.82	13.04
	MAE	8.77	7.01	21.17	4.09	8.59	6.34	9.29	1.81	6.45	6.45	3.09	2.95
	MAPE	50.80	27.96	74.37	24.01	57.49	45.14	40.00	23.81	67.45	67.45	28.01	27.19
	RMSE	11.78	8.80	34.77	5.97	9.94	8.87	11.98	2.67	9.39	9.39	3.98	3.61
	IA	0.48	0.79	0.32	0.96	0.65	0.59	0.66	0.97	0.61	0.61	0.89	0.89
ESNTR	MSE	71.34	115.27	239.23	50.10	44.84	49.51	25.52	8.67	98.79	98.79	11.26	20.20
	MAE	5.87	8.44	10.93	5.27	5.81	6.07	3.74	2.07	6.67	6.67	2.50	3.79
	MAPE	37.37	38.91	28.02	30.08	38.71	41.80	17.33	27.85	71.10	71.10	20.29	40.06
	RMSE	8.45	10.74	15.47	7.08	6.70	7.04	5.05	2.94	9.94	9.94	3.36	4.49
	IA	0.60	0.76	0.66	0.94	0.75	0.50	0.83	0.96	0.55	0.55	0.92	0.80
ARTR	MSE	340.26	390.36	1562.82	223.77	170.67	176.45	126.24	29.43	158.63	158.63	36.32	43.24
	MAE	14.14	15.08	28.68	12.33	11.01	10.87	8.66	3.90	8.53	8.53	4.66	5.70
	MAPE	52.31	44.46	34.82	48.39	35.63	50.34	19.68	63.15	218.30	218.30	23.13	59.52
	RMSE	18.45	19.76	39.53	14.96	13.06	13.28	11.24	5.42	12.59	12.59	6.03	6.58
	IA	0.81	0.89	0.89	0.65	0.89	0.69	0.96	0.86	0.58	0.58	0.84	0.69
PERS	MSE	73.55	105.38	332.57	56.22	46.08	58.54	23.38	10.83	135.86	135.86	13.34	29.02
	MAE	5.70	7.89	12.35	4.94	5.93	6.44	3.91	2.73	8.93	8.93	2.67	4.43
	MAPE	36.23	38.82	32.03	26.35	41.46	45.73	18.04	33.70	82.36	82.36	22.24	37.55
	RMSE	8.58	10.27	18.24	7.50	6.79	7.65	4.84	3.29	11.66	11.66	3.65	5.39
	IA	0.62	0.80	0.56	0.94	0.73	0.46	0.84	0.96	0.59	0.59	0.90	0.80

,

Table A4. Evaluation measures for São Paulo PM₁₀. The best values by month are highlighted in bold.

