Exploring the impact of air pollution on COVID-19 admitted cases

In urban areas, air pollution is one of the most serious global environmental issues. Using time-series approaches, this study looked into the validity of the relationship between air pollution and COVID-19 hospitalization. This time series research was carried out in the state of Kuwait; stationarity test, cointegration test, Granger causality and stability test, and test on multivariate time-series using the Vector Error Correction Model (VECM) technique. The findings reveal that the concentration rate of air pollutants (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {O}_3$$\end{document}O3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SO}_2$$\end{document}SO2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NO}_2$$\end{document}NO2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}$$\end{document}CO, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {PM}_{10}$$\end{document}PM10) has an effect on COVID-19 admitted cases via Granger-cause. The Granger causation test shows that the concentration rate of air pollutants (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {O}_3$$\end{document}O3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {PM}_{10}$$\end{document}PM10, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NO}_2$$\end{document}NO2, temperature and wind speed) influences and predicts the COVID-19 admitted cases. The findings suggest that sulfur dioxide (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SO}_2$$\end{document}SO2), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NO}_2$$\end{document}NO2, temperature, and wind speed induce an increase in COVID-19 admitted cases in the short term according to VECM analysis. The evidence of a positive long-run association between COVID-19 admitted cases and environmental air pollution might be shown in the cointegration test and the VECM. There is an affirmation that the usage of air pollutants (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {O}_3$$\end{document}O3, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SO}_2$$\end{document}SO2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {NO}_2$$\end{document}NO2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}$$\end{document}CO, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {PM}_{10}$$\end{document}PM10) has a significant impact on COVID-19-admitted cases’ prediction and its explained about 24% of increasing COVID-19 admitted cases in Kuwait.

that examines the association between daily COVID-19 admitted cases and air pollution.
• Most notably, this study seeks to explore the dynamic causality between air pollutants (O 3 , SO 2 , NO 2 , CO, and PM 10 ) concentrations rate and the daily COVID-19 admitted cases using the panel Granger causality test based on the vector error correction model (VECM). • The VECM was chosen for this study for the following reasons: The method can allow endogenous variables; the VECM methodology can provide alternative analysis channels to analyze causality that is disregarded by the traditional Granger causality test due to the error correction term (ECM) (Azlina et al., 2014). Meanwhile, the VECM is capable of distinguishing between short-run and long-run causality (Azlina et al., 2014).

Relationship between air pollution and human health
Numerous studies have indicated the major air pollutants causing adverse health effects in Saudi Arabia including O 3 , SO 2 , NO 2 , CO and PM 10 (Al Mulla et al., 2015;Argyropoulos et al., 2016). It has been discovered that incomplete burning of Arabian incense produces emissions of CO, PM 10 , PM 2.5 , black carbon, and polycyclic aromatic hydrocarbons (PAHs), all of which have negative health effects on the population who are exposed to these emissions (Du et al., 2018). Ischemic heart disease (IHD), chronic obstructive pulmonary disease (COPD), and lung cancer have all been linked to these air pollutants (Amoatey et al., 2018).

Impact of air pollution as risk factor to COVID-19 patients
During COVID-19, air pollution was identified as a risk factor in several Italian research. Among the areas of Northern Italy, a correlation with higher levels of pollutants such as PMs has a considerable impact on human health (Domingo et al., 2020;Martelletti & Martelletti, 2020). It has also been discovered that people who live in areas with high levels of air pollution are more likely to acquire chronic respiratory illnesses and are more susceptible to any infectious agent (Distante et al., 2020).
In China, air pollution has been proven to be positively associated with SARS mortality (Cui et al., 2003). Although COVID-19 risk factors are still being investigated, it is probable that environmental variables such as air pollution could substantially impact the epidemic's spread among the population. In the case of SARS-CoV-2, many studies have found a significant relationship between air pollution and the rate at which the virus spreads. Six air pollutants (PM 2.5 , PM 10 , SO 2 , CO, NO 2 , and O 3 ) were significantly linked to confirmed cases in 120 Chinese cities from January 23 to February 29, 2020, according to the Zhu et al. (2020). The most badly afflicted region in Europe is the same as the one with the highest concentrations of PM 10 and PM 2.5 , according to Martelletti and Martelletti (2020). In addition, the majority of fatality cases were in areas with the highest NO 2 concentrations (Ogen, 2020). According to  and Sharma et al. (2020), the associations were also confirmed in California, the United States, and India.

