Development of Multiple Linear Regression for Particulate Matter (PM₁₀) Forecasting during Episodic Transboundary Haze Event in Malaysia

Abstract

Malaysia has been facing transboundary haze events every year in which the air contains particulate matter, particularly PM₁₀, which affects human health and the environment. Therefore, it is crucial to develop a PM₁₀ forecasting model for early information and warning alerts to the responsible parties in order for them to mitigate and plan precautionary measures during such events. Therefore, this study aimed to develop and compare the best-fitted model for PM₁₀ prediction from the first hour until the next three hours during transboundary haze events. The air pollution data acquired from the Malaysian Department of Environment spanned from the years 2005 until 2014 (excluding years 2007–2009), which included particulate matter (PM₁₀), ozone (O₃), nitrogen oxide (NO), nitrogen dioxide (NO), carbon monoxide (CO), sulfur dioxide (SO₂), wind speed (WS), ambient temperature (T), and relative humidity (RH) on an hourly basis. Three different stepwise Multiple Linear Regression (MLR) models for predicting the PM₁₀ concentration were then developed based on three different prediction hours, namely t+1, t+2, and t+3. The PM_{10, t+1} model was the best MLR model to predict PM₁₀ during transboundary haze events compared to PM_10,.t+2 and PM_10,t+3 models, having the lowest percentage of total error (28%) and the highest accuracy of 46%. A better prediction and explanation of PM₁₀ concentration will help the authorities in getting early information for preserving the air quality, especially during transboundary haze episodes.

1. Introduction

Haze pollution has become an international issue as it affects the local, regional, and global air quality, especially in Southeast Asian (SEA) countries, including Malaysia, Singapore, Indonesia, Brunei Darussalam, and Southern Thailand [1,2,3]. Haze occurs annually due to periodic biomass burning, such as forest fires, peatland combustion, and agricultural burning in Sumatra and Kalimantan, Indonesia. The influence of unpredictable monsoon rain and El-Nino phenomenon both worsens the transboundary haze due to the prolonged and drier weather conditions, especially during the southwest monsoon season [3,4,5,6,7,8]. These conditions increase the severity of air quality due to it containing a noxious mix of air pollutants, such as particulate matter and noxious gases, which are collectively influenced by meteorological factors like ambient temperature, relative humidity, and wind speed [9,10]. Malaysia has been facing this awful phenomenon for almost over a decade, which started in the 1980s up until recent years [5,11,12]. Haze is detected when the atmosphere contains a higher concentration of particulate matter suspended in the air, which either can or cannot be observed by the naked eye when the relative humidity is lower than 80% and the visibility is reduced to 10 km [5,13,14,15]. Daily particulate matter with 10 micro aerodynamic diameters (PM₁₀) exceeding 150 µg/m³ for 24 h of permissible limit is thus notified as haze, which is set under the new Malaysian Ambient Air Quality Standard (NAAQS) by the Department of Environment, Malaysia.

Biomass peat soil combustion generally emits the particulate matter and gaseous pollutants, as well as their components such as anions, cations, heavy metals, and levoglucosan [16,17,18,19]. Carbon monoxide (CO) is higher during haze events compared to other gases due to the characteristics of peatland areas, which are rich in carbon materials. It is emitted through the incomplete combustion process of carbonic materials in the presence of a minimum amount of oxygen. Meanwhile, PM₁₀ contains a high concentration of NO₃⁻ anion produced through bacterial nitrification and oxidation process during combustion, while SO₄²⁻ cation is also found in a high amount due to pesticide application in the peat soil, thereby slowing down the accumulation of sulfur [18]. Those ions originate from sulfurous and nitrogenous materials as they will be converted to such particles via gas-to-particle conversion. Similarly, heavy metals from the peatland soil are converted to particulate matter by the combustion process in which the characteristics of heavy metals will be contained in the ash suspended in the air [17,18]. The isomeric anhydrous sugar levoglucosan is found in the fine particulate matter during transboundary haze as it is known as a specific and general indicator of biomass emission composition directly emitted into the atmosphere. It is yielded by some anthropogenic activities such as wood burning and biogenic activities, as well as the by-product of secondary photochemical oxidation of organic precursors [16].