	Metric	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	MSE	83.18	25.43	35.11	40.66	88.37	86.17	96.45	75.08	226.37	19.76	55.82	18.78
	MAE	8.08	4.58	4.75	4.72	7.63	8.20	8.54	7.87	8.88	2.87	6.13	3.06
	MAPE	24.78	17.86	20.37	13.93	27.07	17.34	18.34	32.28	85.16	9.70	22.85	17.52
	RMSE	9.12	5.04	5.93	6.38	9.40	9.28	9.82	8.66	15.05	4.45	7.47	4.33
	IA	0.84	0.71	0.87	0.95	0.84	0.85	0.87	0.95	0.86	0.93	0.61	0.77
RBFPP	MSE	99.12	7.27	34.05	43.42	78.31	98.97	39.80	61.14	370.70	25.03	38.71	9.96
	MAE	8.19	2.15	4.54	5.68	7.22	7.66	5.33	6.57	11.99	3.98	5.08	2.76
	MAPE	23.26	7.64	20.21	17.16	22.83	17.66	9.88	26.51	133.30	11.65	18.38	15.01
	RMSE	9.96	2.70	5.84	6.59	8.85	9.95	6.31	7.82	19.25	5.00	6.22	3.16
	IA	0.76	0.92	0.81	0.92	0.85	0.81	0.95	0.96	0.72	0.87	0.64	0.90
ELMPP	MSE	88.20	16.73	34.62	62.27	107.28	93.21	101.08	135.57	241.65	27.67	51.69	16.74
	MAE	8.21	3.37	4.12	6.17	8.98	8.06	8.51	10.38	10.72	3.78	6.20	3.02
	MAPE	24.44	13.69	14.91	17.48	32.09	21.22	15.26	40.43	108.52	10.73	22.04	17.21
	RMSE	9.39	4.09	5.88	7.89	10.36	9.65	10.05	11.64	15.55	5.26	7.19	4.09
	IA	0.82	0.73	0.81	0.86	0.78	0.82	0.88	0.89	0.82	0.86	0.64	0.77
ESNPP	MSE	73.61	9.31	21.02	68.25	87.18	96.13	71.79	39.88	260.88	48.37	35.96	15.69
	MAE	7.18	2.58	3.66	6.89	7.12	8.75	6.71	5.12	10.70	5.61	4.61	2.87
	MAPE	21.37	11.62	14.34	19.26	28.41	19.03	13.34	18.49	96.85	16.38	17.52	16.72
	RMSE	8.58	3.05	4.58	8.26	9.34	9.80	8.47	6.32	16.15	6.95	6.00	3.96
	IA	0.87	0.91	0.90	0.88	0.88	0.81	0.92	0.97	0.80	0.68	0.72	0.79
ARPP	MSE	75.76	13.27	25.09	81.89	95.36	131.43	126.04	103.74	304.84	46.40	39.04	17.09
	MAE	7.61	2.66	3.88	6.70	7.83	9.90	9.85	8.58	11.67	5.40	5.20	3.51
	MAPE	24.57	12.03	15.83	20.27	31.44	22.02	19.94	38.09	110.48	15.74	19.27	18.95
	RMSE	8.70	3.64	5.01	9.05	9.77	11.46	11.23	10.19	17.46	6.81	6.25	4.13
	IA	0.86	0.83	0.87	0.83	0.85	0.74	0.85	0.92	0.79	0.67	0.67	0.84
MLPTR	MSE	115.94	27.97	31.68	139.21	125.65	136.33	231.53	170.03	284.37	120.30	100.27	17.80
	MAE	9.42	4.44	4.53	10.11	9.42	8.27	13.52	11.16	10.91	8.13	8.68	3.75
	MAPE	29.88	17.28	17.92	27.95	34.94	16.91	24.17	45.27	109.31	23.71	32.66	19.73
	RMSE	10.77	5.29	5.63	11.80	11.21	11.68	15.22	13.04	16.86	10.97	10.01	4.22
	IA	0.78	0.58	0.86	0.69	0.77	0.68	0.62	0.86	0.79	0.28	0.46	0.85
RBFTR	MSE	133.41	26.47	70.20	119.44	192.56	225.62	256.58	180.61	316.18	98.14	103.74	16.50
	MAE	10.03	4.44	7.17	9.86	12.34	14.26	14.40	11.16	10.63	7.61	8.87	3.36
	MAPE	29.25	17.18	28.39	28.42	42.87	32.88	26.20	37.63	108.96	21.48	32.18	17.88
	RMSE	11.55	5.14	8.38	10.93	13.88	15.02	16.02	13.44	17.78	9.91	10.19	4.06
	IA	0.75	0.55	0.67	0.74	0.61	0.35	0.62	0.85	0.82	0.18	0.21	0.85
ELMTR	MSE	124.15	28.85	32.10	135.68	118.77	125.79	207.64	151.44	266.64	110.73	92.64	14.38
	MAE	9.52	4.66	4.69	9.68	9.56	7.50	12.94	10.57	8.93	7.55	8.25	3.41
	MAPE	30.23	18.24	18.23	27.39	33.14	13.98	23.75	42.93	96.96	21.75	31.15	17.45
	RMSE	11.14	5.37	5.67	11.65	10.90	11.22	14.41	12.31	16.33	10.52	9.62	3.79
	IA	0.77	0.61	0.86	0.71	0.79	0.75	0.64	0.88	0.83	0.34	0.50	0.89
ESNTR	MSE	102.98	13.89	28.01	136.71	150.38	171.41	220.79	172.95	270.97	74.31	103.01	15.37
	MAE	8.76	2.54	4.72	10.27	10.02	9.90	13.03	10.87	11.38	7.23	8.57	3.40
	MAPE	27.63	11.45	18.99	32.07	36.30	26.95	23.57	38.10	100.18	22.06	33.02	17.28
	RMSE	10.15	3.73	5.29	11.69	12.26	13.09	14.86	13.15	16.46	8.62	10.15	3.92
	IA	0.83	0.85	0.91	0.75	0.70	0.74	0.64	0.85	0.80	0.58	0.45	0.86
ARTR	MSE	138.64	52.17	55.57	191.96	221.42	306.05	496.17	408.73	562.43	189.19	174.39	26.71
	MAE	10.32	5.87	6.34	11.21	12.49	14.78	20.53	16.81	15.68	10.87	11.37	4.31
	MAPE	30.28	17.99	17.57	28.68	38.44	22.41	27.07	75.76	89.67	24.01	32.63	17.18
	RMSE	11.77	7.22	7.45	13.86	14.88	17.49	22.27	20.22	23.72	13.75	13.21	5.17
	IA	0.86	0.91	0.93	0.83	0.84	0.95	0.88	0.81	0.48	0.85	0.78	0.79
PERS	MSE	131.44	32.44	60.26	148.14	215.47	183.56	231.51	127.88	435.96	138.17	119.08	21.86
	MAE	10.30	5.25	6.82	9.86	12.06	11.67	12.01	8.97	12.57	8.74	8.64	3.81
	MAPE	33.01	20.60	30.08	29.94	48.25	29.56	24.08	29.47	117.95	27.07	35.06	20.77
	RMSE	11.46	5.70	7.76	12.17	14.68	13.55	15.22	11.31	20.88	11.75	10.91	4.68
	IA	0.81	0.67	0.82	0.76	0.74	0.69	0.75	0.92	0.79	0.32	0.46	0.80

,

Table A5. Evaluation measures for São Paulo PM_2.5. The best values by month are highlighted in bold.