The relationship between atmospheric variables and COVID-19 cases
Finally, for other coronavirus epidemics, it is well documented in the literature how climatic circumstances can influence transmission, either promoting or reducing it. Atmospheric variables such as ambient temperature and humidity, as well as sun irradiation, have various impacts on coronavirus survival, for example, Casanova et al. (2010) and Lauc et al. (2020). This indicates that the coronavirus spread is facilitated in dry and cold weather. Nonetheless, it is still unknown if and how the SARS CoV-2 virus spreads or is impacted by meteorological factors like other seasonal viruses. Several recent studies looked at the role of meteorological variables in COVID-19 transmission all over the world. As shown in Pani et al. (2020), studies from China Ma et al., 2020;Shi et al., 2020;, Iran , Spain (Briz-Redón & Serrano-Aroca, 2020), USA Gupta et al., 2020), Indonesia (Tosepu et al., 2020), Norway (Menebo, 2020), and also over the global (Sobral et al., 2020;Wu et al., 2020) are controversial and The World Health Organization (WHO) has stated that more research should be focus on how to quantify how the weather affects the virus's spread.

Time-series analysis to predict COVID-19 cases
It is clear from previous research that time-series models such as exponential smoothing, ARIMA, and SARIMA performed well and provided adequate results for COVID-19 prediction. Many scholars have researched COVID-19 virus infection predictions. All previous research has established that the ARIMA model is the most effective for forecasting (Benvenuto et al., 2020;Jain et al., 2021;Murugesan et al., 2020;Mustafa & Fareed, 2020;Sahai et al., 2020;Sulasikin et al., 2020). Sulasikin et al. (2020) used three approaches to predict the COVID-19 instances (Holt's method, Holt-Winters method, and ARIMA). Among the other models, the ARIMA model was deemed the best by the author. Furthermore, Nguyen et al. (2021) demonstrated that the COVID-19 infection incidence could be effectively incorporated locally into a VECM with the COVID-19 hospital data to improve the existing forecast models and produce precise short-term forecasts and practical situation-based long-term trajectories.

Theoretical notions and the model
The vector autoregressive model (VAR) for analysis was used to evaluate the hypothesis of the influence of industrial pollution on public health. VAR was chosen, because it does not need the assumption of exogeneity of variables a priori and allows each variable to self-interact and interact with other variables without imposing a theoretical structure on the estimates. A Vector Error Correction Model (VECM) is used to approximate the impulse response functions if all variables in our VAR cointegrate with order I (1) and if there are cointegration associations between them. The following multivariate model was studied in the study utilizing the VECM to test the long-run associations.
The cointegration rank in VECM indicates the number of cointegrating vectors. A rank of two, for example, suggests that two linearly independent combinations of the non-stationarity variable are stationary. Any short-term variations between the independent variables and the dependent variable will create a stable long-run relationship between the variables if the error correction model (ECM) coefficient is negative and significant.

Data and variables
The data utilized for the study span the months of March 10, 2020 and December 31, 2020. Kuwait Environment Public Authority provided statistics on air pollutants (O 3 , SO 2 , NO 2 , CO, and PM 10 ) (K-EPA). Kuwait's Ministry of Health provided the daily COVID-19 cases (MOH). (https://corona.e.gov.kw/en) presented summary of the daily COVID-19 cases in Kuwait. All of the variables were converted to their natural logarithms before using the model.

Air Quality Index (AQI)
The Air Quality Index (AQI) is a numerical indicator of a region's air quality. The AQI scale has the range 0 to 500, with a higher AQI value indicating poor air quality and a lower AQI (< 100) signifying good air quality in a given area. AQI values were calculated using 24-h average PM 10 and PM 2.5 , 8-h average CO and O 3 , and 1-h average NO 2 and SO 2 levels in the current study. The maximum AQI observed for a city was used as the overall AQI.