Every time the haze phenomenon hits the country, it will inhibit the economic and social developments; the country will need to bear higher medical costs due to drastically increased outpatient and inpatient numbers. This was estimated to be approximately MYR273,000 (USD91,000) based on the data from 2005 until 2009 for 14 haze-related illnesses suffered by the public [5,20]. Moreover, when the haze event worsens and it is declared unsafe, hundreds of schools in the affected areas are closed, communication becomes limited, and people will need to reduce outdoor activities in order to minimize their exposure to it [21,22]. Therefore, the tourism sector is also affected during these events in terms of the economy, human perception, and the environment. Similarly, huge losses occur when the atmospheric visibility decreases; many flights are cancelled due to unsafe conditions to fly, which decreases the number of tourism activities. Furthermore, the number of extinct plants, animals, and biodiversity will increase due to extreme environmental events, while the circumstances can also change tourism moods due to unsatisfactory environmental conditions and lead to a refusal to revisit [5,10,21,22].

Toxic particles in haze harm human health either in cumulative or acute effects like respiratory mortality, cardiovascular illness, and lung cancer to all groups of people, such as adults and children [9,20]. The small particulate size contained in haze can easily penetrate the lung; at worst, it also goes into the bloodstream [22]. Based on the previous study by [4], long-term exposure to air pollution causes an increase in neurological diseases such as cerebrovascular disease and stroke, along with headache and migraine symptoms. Skin is one of the organs that are directly in contact with air pollution, especially during transboundary haze events. The small particulate matter enters through the skin via the pores, causing allergic symptoms and skin damage, such as skin irritation and inflammation, damaged skin barrier function, increased rate of ageing, and influences on the composition of skin lipid [23,24,25]. In the worst-case scenario, long-term exposure to air pollution causes an increase in the degree of skin sensitivity and causes skin defect, as well as atopic dermatitis [23].

During transboundary haze events, particulate matter, especially the harmful PM₁₀ pollutant, needs to be predicted for determining and understanding its dispersion behavior in the atmosphere. This can provide information to the concerned people and their awareness to reduce outdoor activities at the affected areas [26]. The Multiple Linear Regression (MLR) model is globally and widely used over many years as a method for air pollution forecasting, which can help to attempt the uncertainty of the future simply by relying on past and current data for decision-making [27,28,29]. The fundamental basis of this model represents the relationship between the dependent variable and several independent variables, such as meteorological factors and gaseous pollutants, by uncomplicated computation and easy implementation [30,31]. Previous studies in Malaysia have developed the MLR model to predict PM₁₀ concentration, specifically in the East Coast Peninsular Malaysia, based on different site classifications of rural, suburban, urban, and industrial areas and during different types of monsoon to determine its variation during non-haze periods [27,32,33]. Moreover, [34] used the MLR model for PM₁₀ forecasting during haze events that hit Malaysia based on the data from the affected Air Quality Monitoring Station (AQMS). Therefore, this study aims to determine the annual variation of PM₁₀ concentration during transboundary haze events and develop the models to investigate the relationship linking PM₁₀ with meteorological factors and gaseous pollutants, which are contributing to the high PM₁₀ concentration. PM₁₀ is used in this study as the dependent parameter for the prediction purposes as the Malaysian Department of Environment had started to monitor the PM_2.5 concentration in 2018. However, the episodic haze events need a long period of dataset, which is the main reason to use PM₁₀ in this study. These research findings will help the responsible parties in providing early warning information to come out alongside mitigation and precautionary plans to improve the air quality during haze events, as well as protect the public health.