	Metric	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	MSE	10.30	2.75	7.99	2.46	43.76	36.35	49.64	49.46	65.77	20.48	10.34	6.13
	MAE	2.42	1.26	2.09	1.26	4.71	4.68	6.00	6.03	5.79	3.60	2.63	1.76
	MAPE	12.04	9.09	17.96	6.14	30.28	17.05	22.02	37.94	65.81	16.61	16.52	14.61
	RMSE	3.21	1.66	2.83	1.57	6.62	6.03	7.05	7.03	8.11	4.53	3.21	2.48
	IA	0.96	0.88	0.89	0.99	0.81	0.59	0.83	0.91	0.92	0.64	0.86	0.81
RBFPP	MSE	27.55	3.16	10.34	8.82	34.71	21.27	46.34	47.50	96.53	13.56	17.09	4.80
	MAE	3.55	1.46	2.50	2.44	4.67	3.99	5.30	5.57	7.92	2.87	3.61	1.64
	MAPE	16.13	10.78	20.59	12.40	27.59	15.16	22.95	37.20	100.39	14.79	24.54	14.14
	RMSE	5.25	1.78	3.22	2.97	5.89	4.61	6.81	6.89	9.82	3.68	4.13	2.19
	IA	0.89	0.88	0.85	0.94	0.84	0.80	0.83	0.89	0.78	0.83	0.59	0.83
ELMPP	MSE	15.71	4.26	9.18	20.40	59.60	53.02	40.52	54.93	36.99	21.25	18.95	6.26
	MAE	3.23	1.67	2.21	2.79	6.23	5.84	5.64	5.75	4.80	3.26	3.60	1.83
	MAPE	15.43	12.47	18.57	15.84	37.19	21.53	19.69	37.65	53.99	14.98	22.98	16.54
	RMSE	3.96	2.06	3.03	4.52	7.72	7.28	6.37	7.41	6.08	4.61	4.35	2.50
	IA	0.93	0.81	0.86	0.85	0.74	0.53	0.87	0.88	0.94	0.61	0.52	0.76
ESNPP	MSE	26.91	2.58	10.56	18.69	30.11	36.65	34.22	39.47	67.48	16.16	15.20	7.35
	MAE	4.34	1.29	2.74	3.49	4.30	5.31	4.43	4.05	5.58	3.17	3.09	1.80
	MAPE	21.27	8.73	23.19	17.55	27.69	22.35	19.22	26.16	60.82	14.33	21.69	17.44
	RMSE	5.19	1.61	3.25	4.32	5.49	6.05	5.85	6.28	8.21	4.02	3.90	2.71
	IA	0.87	0.90	0.86	0.86	0.90	0.70	0.91	0.93	0.90	0.75	0.73	0.67
ARPP	MSE	26.65	2.82	12.17	18.55	45.33	52.59	58.11	61.25	100.75	19.41	16.53	6.99
	MAE	4.22	1.40	3.07	3.66	4.98	6.02	6.31	6.58	7.32	3.64	3.40	1.96
	MAPE	22.10	10.12	26.45	19.49	28.69	25.11	26.46	42.02	78.81	16.80	22.97	17.49
	RMSE	5.16	1.68	3.49	4.31	6.73	7.25	7.62	7.83	10.04	4.41	4.07	2.64
	IA	0.87	0.86	0.80	0.87	0.81	0.57	0.72	0.88	0.85	0.67	0.71	0.74
MLPTR	MSE	39.48	5.36	14.21	38.17	61.94	70.72	131.36	78.94	108.48	30.30	40.51	10.96
	MAE	4.97	1.96	2.86	4.86	6.23	7.16	9.14	6.98	6.20	4.52	5.40	2.34
	MAPE	25.39	13.91	20.64	25.32	34.64	28.21	37.59	42.84	78.91	21.65	38.34	20.30
	RMSE	6.28	2.32	3.77	6.18	7.87	8.41	11.46	8.89	10.42	5.50	6.36	3.31
	IA	0.81	0.79	0.85	0.66	0.75	0.26	0.53	0.83	0.83	0.59	0.41	0.70
RBFTR	MSE	39.14	6.52	19.48	31.39	83.84	55.69	107.52	67.57	100.25	38.46	46.33	9.52
	MAE	5.18	2.12	3.62	4.61	7.22	6.15	8.62	6.30	5.86	4.63	6.26	2.57
	MAPE	24.47	15.16	26.46	23.73	41.62	22.57	33.56	35.82	75.62	21.95	42.80	21.49
	RMSE	6.26	2.55	4.41	5.60	9.16	7.46	10.37	8.22	10.01	6.20	6.81	3.08
	IA	0.79	0.66	0.77	0.72	0.67	0.49	0.61	0.86	0.86	0.34	0.21	0.71
ELMTR	MSE	33.93	5.48	13.55	39.54	45.88	54.51	109.71	64.24	104.51	33.89	40.00	10.29
	MAE	4.67	1.77	2.70	5.01	5.64	6.28	8.35	6.77	5.40	4.33	5.36	2.62
	MAPE	22.98	12.85	18.96	26.10	31.49	23.86	33.27	39.05	70.19	19.90	37.18	21.12
	RMSE	5.82	2.34	3.68	6.29	6.77	7.38	10.47	8.02	10.22	5.82	6.32	3.21
	IA	0.84	0.77	0.84	0.64	0.83	0.54	0.57	0.87	0.86	0.50	0.44	0.75
ESNTR	MSE	27.69	5.54	13.17	40.31	59.88	90.64	116.58	76.05	95.36	35.81	41.80	11.45
	MAE	4.21	1.94	2.96	4.52	5.78	7.85	9.28	6.41	6.65	4.53	5.63	2.64
	MAPE	20.97	12.72	22.71	24.13	33.27	32.62	35.17	39.68	79.91	21.70	39.66	22.75
	RMSE	5.26	2.35	3.63	6.35	7.74	9.52	10.80	8.72	9.77	5.98	6.46	3.38
	IA	0.88	0.83	0.87	0.67	0.74	0.43	0.53	0.83	0.84	0.59	0.46	0.69
ARTR	MSE	33.36	6.75	19.42	58.86	89.82	97.71	291.64	153.85	241.77	74.66	79.37	16.97
	MAE	4.62	2.17	3.39	5.55	7.76	8.02	13.53	9.55	10.10	6.90	7.44	3.05
	MAPE	22.47	13.30	21.86	24.89	35.50	26.22	34.59	61.07	100.09	23.75	38.96	19.22
	RMSE	5.78	2.60	4.41	7.67	9.48	9.88	17.08	12.40	15.55	8.64	8.91	4.12
	IA	0.87	0.91	0.81	0.82	0.82	0.71	0.83	0.79	0.51	0.87	0.73	0.75
PERS	MSE	30.93	8.21	22.38	42.97	100.33	79.20	127.24	75.87	146.63	48.68	56.56	11.55
	MAE	4.38	2.20	3.91	4.67	7.52	7.63	8.86	6.79	6.59	5.09	6.34	2.58
	MAPE	23.70	16.31	31.09	26.19	45.59	29.33	38.32	30.89	82.71	25.28	47.25	22.36
	RMSE	5.56	2.87	4.73	6.56	10.02	8.90	11.28	8.71	12.11	6.98	7.52	3.40
	IA	0.88	0.74	0.80	0.71	0.72	0.40	0.64	0.88	0.83	0.42	0.32	0.64