Stationarity test
The ability of a series' stationarity to impact its behaviour is a significant phenomenon. If the x and y series are non-stationary random processes (integrated), modelling the x and y relationship as a simple OLS relationship, as in Eq. (1), will result in a misleading regression The statistical features of a series over time, such as its mean and variance, are known as time-series stationarity. The series is considered to be a stationary process (that is, not a random walk/has no unit root) if both are constant across time; otherwise, the series is defined as a non-stationary process (that is, a random walk/has unit root) (2) If a series is stationary without any differencing, it is designated as I (0), or integrated of order 0. On the other hand, a series that has stationary first differences is designated I (1), or integrated of order one (1). Augmented Dickey-Fuller test suggested by Dickey and Fuller (1979), and the Phillips-Perron test recommended by Phillips and Perron (1988) have been used to test the stationarity of the variables.

Unit-root test
Spurious regression can be reduced by conducting a unit-root test for each variable before analysis, because data are used as an all-time-series. Phillips-Perron (PP), Dickey-Fuller (ADF), and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests were used, and the results are available in Tables 4, 5, 6, and 7. Non-stationary variables in an estimated model can lead to spurious results that cannot be used for inferences. The PP test does not assume homoscedasticity in the error term, but this assumption is required for the ADF test.

Dickey-Fuller tests (DF test and ADF test)
Dickey-Fuller test (Dickey & Fuller, 1979) is one of the best known and most widely used unit-root tests. It is based on the model of the first-order autoregressive process (Box et al., 1970) where φ 1 is the autoregression parameter, and ε t is the non-systematic component of the model that meets the characteristics of the white noise process. The null hypothesis is H 0 : φ 1 = 1, i.e., the process contains a unit root, and therefore, it is non-stationary, and is denoted as I (1), alternative hypothesis is H 1 : |φ 1 | < 1, i.e., the process does not contain a unit root and is stationary, I (0). To calculate the test statistic for DF test, we use an equation that we get if y t1 is subtracted from both sides of Eq. (3) where β = φ 1 − 1. The test statistic is defined as whereφ 1 is a least square estimate of φ 1 and sφ t is its standard error estimate. Under the null hypothesis, this test statistic follows the Dickey-Fuller distribution, and critical values for this distribution were obtained by a simulation and have been tabulated in Dickey (1976) and Fuller (1976).
Model (3) can be expanded by a constant or a linear trend In the case when a non-systematic component in DF models is autocorrelated, the so-called Augmented Dickey-Fuller test is constructed (Dickey & Fuller, 1981). Model (3) is then transformed as and the following equation is used to calculate the test statistic of the ADF test:

Phillips-Perron test (PP test)
There is typically a problem selecting lag p in the regression model when unit-root testing time-series generated by a process with the autocorrelated and heteroscedastic non-systematic component. Instead of using appropriate autocorrelation models to describe the autocorrelation structure of the generating process, Phillips and Perron (1988) employed the usual Dickey-Fuller test with non-parametrically adjusted test statistics. This test is also founded on the models (3) and with the variation being that the linear trend in the last model is replaced by a time variable that is centred.

KPSS test
The null hypothesis states that the time-series y t is integrated of order one, I (1), as tested by all of the following tests. The KPSS test describes the opposite case, namely testing the null hypothesis that the time-series y t is I (0) (Kwiatkowski et al., 1992). The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test determines whether a timeseries is stationary or non-stationary around a mean or linear trend due to a unit root. A stationary time-series has statistical qualities that remain constant across time, such as the mean and variance.
The KPSS test is based on linear regression. It breaks up a series into three parts: a deterministic trend (β t ), a random walk (r t ), and a stationary error (ε t ), with the regression equation If the data are stationary, it will have a fixed element for an intercept or the series will be stationary around a fixed level (Wang, 2006). The test uses ordinary least squares (OLS) find the equation, which differs slightly depending on whether you want to test for level stationarity or trend stationarity (Kočenda &Černỳ, 2015). A simplified version, without the time trend component, is used to test level stationarity.
Data are normally log-transformed before running the KPSS test, to turn any exponential trends into linear ones.