2. Materials and Methods

2.1. Study Area and Data Collection

Malaysia faces a periodic transboundary haze event due to the large-scale biomass combustion in Sumatra, Indonesia, which happens almost throughout the year and affects the Peninsular Malaysia, Sabah, and Sarawak regions [6]. The haze event usually occurs during the months of January to February and June to August every year [22]. Figure 1 and

Table 1. Selected air monitoring stations in Malaysia affected during haze events.

Classification	Station ID	Location	Latitude	Longitude
Industrial	CA0003	Cenderawasih Primary School, Perai	N05° 23.470	E100° 23.213
Industrial	CA0004	Medical Store, Kuching, Sarawak	N01° 33.734	E110° 23.329
Sub-Urban	CA0009	Seberang Jaya II Primary School, Perai, Penang	N05° 23.890	E100° 24.194
Industrial	CA0010	Taman Semarak (Phase II), Nilai, Negeri Sembilan	N02° 49.246	E101° 48.877
Urban	CA0011	Raja Zarina Secondary School, Klang, Selangor	N03° 00.620	E101°24.484
Sub-Urban	CA0026	Sibu Police Main Office, Sarawak	N02° 18.856	E111° 49.906
Sub-Urban	CA0027	Bintulu Police Station, Sarawak	N03° 10.587	E113° 02.433
Sub-Urban	CA0028	Dato Permaisuri Secondary School, Miri, Sarawak	N04° 25.456	E114° 00.731
Sub-Urban	CA0032	Langkawi Sport Complex, Langkawi, Kedah	N06° 19.903	E099° 51.517
Sub-Urban	CA0033	MADA, Behor Temak, Kangar, Perlis	N06° 25.424	E100° 11.046
Urban	CA0040	Islamic Religious Secondary School, Mergong, Alor Setar, Kedah	N06° 08.218	E100° 20.880
Sub-Urban	CA0044	Vocational Secondary School, Muar, Johor	N02° 03.715	E102° 35.587

show the location of the affected Air Quality Monitoring Station (AQMS) where the air pollution data are obtained. Data were obtained from the years 2005 until 2014 with the exclusion of years 2007 to 2009 from the Air Quality Division, Department of Environment (DOE), Ministry of Natural Resources and Environment of Malaysia. They were tabulated and arranged based on the chronological timeline of haze episodes in Malaysia [14] in Microsoft Excel Spreadsheet^® 2016 and analyzed using Statistical Packages for Social Sciences (SPSS^®) version 25. The parameters used in this study were particulate matter with an aerodynamic diameter less than 10 µm (PM₁₀, µg/m³), ambient temperature (T, °C), relative humidity (RH, %), wind speed (WS, km/hr), ground-level ozone (O₃, ppm), nitrogen oxide (NO, ppm), nitrogen dioxide (NO₂, ppm), carbon monoxide (CO, ppm), and sulphur dioxide (SO₂, ppm) to gain a better picture of PM₁₀ variability during transboundary haze. The relationship between these parameters was examined using bivariate correlation analysis in which the PM₁₀ concentration was measured using the β-ray attenuation mass monitor (BAM-1020) as manufactured by Met One Instruments Inc. [27]. Meanwhile, the meteorological parameters were measured using Met One 062 sensor for ambient temperature, Met One 083D sensor for relative humidity, and Met One 010C sensor for wind speed [35]. The Teledyne API Model 400/400E instrument hourly through UV absorption (Beer-Lambert) method with a 0.4ppb detection limit and 0.5% of precision level and Model 200A NO/NO₂/NO_x analyzer, which applies chemiluminescence detection principles was used to detect O₃, NO₂, and NO concentrations in ambient air, respectively [36,37]. The SO₂ and CO concentrations were monitored and measured by the Teledyne API Model 100A/100E and Teledyne API Model 300/300E, with the lowest detection level of SO₄ at 0.04 ppb by the UV fluorescence method. Meanwhile, the CO level was measured with 0.5% precision and the lowest detection was found at 0.04 ppm by the non-dispersive and infrared absorption (Beer-Lambert) method [37]. Therefore, all instruments were set to have daily calibration using zero air and standard gas concentration to guarantee the quality control and assurance of data monitoring and validation processes, which were revised before they were transferred to the DOE [38]. Missing data might occur due to equipment malfunction and the calibration program, which were thus removed to reduce the bias in the prediction and conservative results [39].