,

Table A6. Evaluation measures for Campinas PM₁₀. The best values by month are highlighted in bold.

	Metric	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	MSE	14.87	11.50	64.03	33.67	91.46	59.00	76.03	302.27	42.71	37.54	32.52	43.23
	MAE	3.01	2.57	6.92	4.86	7.38	6.26	6.93	14.58	5.46	4.71	4.57	5.67
	MAPE	13.97	8.71	23.62	15.23	15.92	18.70	12.43	43.74	20.18	12.19	17.59	27.07
	RMSE	3.86	3.39	8.00	5.80	9.56	7.68	8.72	17.39	6.54	6.13	5.70	6.57
	IA	0.84	0.80	0.76	0.81	0.89	0.90	0.37	0.59	0.98	0.70	0.82	0.83
RBFPP	MSE	7.84	9.42	31.84	28.78	104.30	74.89	44.87	276.74	94.13	33.39	32.20	67.83
	MAE	2.33	2.71	4.61	5.02	8.15	7.55	5.02	13.92	7.63	4.38	4.55	6.97
	MAPE	11.02	9.29	16.94	15.85	15.55	23.94	9.49	41.24	32.22	11.30	21.09	35.39
	RMSE	2.80	3.07	5.64	5.36	10.21	8.65	6.70	16.64	9.70	5.78	5.67	8.24
	IA	0.91	0.74	0.84	0.82	0.86	0.85	0.67	0.64	0.93	0.77	0.65	0.62
ELMPP	MSE	10.61	9.48	47.14	36.83	88.62	97.08	43.59	359.92	38.84	59.05	29.68	47.04
	MAE	2.64	2.22	5.65	4.94	6.93	8.50	4.92	15.71	5.26	6.37	4.16	5.88
	MAPE	11.51	7.91	21.46	15.38	15.57	27.52	9.24	48.03	20.88	16.50	19.73	28.88
	RMSE	3.26	3.08	6.87	6.07	9.41	9.85	6.60	18.97	6.23	7.68	5.45	6.86
	IA	0.89	0.70	0.73	0.77	0.92	0.77	0.64	0.56	0.98	0.66	0.67	0.81
ESNPP	MSE	16.19	14.89	43.80	20.99	46.39	107.17	38.97	238.39	39.71	40.45	17.74	36.03
	MAE	3.42	3.43	5.68	3.81	5.77	8.69	5.01	12.09	5.28	4.31	3.52	5.13
	MAPE	16.05	12.45	20.56	12.04	12.93	28.54	8.81	39.28	19.88	10.59	15.23	24.07
	RMSE	4.02	3.86	6.62	4.58	6.81	10.35	6.24	15.44	6.30	6.36	4.21	6.00
	IA	0.79	0.49	0.77	0.89	0.96	0.77	0.77	0.65	0.98	0.72	0.86	0.85
ARPP	MSE	14.82	12.04	79.41	21.58	71.48	118.86	56.20	384.12	79.95	60.59	27.02	45.84
	MAE	3.58	3.13	6.74	4.16	6.00	8.97	5.89	15.74	7.64	6.39	4.36	5.87
	MAPE	15.95	11.35	23.74	13.22	14.04	28.60	11.40	53.87	29.58	16.88	18.56	28.87
	RMSE	3.85	3.47	8.91	4.65	8.45	10.90	7.50	19.60	8.94	7.78	5.20	6.77
	IA	0.78	0.57	0.65	0.90	0.93	0.73	0.65	0.43	0.95	0.48	0.79	0.79
MLPTR	MSE	12.00	12.01	75.01	36.68	122.75	91.17	56.64	354.30	51.96	72.35	26.60	39.30
	MAE	2.81	2.72	7.43	5.39	8.86	7.86	6.26	15.98	5.55	6.69	3.95	5.35
	MAPE	12.29	9.17	26.74	16.20	18.07	23.82	11.72	42.90	23.66	16.86	15.90	24.67
	RMSE	3.46	3.46	8.66	6.06	11.08	9.55	7.53	18.82	7.21	8.51	5.16	6.27
	IA	0.86	0.72	0.66	0.81	0.81	0.84	0.57	0.54	0.96	0.57	0.84	0.87
RBFTR	MSE	13.47	16.47	94.06	48.51	265.75	71.91	68.07	320.24	63.64	82.74	28.48	41.46
	MAE	2.78	2.96	8.18	6.22	14.29	7.06	6.43	15.41	6.24	7.46	4.42	5.52
	MAPE	11.53	9.84	30.29	18.04	27.24	20.85	11.78	39.17	26.87	19.20	17.76	25.17
	RMSE	3.67	4.06	9.70	6.97	16.30	8.48	8.25	17.90	7.98	9.10	5.34	6.44
	IA	0.86	0.66	0.57	0.72	0.27	0.88	0.47	0.56	0.95	0.51	0.82	0.87
ELMTR	MSE	13.85	13.33	75.25	36.34	105.96	80.75	51.02	212.47	48.42	63.18	27.62	38.44
	MAE	2.94	2.76	7.06	5.01	8.90	7.03	6.14	13.40	5.74	6.18	3.93	5.57
	MAPE	12.83	9.23	25.80	14.43	17.35	20.98	11.57	33.45	24.46	15.59	15.53	25.46
	RMSE	3.72	3.65	8.67	6.03	10.29	8.99	7.14	14.58	6.96	7.95	5.26	6.20
	IA	0.84	0.72	0.67	0.81	0.90	0.87	0.54	0.72	0.97	0.59	0.84	0.87
ESNTR	MSE	8.75	17.38	57.54	35.75	78.01	49.80	52.17	380.44	39.54	63.29	21.21	48.57
	MAE	2.21	3.21	6.49	4.89	6.44	6.70	5.77	14.99	5.40	6.48	3.66	5.87
	MAPE	10.00	10.96	23.45	13.20	14.21	19.98	10.67	41.49	22.61	16.14	14.37	27.96
	RMSE	2.96	4.17	7.59	5.98	8.83	7.06	7.22	19.50	6.29	7.96	4.61	6.97
	IA	0.92	0.71	0.75	0.82	0.93	0.91	0.75	0.64	0.97	0.54	0.88	0.85
ARTR	MSE	47.70	30.00	200.80	188.40	340.38	219.91	127.13	993.01	119.35	269.66	85.60	103.41
	MAE	6.03	4.81	11.77	11.52	13.82	12.89	9.65	25.08	9.32	12.92	7.44	9.00
	MAPE	18.83	12.05	33.93	24.79	20.92	34.20	13.61	50.76	39.72	26.60	24.68	30.82
	RMSE	6.91	5.48	14.17	13.73	18.45	14.83	11.28	31.51	10.92	16.42	9.25	10.17
	IA	0.83	0.94	0.36	0.89	0.97	0.53	0.95	0.75	0.92	0.11	0.30	0.35
PERS	MSE	14.13	20.62	116.89	42.52	96.52	85.77	76.56	578.28	74.19	105.49	40.91	60.30
	MAE	2.89	3.45	9.05	5.72	8.07	7.67	6.72	17.50	7.63	8.23	4.90	6.50
	MAPE	12.21	11.79	33.44	17.98	18.34	21.91	12.80	54.16	29.50	21.37	18.98	29.60
	RMSE	3.76	4.54	10.81	6.52	9.82	9.26	8.75	24.05	8.61	10.27	6.40	7.77
	IA	0.86	0.64	0.53	0.85	0.92	0.88	0.59	0.53	0.96	0.44	0.77	0.83

