Jiangsu Province, located at the Yangtze River in eastern China (Figure 1), is one of the most developed areas of the country. The province has a large population and well-developed industrial sectors. Occupying an area of around 107,200 km², it has 13 cities and, as of 2019, a population of approximately 80.5 million. In recent years, due to rapid economic development, Jiangsu Province has experienced the worst air quality (Zhang et al., 2020; Bhatti et al., 2022).

Data on the daily average concentrations of air pollutant factors, including PM₁₀, PM_2.5, SO₂, NO₂, CO, and O₃, were collected between 1 January 2016 and 31 December 2020. The website of historical data of air quality in China has allowed downloading of air pollution data since 13 May 2014 (Wang 2019). The data on the selected air pollutants were from the China Environmental Monitoring Station (CNEMC, 2019). In Jiangsu Province, 72 monitoring stations that collect and record air quality data are scattered over 13 cities. The distribution of these monitoring stations is shown in Figure 1.

To predict the concentrations of air pollutants, to meet the input requirements of the model, the values were manually processed in Excel for appropriate fitting and to satisfy the PFM formatting requirements, with timestamps in YYYY-MM-DD format. PFM has the broad ability to replace missing values with nearby points by fitting the model for the prediction, and any error was replaced with “NA” read from the devices denoted by “-1”.

For analyzing time series and forecasting with trends, seasonality, and holidays, PFM is an influential and powerful tool for accurate and effective prediction, and it takes only a few seconds to fit the model. The model uses the following formula: y ( t ) = g ( t ) + s ( t ) + h ( t ) + ∈ t . (1)

To evaluate the performance of the PFM, Eq 1 was employed, where y(t) is the predicted value determined by a linear or logistic equation; g(t) and s(t) represent seasonality or time series based on yearly, monthly, daily or another period; h(t) is the holiday outliers; and €t represents the unexpected error. For better understanding, the model has numerous parameters and the type of model can be assumed as linear or logistic. There is no maximum or minimum limit set in a linear model, while in a logistic model, the highest and lowest values are specified and used for saturated forecasts. Linear models were utilized to make sure the PFM reported and accounted for the typical outliers observed in air quality tendencies. To forecast and smooth time series data, the model accepts a Bayesian-based curve fitting technique, which is one of the model’s most distinctive features compared to other forecasting models, such as ARIMA and the Holt-Winters method. PFM has more power to handle temporal patterns easily compared to traditional exponential smoothing models and has requirements for frequent measurements (Taylor and Letham, 2017).

In PFM, change points are significant parameters and the explicit values of change points or the fitting scale can be specified; with higher change points, the model showed better performance when fitting the data. However, in predicting future trends, the model lost efficacy and effectiveness due to the use of fewer change points and was unable to be well-fitted. Initially, PFM plots a large value to determine the number of change points, and then the model uses L1 regularization to pick out a few points to use. To avoid overfitting due to a lack of change points, L1 regularization was used for this purpose, which picks out only the significant change points. L ( x , y ) ≡ ∑ i = 1 n ( y i − h θ ( x i ) ) 2 + λ ∑ i = 1 n | θ i | (2)

Eq 2 represents L1 regularization, where x and y are the coordinates of the change points.

∑ i = 1 n ( y i − h θ ( x i ) ) 2 represents the change between actual and forecasted value squared. The purpose of λ ∑ i = 1 n | θ i | , is to maintain the balance in weights to avoid overfitting, where λ shows how much the weights are penalized; a high-value results in underfitting, while a low value means high bias. PFM has a value in determining the value of λ based on the number of estimators, or the average rate of change value can be specified.

Seasonality is another important parameter in predicting new values. PFM represents seasonality over daily, weekly, yearly, or other periods (Figure 2). Figure 2 shows the seasonality of PM_2.5 concentrations with daily, weekly, yearly, and overall time trends. PFM can also plot any custom seasonality or holiday component. Cross-validation was performed for the model to forecast the error given historic data. Data from the first 4 years (2016–2019) comprised the initial training data. PFM was used to forecast air quality for 2020 after training data from 2016 to 2019. To determine the model performance, these values were compared to the actual values. The model then predicted air quality for the upcoming 2.5 years.