Johansen and Juselius cointegration test
Johansen procedures (Johansen & Juselius, 1990) use two tests to determine the number of cointegration vectors: the Maximum Eigenvalue test and the Trace test. The Maximum Eigenvalue statistic tests the null hypothesis of r cointegrating relations against the alternative of r + 1 cointegrating relations for r = 0, 1, 2 . . . n − 1. This test statistics are computed as where λ is the maximum eigenvalue and T is the sample size. Trace statistics investigate the null hypothesis of r cointegrating relations against the alternative of n cointegrating relations, where n is the number of variables in the system for r = 0, 1, 2 . . . n − 1. Its equation is computed according to the following formula: In some cases, trace and maximum eigenvalue statistics may yield different results, and Alexander (2001) indicates that in this case, the results of trace test should be preferred.

Granger causality test
Initially, we will assume that all variables are stationary. If the original variables have unit roots, then we assume that differences have been taken, such that the model includes the changes in the original variables (which do not have unit roots).
When we investigated Granger causality between X and Y , we began with an Autoregressive Distributed Lag Model ADL( p, q) model for Y as the dependent variable.
An ADL( p, q) model assumes that a time-series Y t can be represented by a linear function of p of its lagged values and q lags of another time-series X t is an autoregressive distributed lag model with p lags of Y t and q lags of X t , where We used this model to investigate if X Granger caused Y . We then went on to consider causality in the other direction, which involved switching the roles of X and Y in the ADL. In particular, X became the dependent variable. We can write the two equations as follows: The first of these equations tests whether X Granger causes Y ; the second, whether Y Granger causes X . Note that now the coefficients have subscripts indicating which equation they are in. The errors now have subscripts to denote the fact that they will be different in the two equations.

Cointegration and VECM
When cointegration is identified between series, it is known that there exists a long-term equilibrium relationship between them, so we use VECM to evaluate the cointegrated series' short-run features. If there is no cointegration, we skip VECM and go straight to Granger causality tests to determine the causal associations between variables. The regression equation form for VECM is as follows: All variables are transformed in their log forms to mitigate inconsistency in the data and ease interpretation of the results via elasticities, the following is the empirical specifications for the model can be quantified as: where COVID-19 admitted cases are the dependent variable, while O 3 , SO 2 , NO 2 , CO, PM 10 , temperature, relative humidity (RH), and wind speed (WS) are the explanatory variables in days t, ε t is the error term, and β 0 , β 1 , β 2 , β 3 , β 4 , β 5 , β 6 , β 7 , β 8 and β 9 are the elasticities to be estimated.
However, a linear function can be used to express the relationship between number of COVID-19 cases and air pollution in Kuwait, as showed in the following expression: Vector autoregression (VAR) model is first considered in the study following the work of Asumadu-Sarkodie and Owusu (2016), Chang (2010) and Gul et al. (2015). Which can be expressed as The corresponding VEC model can be expressed as where y t = α 0 + α 1 x t is the long-run cointegrating relation existing between two variables of interest, and λ y and λ x are the error correction parameters measuring the reaction of y and x towards the deviations from long-run equilibrium Long run and cointegration between variables can be examined via several methods [e.g., Engle & Granger 1987, Johansen's method (Johansen, 1995), Dynamic Ordinary Least Squares (DOLS), Fully Modified Ordinary Least Squares (FMOLS), and VEC models] for which variables need to be either I (1) or there needs to be prior knowledge and specification of variables as I (0) and I (1). An ARDL model can be used to estimate cointegration among variables at either I (0) or I (1) without the need to pre-specify which variables are I (0) or I (1) (Pesaran et al., 1995). Furthermore, an ARDL model does not require symmetry lag lengths and can have different number of lag terms unlike other cointegration estimation methods (Pesaran et al., 1995). In the present study, the long-run equilibrium relationship between number of COVID-19 cases and the independent variables (SO 2 and O 3 ) was estimated using the VEC model of cointegration. Table 1 shows the descriptive statistics for the air pollutant variables. The mean value corresponding to O 3 , CO, PM 10 , SO 2 and NO 2 was 24.82 ± 7.20, 9.11 ± 3.61, 79.51 ± 24.45, 11.24 ± 5.21, and 26.72 ± 13.00, respectively. It is also evident that except O 3 , all the pollutants were positively skewed, i.e., mean values of these pollutants were high as compared to the median value. Moreover, Shapiro-Wilk test shows that the distributions of the variables were significantly differ from normal distribution. Therefore, log-transformation will be applied on the variables to convert the distribution of the variable to be normal distribution, before performing any further analysis. Minimum, maximum and percentile values of the pollutants are also shown in Table 1.