and

Table A7. Evaluation measures for Ipojuca PM₁₀. The best values by month are highlighted in bold.

	Metric	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
MLPPP	MSE	41.26	81.25	19.32	20.55	176.04	72.43	53.04	21.50	19.38	43.25	20.11	6.56
	MAE	5.35	7.51	3.58	4.14	11.02	7.30	4.95	4.23	3.71	5.44	3.56	1.97
	MAPE	12.13	32.17	13.06	15.26	58.20	19.43	12.96	14.76	10.73	13.83	10.68	6.58
	RMSE	6.42	9.01	4.40	4.53	13.27	8.51	7.28	4.64	4.40	6.58	4.48	2.56
	IA	0.80	0.29	0.81	0.32	0.55	0.78	0.68	0.91	0.84	0.75	0.88	0.89
RBFPP	MSE	97.72	38.99	22.46	21.20	137.01	62.80	33.18	79.39	9.88	53.88	31.14	11.34
	MAE	8.60	5.55	4.14	3.98	9.86	6.57	4.59	7.25	2.62	5.87	4.52	2.93
	MAPE	19.31	21.24	14.98	14.72	58.08	16.43	10.92	25.38	7.57	14.81	15.49	9.83
	RMSE	9.89	6.24	4.74	4.60	11.71	7.92	5.76	8.91	3.14	7.34	5.58	3.37
	IA	0.04	0.77	0.74	0.43	0.50	0.67	0.78	0.63	0.93	0.39	0.61	0.75
ELMPP	MSE	102.74	33.55	33.03	24.10	176.59	58.18	34.86	49.75	21.46	44.68	11.47	8.12
	MAE	8.72	5.28	5.27	4.43	11.53	5.98	4.65	6.29	3.90	5.14	2.39	2.06
	MAPE	19.48	19.20	21.16	16.63	62.69	15.46	11.98	22.41	11.34	12.79	7.98	7.04
	RMSE	10.14	5.79	5.75	4.91	13.29	7.63	5.90	7.05	4.63	6.68	3.39	2.85
	IA	0.03	0.83	0.47	0.21	0.52	0.80	0.82	0.70	0.81	0.57	0.92	0.89
ESNPP	MSE	23.11	16.03	26.33	16.35	108.81	46.49	40.17	73.25	11.57	30.73	19.35	7.63
	MAE	3.90	3.63	3.84	3.56	9.13	5.05	4.49	5.43	2.58	4.31	3.49	2.30
	MAPE	8.95	13.38	13.36	12.87	47.20	12.17	10.90	17.62	7.75	9.37	11.91	7.68
	RMSE	4.81	4.00	5.13	4.04	10.43	6.82	6.34	8.56	3.40	5.54	4.40	2.76
	IA	0.86	0.93	0.72	0.57	0.73	0.84	0.75	0.81	0.92	0.85	0.83	0.86
ARPP	MSE	21.98	20.80	26.80	15.74	87.27	48.01	45.54	127.38	20.42	52.57	23.03	3.80
	MAE	3.97	3.75	4.28	3.20	8.04	5.54	5.09	8.66	3.70	5.68	3.94	1.46
	MAPE	9.36	14.63	16.33	11.42	41.53	14.44	12.85	29.92	10.86	14.00	13.59	4.89
	RMSE	4.69	4.56	5.18	3.97	9.34	6.93	6.75	11.29	4.52	7.25	4.80	1.95
	IA	0.87	0.89	0.58	0.76	0.78	0.76	0.75	0.50	0.81	0.54	0.74	0.94
MLPTR	MSE	34.84	44.61	38.83	15.46	147.92	100.06	57.74	89.10	13.78	72.92	14.47	8.24
	MAE	5.13	5.57	5.36	2.98	10.84	7.89	6.26	7.87	2.98	7.20	3.36	2.32