2.2. Multiple Linear Regression

Stepwise Multiple Linear Regression (MLR) statistical models were developed in this study with a 95% confidence interval and the dataset was separated according to 7:3 ratios for model development and validation, respectively [40,41]. Based on the data tabulated in the Microsoft Excel Spreadsheet^® 2016, 70% of the earlier data in this spreadsheet were used for model development, while the remaining 30% were used for model validation. This statistical model can relate the single dependent variable with two or more independent variables and the equation of the MLR model is stated in Equation (1) [27].

y = b₀ + ∑_{iⁿ = 1}b_i X_i + ε

(1)

where, b_i is the regression coefficient (independent variables), ε is the stochastic error associated with the regression.

In the air pollution modelling, the dataset consisted of different types of units and it required normalizing before the development of models in order to improve the accuracy of the numeric computation, which was scaled within the range of 0 to 1. Hence, these normalization steps can interpret all relationships in the data precisely and reduce bias [27,31]. Equation (2) shows the normalization equation used in this study.

z_i = (x_i) − min(x)/max(x) − min(x)

(2)

where x = (x₁, …, x_n) and z_i is normalised data.

Variance Inflation Factor (VIF) is the multicollinearity assumption together with regression output, whereby the average of VIF values must be below ten to indicate no multicollinearity problem between the independent variables [27,42]. The VIF equation is shown in Equation (3).

$$VI{F}_i=\frac{1}{1-R_i^2}$$

(3)

where, VIF_i is the variance inflation factor with ith predictor, R_i² is the determination in a regression of the ith predictor on all other predictors.

The Durbin–Watson (DW) test was used to determine the autocorrelation ability of PM₁₀ concentration during the current hour to predict PM₁₀ in the subsequent hour. The range values of the test must be between 0 and 4 with a value of 2, showing that the residuals are uncorrelated [27,42]. The DW equation is shown per Equation (4).

$$DW=\frac{{{\displaystyle \sum }}_{i=1}^n{(e_i-e_{i-1})}^2}{{{\displaystyle \sum }}_{i=1}^n{e_i}^2}$$

(4)

where, n is the number of observations, ei = yi − yi; (yi = observed values and yi is the predicted values).

Coefficient of Determination (R²) was one of the indicators used to determine whether the data provided enough evidence to indicate that the overall models contributed sufficient information for the prediction of PM₁₀ concentrations. It also acts as an indicator to measure the extent to which the prediction models fit the data [27,42]. The R² equation is shown per Equation (5).

$$\mathrm{R}{2}^{ }={(\frac{{{\displaystyle \sum }}_{i=1}^n\left(Pi-\overline{P}\right)\left(Oi-\overline{O}\right)}{n.S_{pred}{S}_{obs}})}^2$$

(5)

where, n = total number measurements at a particular site, P_i = predicted values, O_i = observed values, $\overline{P}$ = mean of predicted values, $\overline{O}$ = mean of observed values, S_pred = standard deviation of predicted values, and S_obs = standard deviation of the observed values.

2.3. Performance Indicator

The models were evaluated based on the model’s error and accuracy by using several performance indicators, namely Root Mean Square Error (RMSE), Normalized Absolute Error (NAE), and Prediction of Accuracy (PA). The best-fitted model is chosen when it has high accuracy in which the PA is closer to 1 while the minimal error (i.e., RMSE and NAE) is close to 0 [32,35,40]. Equations (6)–(8) show the performance indicators’ formula used in this study.