The descriptive statistics
Descriptive statistics for daily climatology variable (RH, Temp, WD, and WS), COVID-19 cases, and COVID-19 deaths are shown in Table 2. The mean value for RH, Temp, WD, and WS is 35.51 (SD = 20.06), 30.26 (SD = 7.96), 206.138 (SD = 54.48), and 2.18 (SD = 0.66), respectively. Moreover, on an average, 506 cases of COVID-19 and 3 deaths due to COVID-19 were reported in the study period. Results of Shapiro-Wilk test shows that the distributions of the climatology parameters, COVID-19 cases, and COVID-19 deaths were different from the normal distribution. Therefore, log-transformation will be applied on the variables to convert the distribution of the variables to be normal. The value of other test statistics, i.e., median, skewness, kurtosis, minimum, maximum, and percentile for each variable is also shown in Table 2. Table 3 present results of the correlation analysis for air pollutants, climatology parameters, and COVID-19 cases. A strong significant positive correlation was observed between temperature and COVID-19 cases (r p = 0.61), indicated that as the value of temperature increases, COVID-19 cases also increase, whereas a negative significant correlation was observed between RH and COVID-19 cases (r p = −0.49), indicated that as the value of relative humidity (RH) increases, COVID-19 cases decrease. Moreover, a small effect of O 3 (r p = 0.25), CO (r p = 0.24), PM 10 (r p = 0.18) and NO 2 (r p = 0.22) was also observed on COVID-19 cases.

Results of Granger causality test
Granger causality test has been conducted to check if the series of independent variables is useful for making prediction or not. Results of the Granger causality test have been shown in the following subsection.

Results of the unit-root tests
Unit-root tests for each variable were conducted before the main analysis to avoid spurious regression in time-series research (Mahadeva & Robinson, 2004). Some air pollutant and climatology parameters were significantly associated with COVID-19, so VECM analysis was done to assess the short-and long-term relationship of these variables. Since non-stationary series may also product spurious regression results for VECM (Asari et al., 2011;Latief et al., 2021), stationary tests on the time-series data were performed using the conventional Augmented Dickey-Fuller (ADF-GLS), and Phillips-Perron (PP) and KPSS Tests. ADF results are shown in Tables 4 and 5, and PP and KPSS tests are shown in Tables 6 and 7.
Tables 4 and 5 present the results of the ADF-GLS unit roots test in levels and first differences (results with constant are presented in Table 4, and results with constant and trend are presented in Table 5). The results of test confirm that all variables used in research (COVID-19 cases, O 3 , SO 2 , NO 2 , CO, and PM 10 ) are integrated of first order I (1). The ADF-GLS test results for COVID-19 cases, CO, PM 10 and SO 2 where the null hypothesis of non-stationarity is rejected for levels (test with constant), what means that recreation COVID-19 cases because of air pollution (CO, PM 10 and SO 2 ) could be a stationary process. In addition to that, the ADF-GLS (test with constant and trend (c + t)) results for O 3 , SO 2 , NO 2 , CO, and PM 10 where the null hypothesis of non-stationarity are rejected for levels, what means that recreation COVID-19 cases because of air pollution (O 3 , SO 2 , NO 2 , CO, and PM 10 ) could be a stationary process over a trend. However, the KPSS test (where the null hypothesis of stationarity is rejected for levels) suggest the first order of integration (I (1)) for all variables except SO 2 (see Table 6). Because of the inconsistency in ADF test, we diced to take the KPSS test results under consideration. Hence, all variables except SO 2 in levels are I (1) variables, and then, the cointegration analysis were conducted in next step.
ADF root test with constant shows that the time-series for pollutants CO, PM 10 , SO 2 and series of COVID-19 cases is stationary at 5%-level Dickey-Fuller criterion, whereas series of O 3 and NO 2 was stationary at first difference (Table 4). The results of ADF test with constant and trend demonstrate that the series of all the pollutants are stationary at level, whereas series of COVID-19 was stationary at first difference ( Table 5). The results of PP unit-root test shows that the series of all the pollutant variables and COVID-19 cases is stationary at level as well as on the first difference ( Table 7). The results of KPSS test shows that the series of all the pollutants (except SO 2 ) and COVID-19 cases are non-stationary at level, though all the series are found to be stationary at first difference (Table 6).    2.18e−11*** *Stationarity at 10% significance levels, **stationarity at 5% significance levels, ***stationarity at 1% significance levels  1.47e−11*** *Stationarity at 10% significance levels, **stationarity at 5% significance levels, ***stationarity at 1% significance levels  *Stationarity at 10% significance levels, **stationarity at 5% significance levels, ***stationarity at 1% significance levels  8.81e−08*** *Stationarity at 10% significance levels, **stationarity at 5% significance levels, ***stationarity at 1% significance levels