	MAPE	11.80	22.45	19.70	10.50	60.17	18.61	15.79	27.74	8.62	18.39	11.02	7.57
	RMSE	5.90	6.68	6.23	3.93	12.16	10.00	7.60	9.44	3.71	8.54	3.80	2.87
	IA	0.74	0.73	0.47	0.68	0.51	0.48	0.60	0.62	0.90	0.39	0.89	0.87
RBFTR	MSE	31.00	147.25	37.94	19.70	126.84	89.11	63.83	173.77	11.00	75.68	15.58	11.54
	MAE	4.67	9.99	5.15	3.74	9.79	7.89	6.62	12.28	2.69	7.56	3.57	2.72
	MAPE	10.69	42.46	19.05	13.42	55.66	19.63	15.94	42.87	7.86	19.46	11.59	8.82
	RMSE	5.57	12.13	6.16	4.44	11.26	9.44	7.99	13.18	3.32	8.70	3.95	3.40
	IA	0.78	0.25	0.42	0.54	0.56	0.43	0.43	0.16	0.92	0.45	0.89	0.83
ELMTR	MSE	33.24	61.78	32.99	14.70	126.62	104.05	59.12	41.04	15.78	78.06	13.62	8.44
	MAE	4.93	6.30	4.69	2.69	9.28	7.99	6.14	5.43	3.28	6.96	2.95	2.38
	MAPE	11.43	22.94	17.79	9.43	59.67	18.70	15.43	18.52	9.56	18.07	9.48	7.77
	RMSE	5.77	7.86	5.74	3.83	11.25	10.20	7.69	6.41	3.97	8.84	3.69	2.90
	IA	0.77	0.76	0.61	0.72	0.52	0.58	0.59	0.87	0.88	0.47	0.90	0.87
ESNTR	MSE	23.10	43.11	31.63	9.11	121.14	86.48	39.17	135.14	17.35	62.38	13.20	8.51
	MAE	4.38	5.37	4.87	2.69	9.62	7.84	5.76	9.00	3.31	6.59	3.11	2.32
	MAPE	10.37	22.22	18.12	9.77	54.94	19.56	15.28	31.35	9.75	17.45	10.35	7.48
	RMSE	4.81	6.57	5.62	3.02	11.01	9.30	6.26	11.62	4.17	7.90	3.63	2.92
	IA	0.87	0.68	0.59	0.78	0.58	0.56	0.79	0.45	0.86	0.47	0.90	0.88
ARTR	MSE	45.91	46.49	79.73	61.37	563.32	238.31	102.43	248.19	34.55	99.80	29.17	21.24
	MAE	6.02	5.64	7.97	7.23	21.00	12.75	7.92	12.21	4.40	8.21	4.41	3.66
	MAPE	13.18	54.68	25.59	27.82	512.60	28.11	16.23	75.21	12.01	29.81	14.91	11.43
	RMSE	6.78	6.82	8.93	7.83	23.73	15.44	10.12	15.75	5.88	9.99	5.40	4.61
	IA	0.82	0.94	0.77	0.24	0.41	0.59	0.91	0.78	0.26	0.84	0.75	0.50
PERS	MSE	37.05	49.25	46.55	19.90	227.81	141.80	66.80	213.59	18.60	84.85	16.96	16.98
	MAE	5.12	5.31	6.09	3.13	12.87	11.21	7.05	7.26	3.80	7.65	3.59	3.41
	MAPE	12.33	17.07	23.33	10.59	61.79	28.93	19.10	23.17	10.86	18.44	11.10	10.90
	RMSE	6.09	7.02	6.82	4.46	15.09	11.91	8.17	14.61	4.31	9.21	4.12	4.12
	IA	0.81	0.84	0.53	0.70	0.52	0.52	0.75	0.59	0.88	0.55	0.91	0.79

in Appendix A present the values for MAE, MAPE, RMSE, and IA.