In this work, four metrics were employed to evaluate the model’s performance: correlation coefficient (R), mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE). The correlation coefficient (R) was used to determine the degree of fit of the forecasted values to the overall actual values. MSE is the average change of actual and forecast values, and RMSE is the square root of MSE, while MAE is proposed as the average change between actual and predicted values. Compared with MAE, RMSE places higher importance on the variance between data outliers. These metrics are calculated with the following formulas: R = n ∑ i = 1 n ( x i x ^ i ) − ( ∑ i = 1 n x i ) ( ∑ i = 1 n x ^ i ) n ∑ i = 1 n x i 2 − ( ∑ i = 1 n x i ) 2 n ∑ i = 1 n x ^ i 2 − ( ∑ i = 1 n x ^ i ) 2 (3) M S E = 1 n ∑ i = 1 n ( x i − x ^ i ) 2 (4) R M S E = 1 n ∑ i = 1 n ( x i − x ^ i ) 2 (5) M A E = 1 n ∑ i = 1 n | x i − x ^ i | (6) where x i and x ^ i are the actual and predicted values and n represents the number of samples.

A linear model was inputted to specify the features of PFM, and error and change points were determined using the LI regularization technique from PFM. The model accurately predicts PM₁₀ concentrations, and it is not overfitted during the entire year of 2020. We can see that all of the statistical indicators (R, MSE, RMSE, and MAE) show that the model predicts PM₁₀ concentration more accurately for the long-term prediction than short-term. In a 15 days prediction, the model predicted PM₁₀ with R, RMSE, and MAE values of 0.31, 28.91 μg/m³, and 24.25 μg/m³, respectively (Table 1). It can be seen that as the prediction time increased, the RMSE value decreased. The MAE value also showed a decreasing trend with the increase of time from 15 days to 1 year. In the 1 year prediction of PFM, the R, RMSE, and MAE values for PM₁₀ are 0.40, 16.37 μg/m³, and 11.74 μg/m³, respectively (Table 1). The decreasing error values show that the model predicts PM₁₀ with high accuracy as the time frame increases. Sayegh et al. (2014) developed five models to predict PM₁₀ concentration, while Ye (2019) utilized an ARIMA-PFM model to predict PM₁₀ concentrations in the time frame of 2 days. All indicators show that in the current work, PM₁₀ concentrations are forecast more effectively compared with those studies. The results of predicted PM₁₀ concentrations in Jiangsu Province are shown in Figure 3 and Table 1.

To illustrate the performance of PFM, in a 15 days prediction the model predicted PM_2.5 with R, RMSE, and MAE values of 0.39, 25.16 μg/m³, and 21.30 μg/m³, respectively (Table 2). The results demonstrate that as the time increased from 15 days to 1 year the model predicted PM_2.5 more efficiently according to the statistical indicators shown in Table 2. In a 1-year prediction by PFM, the R, RMSE, and MAE values for PM_2.5 were 0.52, 12.07 μg/m³, and 8.22 μg/m³, respectively (Table 2). The results indicate that the model appropriately forecast the concentration of PM_2.5 in Jiangsu Province, as shown in Figure 4 and Table 2. Many studies have proposed methods for predicting PM_2.5 concentrations (Li et al., 2015; Xi et al., 2015; Deters et al., 2017; Ye, 2019), and compared with these studies our study provides more accurate results for PM_2.5 concentrations.

In the prediction of SO₂ concentrations by PFM, within the time frame of 15 days, the R, RMSE and MAE values for SO₂ are 0.16, 2.76 μg/m³, and 2.32 μg/m³, respectively (Table 3). Similarly particulate prediction, the performance of the model in predicting SO₂ concentrations improved with an increase of time as indicated by RMSE and MAE values. In the 1-year time frame, the model predicts SO₂ concentrations with R, RMSE, and MAE values of 0.17, 1.57 μg/m³, and 1.16 μg/m³, respectively (Table 3). In previous studies, Shaban et al. (2016) developed M5P model trees, artificial neural network (ANN), and support vector machine to predict short-term air pollution, and Ye (2019) proposed an ARIMA-PFM model to forecast air pollution. Compared with these studies, our results of RMSE and MAE values in the prediction of SO₂ concentrations are improved. The prediction results of PFM for SO₂ in Jiangsu Province are presented in Figure 5 and Table 3.

PFM provides better performance in predicting NO₂ concentrations in Jiangsu Province, with R, RMSE and MAE values of 0.37, 5.46 μg/m³, and 4.57 μg/m³, respectively, for a period of 15 days (Table 4). PFM predicted NO₂ with an R of 0.68, which was the best performance in predicting NO₂ concentrations within the time frame of 1 month. The results indicate that in contrast to other air pollutants, the model provides better performance in short-term prediction with RMSE and MAE values for NO₂. It can be seen that there were slight fluctuations in these values over an entire year (2020). In 1-year prediction by PFM, the R, RMSE, and MAE values for NO₂ are 0.54, 6.72 μg/m³, and 4.99 μg/m³, respectively (Table 4). Comparing short- and long-term predictions, the MAE and RMSE values for NO₂ are similar in Jiangsu Province, with small differences (Figure 6 and Table 4).