Estimation of VAR model
After checking the stationarity of the series, the next step is to determine the number of optimal lags. To choose the number of lags need to be included in the VAR model, VARselect function has been taken into consideration. This function calculates three different information criteria across a number of different lags (up to a maximum specified within the function) and chooses the lag that has the lowest information criteria for each of the three statistics. The asterisks symbol indicate the best values under the respective information criteria, AIC = Akaike criterion, BIC = Schwarz Bayesian criterion, and HQC = Hannan-Quinn criterion. Table 8 illustrates the results of lag order statistics. Akaike information criteria statistics suggests that the optimal lag order for the model is 3.

Johansen cointegration tests
The long-term relationship among variables was checked with the Johansen cointegration test (Johansen, 1995) by max-eigenvalue and trace methods (Table 9). Based on these results and a 5% significance level, we reject the null hypothesis of no cointegration (r = 0, trace test = 252.42, p = 0.00) and fail to reject the null hypothesis that there are one or two cointegrating equations in the multivariate model. This reveals that there exists at least one level of cointegration equation, which indicated that the variables have long-term relationship. Furthermore, the results of cointegration test show that exist at most two level of cointegration (r ≤ 2, trace test = 134.04, p = 0.0127) between the times series of Log(COVID-19 Kuwait), Log(O 3 ), Log(SO 2 ), Log(NO 2 ), Log(CO), and Log(PM 10 ) (Table 9). Table 9 Johansen test for selecting the number of cointegration that reflect linear combination of underlying series to form a stationary series for Log(COVID-19 Kuwait), Log(O 3 ), Log(SO 2 ), Log(NO 2 ), Log(CO), and Log(PM 10 ) with weather factors (temperature, relative humidity and wind speed) Moreover, Engle and Granger (1987) suggested a two-step process to test the cointegration (an OLS regression and a unit-root test). According to Engle and Granger (1987), if a set of variables are cointegrated, then there exists a valid error correction representation of the data, and vice versa. Therefore, an analysis of OLS regression and error correction model has been performed to testing the cointegrating relationship (r = 2) in a system of k = 2, I (1) variables. The results of cointegration regression analysis (Table 10) confirm that there is a long relationship between the series Log(COVID-19 Kuwait), Log(O 3 ), Log(SO 2 ), Log(NO 2 ), Log(CO), and Log(PM 10 ). Figure 1 shows the simultaneous variation of Log(COVID19) with Log(O 3 ) and Log(SO 2 ). *, **, *** imply that we can reject the null hypothesis at 10%, 5% and 1% significant levels, respectively

Determination of optimal VECM
VECM analysis with restricted constant and restricted trend results is shown in Table 11. Past COVID-19 cases, NO 2 , SO 2 , Temp, RH and WS, were significantly associated with future COVID-19 cases in Kuwait. The Error Correction Model (ECT) shows how fast variables return to long-run equilibrium when a cointegration relationship exists. EC1 is negative and significant indicating a long-run causality of future COVID-19 cases with past COVID-19 cases. The error correction term explains 5.102% disequilibrium of COVID-19 cases in Kuwait compared to other variables. The speed of adjustment at 5.102% towards the long run is also explained at the 1% significance level.   Figure 2 shows the future trend of COVID-19 using VECM. From Fig. 2, it can be observed that the forecasted value shows a linear trend and the predicted value lies within 95% the confidence interval.