When using the proposed approach, 12 models are adjusted using the training approach. In this case, the samples are separated per month. On the other hand, the traditional approach uses just one predictor and all training samples.

The results regarding Kallio PM₁₀ (Table 4) allow an interesting observation about error metrics. There is a divergence among the best performance (MSE, MAE, MAPE, RMSE, or IA). Although this behavior does not happen very often, to October, we can note that the best MSE, RMSE and IA were achieved by the RBF_PP, the best MAE was from the ESN_pp, while the smallest MAPE belongs to the ELM_PP (see Table A1). In this case, we choose MSE as the primary metric, as it is minimized during the ANNs training process, and in the adjustment of the AR model [28,63,75]. Note that the RMSE is directly proportional to the MSE.

The comparison between the traditional and the monthly approach reveals that the decomposition increased the predictors’ performance for almost all months, except for the ELM. In this sense, only April showed the best result for ELM_TR. The other months had mainly RBF_PP reaching the smallest errors (seven months), and MLP_PP and ESN_PP in two cases each.

Figure 6 shows the real and predicted values for the Kallio PM₁₀ series, considering the best predictor, the RBF_PP, the correspondent to the traditional approach (RBF_TR), and the samples from the test set. The best prediction capability of the monthly approach is clear. It is important to highlight the monthly approach improved the prediction of some extreme events of high air pollutants level.

Table 5 shows the results for Kallio PM_2.5. The best results related to Kallio PM_2.5 for each month showed different behavior than Kallio PM₁₀. Again, the ELM_TR overcame the others for one month (January), while the RBF_PP, MLP_PP, and ESN_PP reached the best MSE for 4, 4, and 3 months, respectively. The monthly proposal was superior to the traditional method.

We noticed again a tendency of reduction in the error comparing distinct approaches for the same architecture. Despite the ELM_TR presenting the best overall result for one month, the ELM_PP showed smaller MSE for eight months, overcoming the traditional methodology. We highlight that the RBF_TR gave the worse errors, an intriguing finding since its counterpart RBF_PP was one of the bests. Once again, we observed a discrepancy regarding the best predictors and error metrics in Table A2. Seven times, the best IA did not match with the MSE and RMSE, while MAE five times, and MAPE six times.

Figure 7 presents the best prediction in the test set for RBF_PP and MLP_PP, and the same ANNs using the traditional approach (RBF_TR and MLP_TR). Again, it is clear the best performance of the monthly approach. Additionally, extremely high and low air pollution events were well predicted.

Table 6 summarizes the results of the Vallila PM₁₀. The predictors’ performances to the Vallila station were favorable to the monthly approach, concerning the MSE. The RBF_PP was the one reaching the smallest MSE more times (four months).

Since RBF_PP and ESN_PP achieved the best MSE in four months and considering the number of best results and months, we present their output responses in Figure 8, with the same to the traditional approach (RBF_TR and ESN_TR). It is interesting to observe the differences between the proposed and the traditional approaches. While the proposed methodology presented an adequate prediction capability to the whole test set, the original approach fits well for specific samples (some days of March, for example), but have significant discrepancies in others (beginning of September and October, for example).

Table 7 shows the errors achieved for the São Paulo PM₁₀. The behavior found for the São Paulo PM₁₀ was very similar to those related to the Vallila one. The monthly approach reached all the best errors based on the MSE metric, with the RBF_PP presenting the best results five times, MLP_PP four times, and ESN_PP three times.

Figure 9 presents the predictions achieved by the RBF_PP in the São Paulo PM₁₀ time series, compared to the RBF_TR and the original data. In this time series, we can observe that the RBF_PP architecture could not lead to small prediction errors to all the air pollution peaks and valleys, probably due to external factors that affect air pollution compared to previous time series. However, it still has a better prediction performance than the traditional approach.

Table 8 shows the results for the São Paulo PM_2.5 series. Once again, the results presented 100% of the best values of MSE favorable to the monthly approach, highlighting the ESN_PP and the MLP_PP, which were the best in 4 cases, RBF_PP (three cases), and ELM_PP (one case). It is the first time the RBF was not the best in most scenarios, showing the importance of applying different ANNs.

Figure 10 shows the MLP_PP and MLP_TR results compared to the original data to the São Paulo PM_2.5 test set.

Table 9 has the results for Campinas PM₁₀. Analyzing the metrics in Table 9, we can observe that the traditional approach led to the smallest errors for June (ESN_TR) and August (ELM_TR). The monthly proposal (RBF_PP—four, ESN_PP—five, and ELM_PP—one) was the best to the remaining ten months. As in the São Paulo PM_2.5 time series, the ESN found the best monthly performances.

Figure 11 presents the predictions found by the ESN_PP and ESN_TR in the test set compared to the original data.

Finally, Table 10 reveals the results for the last station considered in this work, Ipojuca PM₁₀. The traditional approach achieved the smallest errors only for April (ESN_TR). To the other months, the ESN_PP showed the best values for MSE, five times. The MLP_PP was the best for three months, RBF_PP for two months, and the ELM_PP only one month. In most cases, the general performances of the neural models were improved using the monthly approach. Additionally, in some instances, the best results considering distinct metrics did not match.

Figure 12 presents the forecasts achieved by the ESN_PP, compared to the ESN_TR and the original data of the Ipojuca PM₁₀ time series. Again, the monthly approach seems to have a good prediction power.