In predicting CO concentrations, PFM predicts with R, RMSE and MAE of 0.26, 0.20 μg/m³, and 0.17 μg/m³, respectively, in a period of 15 days (Table 5). The model predicts CO with R of 0.46 in 3-months prediction. Similar to other air pollutant parameters, the results show that the accuracy of the model improved with an increase of time for CO prediction. From 15 days to 1 year, the RMSE and MAE values gradually decreased from 0.20 to 0.12 μg/m³ and 0.17 to 0.09 μg/m³, respectively. With 1 year prediction, the model predicts with R = 0.38, RMSE = 0.12, and MAE = 0.09 in Jiangsu Province (Table 5). Overall, the results demonstrate that PFM provides significant results for CO concentrations over long-term prediction intervals in Jiangsu Province (Figure 7 and Table 5).

PFM provides superior results in both short-term and long-term O₃ prediction in Jiangsu Province. In 15 days prediction, the model predicts with R = 0.47, RMSE = 6.34 μg/m³, and MAE = 5.14 μg/m³ for O₃ forecasting. PFM has the best R value for O₃ (0.84) in 1 month prediction. The smallest and highest RMSE and MAE values are 6.34 and 11.69 μg/m³ and 5.14 and 8.98 μg/m³, respectively. Compared with other air pollutant factor prediction, PFM has superior performance for O₃ prediction. In 1-year prediction by PFM, the R, RMSE, and MAE values for O₃ are 0.66, 11.33 μg/m³, and 8.84 μg/m³, respectively. We can see that all statistical measures demonstrate that the model has adequate performance. The forecasting values for O₃ and the actual and predicted values are significantly fitted. The prediction results of PFM for O₃ in Jiangsu Province are presented in Figure 8 and Table 6.

It is best to stop air pollution at its source, but until that day comes, experts suggest the following. Avoid spending time on busy roads and places with pollution. When you walk or bike away from congested streets, you can reduce exposure by half by using backstreet routes. Even on busy streets, cyclists experience less pollution than drivers. Scientists recommend parents cover their buggies with covers to protect their infants. Make sure you get to work early before rush hour begins and pollution levels rise. Exercise indoors or reduce strenuous outdoor exercise when air pollution is high or if you have a lung condition such as asthma.

(1) Comprehensively implement pollution reduction. Coordinate and promote structural emission reduction, engineering emission reduction and management emission reduction: It is strictly forbidden to build new capacity projects in industries with severe overcapacity, adjust and optimize the industrial structure, and promote industrial transformation and upgrading. Eliminate outdated thermal power units and cement production capacity, strictly control the newly added emissions of sulfur dioxide and nitrogen oxides in the power industry, and simultaneously build and put into operation flue gas desulfurization and denitrification facilities for newly built coal-fired units. Focus on the reduction of emissions in the thermal power industry.

In current study, we used the PFM model to predict six air pollutants (PM₁₀, PM_2.5, SO₂, NO₂, CO, and O₃) in Jiangsu Province, China. The model shows good performance and provides better results in predicting air pollutant concentrations. The current research emphasizes air quality, the model should also be used in other fields as a forecasting method, such as in environmental economics to evaluate economic variations and the impact of climate change on the market. After the identification of the COVID-19 pandemic, strict restrictions and control measures have been taken to control its rapid spread by the affected countries. Many scholars reported that due to strict restrictions and control actions, the air quality of these areas and regions was improved at a significant level (Li et al., 2020; Hasnain et al., 2021; Islam et al., 2021). Future research can be conducted to predict air quality trends during the COVID-19 pandemic and the current trends. The results of both periods can be compared to find out the changes and obtain new findings for policy implications. The study can be further extended to explore the impact of the COVID-19 pandemic on economic and industrial activities. Moreover, the current study focuses to predict air pollutants; future work can be conducted to predict meteorological factors. In the future, the model should also be used to predict the impact of climate change on agriculture production. The next step of the research is to extend the PFM to other fields and regions to obtain new findings, and it will be useful in areas such as effective preparation, health alarms for liable categories, reduced monitoring expenditures, etc.