Conclusion and recommendations
The primary goal of the current study is to look into the association between changes in daily admitted COVID-19 cases and air pollution levels during the Corona pandemic from March to December 2020. Medical analysts, policymakers, environmental decision-makers, and anyone interested in measuring the causality relationship between daily admitted COVID-19 cases and air pollution, such as the World Health Organization (WHO), through a series of policies for this situation. Based on a descriptive analysis of the variables, the association between air pollutants (O 3 , SO 2 , NO 2 , CO, and PM 10 ) and daily admitted COVID-19 patients has been established; this is consistent with the literature reviewed. This research used the vector error corrected model (VECM) with cointegration technique to look at the long-and short-run association between the effect of air pollution (O 3 , SO 2 , NO 2 , CO, and PM 10 ) and the daily admitted COVID-19 cases. We discovered that for COVID-19 patients, a greater AQI was linked to a higher number of hospitalizations. The outcomes for COVID-19 patients showed that increasing the air quality index has a positive and significant effect on increasing the admitted number of COVID-19 patients. The lags of the dependent variable are significant until the second lags, implying that increasing the air quality index, particularly for O 3 and SO 2 , affects increasing the number of COVID-19 patients with long delays. The model for correcting errors revealed that about 7% of the short-term imbalance is rectified in the event of a shock to achieve long-term balance in just one day. In the long run, boosting the air quality index for O 3 and SO 2 has been successful in increasing the admitted number of COVID-19 patients.
The coefficient of the air pollution index is positive and substantial for COVID-19 patients who are hospitalized. This suggests that raising the air quality index (O 3 and SO 2 ) can increase the number of COVID-19 patients that are admitted to the hospital. This is in line with a study that found a link between COVID-19 infection and air pollution, which has a significant impact on infection and mortality rates (Frontera et al., 2021). Using a time-series method, another study in Chile, Dales et al. (2021), found a significant association between acute IQR increases in CO, NO 2 , and PM 2.5 and increases of around 6% in daily COVID-19 associated deaths.
When the health variables were examined, it was shown that the majority of the people infected with COVID-19 were already exposed to air pollution, because Kuwait's regions have significant pollution rates. The biggest cause of pollution has been air pollutants emitted by cars and businesses (Hamoda et al., 2020). COVID-19 impacts the human respiratory system, and people who are already susceptible to the respiratory disease have a propensity to be affected by the pandemic (Ghanim, 2021).
COVID-19's lockdown analyzed human activities, mostly involving vehicle usage and public transportation, as well as industrial processes (Gautam, 2020;Pata, 2020;Shehzad et al., 2020). The importance of air pollution and COVID-19 has been demonstrated in numerous studies. The spread of COVID-19 has been found predominant through airborne bio-aerosol droplets together with various aspects of urban air pollution . Past exposure to air pollution has led to an increase in the cases of COVID-19. The ability to transfer these viruses is demonstrated by air pollution. We approximated the error correction model based on the VECM procedure to obtain short-term coefficients after investigating the long-term findings. The results show that while O 3 and SO 2 have an increasing short-term effect, they have a longterm positive effect on the daily admitted COVID-19 case. The error correction term (ECT) is statistically significant and has a negative value, indicating that a deviation from the long-term equilibrium will be repaired. The findings show that the short-term coefficients of O 3 and SO 2 are lower than the long-term coefficients.
Our research has several limitations. We have to revert to the air quality index as a measure of air pollution level due to inadequate reporting on certain pollutants. This, however, may obscure the impact of certain contaminants on the number of hospitalizations. Furthermore, because our estimates focused on a single link between factors, any ascribed cost estimation should be cautiously approached. Other aspects, such as humidity, wind speed, and seasonality level, may need to be adjusted in the model (winter, autumn, spring, and summer). However, because their data were not available or valid in this study, we did not alter them.
Other time-series methods, such as the vector autoregression (VAR) model, which is one of the most effective, flexible, and user-friendly models for multivariate timeseries analysis, could be recommended for future investigations. The basic model for studying a stationary time-series in terms of two polynomials is the autoregressivemoving average (ARMA) process. Other multivariate time-series analysis techniques include Vector Autoregression Moving-Average (VARMA), VARMAX (VARMAX with Exogenous Regressors), and Holt Winter's Exponential Smoothing (HWES). A spatial multivariate time-series approach could be used to assess the distance between a job or a living area and a pollution source. Furthermore, taking critical key elements like wind speed and air humidity into account can help to minimize the disruption of damaged components.