(a) Root Mean Square Error

$$RMSE={(\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n[P_i-O_{i }]}^2{)}^{1/2}$$

(6)

(b) Normalized Absolute Error

$$NAE=\frac{{{\displaystyle \sum }}_{i=1}^n\left|P_i-O_{i }\right|}{{{\displaystyle \sum }}_{i=1}^n{O}_i}$$

(7)

(c) Prediction of Accuracy

$$PA={{\displaystyle \sum }}_{i=1}^n\frac{{( P_{i }-\overline{P})}_{ }}{\left(n-1\right)S_{pred} S_{Obs}}$$

(8)

where, n = total number of data; P_i = predicted values; O_i = observed values; $\overline{P}$ = mean of predicted values; S_pred = standard deviation of predicted values; S_obs = standard deviation of observed values

3. Results and Discussion

The maximum daily average of PM₁₀ concentration during a transboundary haze event in Malaysia in the years of 2014 and 2013 was 995 µg/m³, while the minimum value of PM₁₀ concentration was 150 µg/m³ in all years as this was the minimum concentration for notification as haze [5,40,43].

Table 2. Summary of descriptive statistics during periodic haze events in Malaysia.

Descriptive Statistical	2005 (N = 369)	2006 (N = 918)	2010 (N = 61)	2011 (N = 260)	2012 (N = 402)	2013 (N = 236)	2014 (N = 613)
Mean (µg/m3)	274.860	199.100	275.100	178.930	204.270	260.650	233.520
Median (µg/m3)	237.000	180.000	196.000	168.000	181.000	210.000	187.000
Std. Deviation (µg/m3)	136.103	56.435	170.717	37.299	63.071	141.508	131.163
Variance	18524.096	3184.955	29144.323	1392.180	3977.931	20024.500	17203.855
Minimum (µg/m3)	150.000	150.000	150.000	150.000	150.000	150.000	150.000
Maximum (µg/m3)	994.000	573.000	866.000	497.000	533.000	995.000	995.000

summarizes the descriptive statistics during the chronology of haze events that happened in Malaysia from the years 2005 until 2014. The highest mean concentration of PM₁₀ was recorded in the year 2005 at 274.860 µg/m³ (150.000−994.000 µg/m³), while the lowest mean concentration of PM₁₀ was 178.930 µg/m³ in the year 2011 (150.000–497.000 µg/m³). The Department of Environment Malaysia sets a guideline to justify the status of air quality in the country under the New Ambient Air Quality Standard (NAAQS), whereby the daily 24 h PM₁₀ concentration is 150 µg/m³ [33,44]. Combustion activities due to the agriculture sector such as biomass and peatland combustion in Indonesia for land clearing thus creates haze pollution that has further affected the neighboring countries, especially Malaysia. Altogether, the higher concentration of hazardous PM₁₀ are transported thousands of kilometers by the wind and monsoon [13,17]. The transboundary haze events frequently happen during the dry season in July to October and are extended to southwest monsoon in February to March, which prolongs the combustion activities due to less amount of rainfall and drier condition of the land [5,13].

The Spearman bivariate analysis was applied as the data were not normally distributed and non-parametric in order to see the relationship linking PM₁₀ with meteorological factors and other gaseous pollutants during the periodic haze events in Malaysia as tabulated in

Table 3. Spearman correlation of PM₁₀ between meteorological factors and other gaseous pollutants during periodic haze events.

Parameter	PM10	WS	T	RH	NO	SO2	NO2	O3	CO
PM10	1.00	0.043	0.055 *	−0.076 **	−0.025	0.131 **	0.059 **	0.046 *	0.512 **
WS		1.00	0.517 **	−0.537 **	−0.380 **	−0.029	−0.372 **	0.615 **	−0.206 **
T			1.00	−0.820 **	−0.259 **	0.050 *	−0.088 **	0.621 **	0.006
RH				1.00	0.230 **	−0.196 **	0.003	−0.590 **	−0.038
NO					1.00	0.259 **	0.617 **	−0.671 **	0.325 **
SO2						1.00	0.458 **	−0.141 **	0.356 **
NO2							1.00	−0.443 **	0.437 **
O3								1.00	−0.243 **
CO									1.00

Note ** Correlation is significant at the 0.01 level (2-tailed), * Correlation is significant at the 0.05 level (2-tailed).