Lastly, it is worth mentioning that we applied Friedman’s Test to the MSE of the test sets for all experiments, to verify if the results were significantly different [43]. The p-values ranged from 5.2771 × 10⁻¹² to 0.0112. Therefore, we can assume the hypothesis that a change in the predictor leads to different results.

4.2. Discussion

The computational results presented in Table 4, Table 5, Table 6, Table 7, Table 8, Table 9 and Table 10 allow some essential remarks. Initially, we elaborated

Table 11. Ranking of the best predictors by month regarding the mean squared error (MSE) in the test sets.

	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Total
MLPPP	1	1	3	3	-	1	1	2	2	1	2	1	18
RBFPP	3	2	2	1	2	1	2	2	3	3	2	4	27
ELMPP	-	-	-	-	1	-	-	-	2	-	2	-	5
ESNPP	1	3	2	1	3	4	4	2	-	3	1	1	25
ARPP	1	1	-	-	1	-	-	-	-	-	-	1	4
MLPTR	-	-	-	-	-	-	-	-	-	-	-	-	-
RBFTR	-	-	-	-	-	-	-	-	-	-	-	-	-
ELMTR	1	-	-	1	-	-	-	1	-	-	-	-	3
ESNTR	-	-	-	1	-	1	-	-	-	-	-	-	2
ARTR	-	-	-	-	-	-	-	-	-	-	-	-	-
PERS	-	-	-	-	-	-	-	-	-	-	-	-	-

, which shows how many times each model achieved the best performance by month. The goal is to analyze if the month decomposition brings gains to any neural network performance, independently of the characteristics of the studied time series.

Considering the 12 months of the seven test sets, we have 84 scenarios. The main observation is that in 79 out of 84 months (94%), the monthly approach achieved the best overall results, a clear indication that the use of disaggregated series and 12 predictors instead of only one model to the whole series is an advantage.

Comparing the same neural architecture (RBF_PP and RBF_TR) using the traditional and the monthly approach is favorable to our proposal in almost all cases. It is essential to highlight that we used seven time series from four different cities of two countries to distinct years, with diverse characteristics.

With regard to the neural models, the RBF_PP and ESN_PP presented similar results concerning the number of best monthly results found. For Kallio PM₁₀ and São Paulo PM₁₀, the RBF stands out. For Kallio PM_2.5, both RBF and MLP showed the best results and for Vallila PM₁₀, the RBF, and the ESN. The other three time series were favorable to the ESN.

We cannot state which the best predictor for such a task is. Therefore, in related problems, we should test both RBF and ESN models. Related works that used the disaggregated method, like in streamflow series [27,28,58], indicated that the ELM overcame its organized counterpart (MLP), but it was the worse in this work. On the other hand, in [59] and [63], the fully trained approaches were the winner. It seems clear that the evaluation of some distinct neural architectures is essential in time series forecasting tasks. In addition, the neural approaches overcame the linear AR model and the persistence model, except for the February of Kallio PM₁₀ time series.

In this work, we followed the premises found in other investigations of prioritizing MSE [27,28,59,63], since it penalizes higher errors. However, some studies pointed to other error metrics. In [76], the authors advocate the use of MAE. In this sense, we calculated the number of times our proposition achieved the best values for all metrics. For each case, we found: (i) MAE—89%; (ii) MAPE—86%; RMSE—94%; IA—61%. These results allowed us to ensure the gains in applying the new methodology based on decomposition.

During extreme events of high air pollution, the health systems collapse due to overcrowding, and the government needs to take quick measures to assure treatment to the whole population. To this end, the monthly approach was robust to all considered time series, but the power of prediction may differ depending on each time series behavior.

Lastly, PM emissions are mainly anthropogenic, then life cycle assessment (LCA) thinking may help to better understand their impacts on human health. One scientific challenge of the LCA community is the regionalization of life cycle impact assessment (LCIA) methods, as the source location and its surrounding conditions are paramount to a reliable and accurate result [77,78]. In this sense, our study may assist the development and/or regionalization of PM formation methods in LCIA context.

5. Conclusions

This paper proposed a methodology based on monthly decomposition to PM concentration forecasting. We applied 12 independent predictors in this approach, each one responsible for predicting the data from each month. The traditional methodology just uses one predictor for the whole series.

Four different neural network architectures, a linear model, and a persistence model were addressed using both methodologies. Our approach based on the time series disaggregation improved air pollutants concentration forecasting with the best capability to predict air pollution in 94% of the scenarios analyzed. It is important to highlight our approach’s robustness, since the predictors increased their performance compared to the traditional method, for various databases from different locations and pollutants.

Regarding the best forecasting approach, the RBF and ESN neural networks achieved the smallest errors in most cases, followed by the MLP, when using the new decomposition approach. However, we cannot state which ANN is the adequate neural model, reinforcing the necessity of testing various architectures. On the other hand, the ANNs overcame the AR model and the Persistence approach.

Considering the United Nations sustainable development goals (SDG) [79], which are to change the world, our study has an important contribution to foresee air quality and then help governments to take measures aiming air pollution reduction and preparing hospitals during events of extreme air pollution, which is related to SDG 3-good health and well-being and SDG 11-sustainable cities and communities.

Future works should include the use of variable-sized time windows in the time series decomposition, the use of selection and combination of predictors, and the application of other computational intelligence approaches, such as deep learning, hybrid methods, and ensembles. Additionally, exogenous variables as meteorological information could be addressed as an input of the models [80], and other time series or even variable sizes of the training, validation, and test sets.