. The CO (r = 0.512, p < 0.01) showed a strong and positive correlation by increasing the concentration of PM₁₀ at the atmosphere. Meanwhile, T (r = 0.055, p < 0.05), SO₂ (r = 0.131, p < 0.01), NO₂ (r = 0.059, p < 0.01), and O₃ (r = 0.046, p < 0.05) were weakly and positively correlated to PM₁₀ concentration. Similarly, RH was weakly and negatively correlated with r = −0.076, p < 0.01. Open burning from land clearing activities at Sumatra (Indonesia) has been contributing to a high concentration of carbon dioxide in the atmosphere during such periodic haze events [3]. The incomplete combustion of carbon thus generates CO₂ concentration via some chemical reactions with another atmospheric constituent [3,5]. Hence, high emission of CO also causes a high emission of particulate matter and toxic organic air contaminants, which have an adverse impact on human health [45,46].

A statistical model to precisely forecast the PM₁₀ concentrations during haze events using MLR was founded using 70% of the dataset, while the remaining 30% were used for model validation. The MLR models were developed based on three different prediction hours, which were to predict the first hour of PM₁₀ concentration up until the next three hours of PM₁₀ concentration. A summary of the models is tabulated in

Table 4. Model summary for PM₁₀ concentration forecasting during transboundary haze events in Malaysia.

Prediction Hour	Model	R2	VIF	Durbin-Watson
Hour 1, t+1	PM10,t+1 = 0.004 + 0.673 PM10 + 0.230 CO − 0.057 NO	0.638	1.275–2.149	2.125
Hour 2, t+2	PM10,t+2 = 0.019 + 0.597 PM10 + 0.141 CO − 0.053 NO	0.452	1.275–2.149	1.201
Hour 3, t+3	PM10,t+3 = 0.069 + 0.586 PM10 − 0.047 RH − 0.046 O3	0.353	1.006–1.629	0.932

. All models were developed from the PM₁₀ concentration during the transboundary haze event occurring in Malaysia. Based on the models, the first prediction hour of PM₁₀,_t+1 had a higher coefficient of determination (R²) at 0.638 compared to the second (PM₁₀,_t+2) and third (PM₁₀,_t+3) prediction hour at 0.452 and 0.353, respectively. Furthermore, the VIF values for all three models (i.e., range between 1.006 and 2.149) were lower than 10, which indicated no multicollinearity problem present between the independent variables. Moreover, the DW test showed that the range values for all models were 2.125, 1.201, and 0.932 for PM_10,t+1, PM1_{0, t+2}, and PM_10,t+3, respectively. Hence, it indicated that all of the models did not have any first-order autocorrelation problem as the range values were still within 0–4 [27,42]. Thus, the PM_10,t+1 forecasting model, which was considered as the best-fit model in this study, revealed acceptable values of R² as discovered in the previous study of PM₁₀ forecasting models by [27,40,47] and higher R² values compared to the other two models.

For the first prediction hour of model forecasting, the significant predictors for PM₁₀,_t+1 was CO and NO. The predicted PM₁₀,_t+1 concentration increased by 0.673 unit when the PM₁₀ variables increased by one unit, an increase of 0.230 unit by one unit of CO, and a decrease of 0.057 unit by one unit of NO. Meanwhile, this was also applicable for PM₁₀,_t+2: the same variable influenced it with PM₁₀,_t+1 in which one unit of PM₁₀ increased one unit of PM₁₀,_t+2. There was an increase of 0.141 and decrease of 0.053 PM_10,t+2 by one unit of CO and NO, respectively. Moreover, PM₁₀,_t+3 was influenced by three different variables, namely PM₁₀, RH, and O₃. The increase in unit for PM₁₀ and one unit decrease of RH and O₃ led to the increase of 0.568 unit and decrease of 0.047 and 0.046 units of PM₁₀,_t+3, respectively. Generally, the biomass combustion activities emit several compounds such as aerosols in the form of organic carbon, black carbon, and inorganic carbon; greenhouse gases such as carbon dioxide (CO₂); and photochemical reactive gases like CO and nitrogen oxide (NO_x) [48]. The O concentration represents the dominant species after carbon dioxide and it is used as a tracer of biomass burning plumes in the remote troposphere in the form of smoke particles [19,48].

The normal distribution of residuals is illustrated with zero mean and constant variances for all three models in Figure 2a–c. Meanwhile, the fitted values plot with PM₁₀ prediction model’s residuals show that the residuals are uncorrelated due to the residuals accumulating around the horizontal band, further indicating that the variance is constant and uncorrelated as depicted in Figure 2d–f. Unfortunately, more residuals dispersed away from the horizontal band as the prediction hour increased to the second to third hour of PM₁₀ prediction time. Hence, this condition would hinder the best fit of the models, which reduced the precision of PM₁₀ concentration forecasting.

The predicted daily PM₁₀ concentration was plotted against the observed PM₁₀ concentration by prediction hour based on the 30% of haze chronology event data. Figure 3a–c illustrates the goodness-of-fit of the PM₁₀ forecasting models in Malaysia. The regression lines drawn showing 95% confidence interval and most of the points were accumulated in between lines A and B, which were the upper and lower ranges of 95% confidence interval for the regression model. The accuracy of the predicted model for the next hour (PM_10,t+1) was thus proven by having the highest R² values of 0.447 compared to models PM_10,t+2 (0.186) and PM_10,t+3 (0.129). Hence, the increase of prediction hours of the models reduced their respective performance by increasing some of the errors of the prediction models, rendering it less precise [29,49].

The RMSE, NAE, and PA components were chosen in this study to measure the performance of the models. RMSE and NAE are considered as suitable indexes for determining model accuracy in which the model is noted as having a high accuracy when their values are close to zero, while the PA value is nearest to 1 [32,50,51]. According to a previous study [32], a comparison of the best statistical PM₁₀ forecasting methods with the lowest values of RMSE and NAE and the highest PA value has been conducted to select the best-fit prediction model.

Table 5. Summary of performance indicator for all PM₁₀ forecasting models during the transboundary haze events.

Prediction Hour	RMSE	NAE	PA
Hour 1, t+1	126.728	0.325	0.668
Hour 2, t+2	156.506	0.403	0.431
Hour 3, t+3	164.978	0.429	0.359

depicts the performance indicator values for all PM₁₀ forecasting models in this study. It showed that the PM_10,t+1 model yielded the lowest value of RMSE (126.728) and NAE (0.325), while it had the highest PA value (0.668) compared to the PM_10,t+2, and PM_10,t+3 models. Based on the results from this performance error and accuracy measures, the PM_10,t+1 model provided better PM₁₀ concentration forecasting capacity compared to model PM_10,t+2, and model PM_10,t+3 in Malaysia during transboundary haze events.

4. Conclusions

The maximum PM₁₀ concentration was higher during transboundary haze events in the years 2013 and 2014 at 995 µg/m³ and the higher mean values of PM₁₀ concentration was 274.860 µg/m³ (150–994 µg/m³) in the year 2005. Meanwhile, the lowest mean value obtained was 178.930 µg/m³ (150–497 µg/m³) in the year 2011. Next, the Spearman correlation analysis showed that CO was strongly and positively correlated with r = 0.512, p < 0.01. This was due to its higher emission through large-scale biomass combustion from neighboring countries. Furthermore, the best-fitted MLR model for PM₁₀ prediction during transboundary haze events was PM_{10, t+1}, which had a higher R² of 0.447 compared to PM_10,t+2 (0.186) and PM_10,t+3 (0.129). On the other hand, PM_10,t+1 was the best-fitted model with a higher accuracy of 0.668 and lower values of RMSE (126.728) and NAE (0.325) compared to models PM_10,t+2 and PM_10,t+3. The development of this model may thus aid the responsible parties in obtaining early information that can improve or initiate strategies in mitigating for better air quality.