Persistence of nitrogen oxides emissions using historical time series data: evidence from 37 countries

ABSTRACT Two features in time series data: the existence of time trends and the degree of persistence, are examined in this work on the nitrogen oxides emissions from 37 OECD countries. Updated techniques in time series are used that allow for fractional degrees of differentiation in the data. Thus, if the number of differences required is one, nitrogen oxides emissions are not mean reverting in the sense that if there is an exogenous shock (resulting from a technological advancement to change nitrogen oxides emissions), the effect of such shock on nitrogen oxides emissions will be permanent. Time trends are observed in half of the series. For these countries the trend coefficient is found to be positive in all cases. This is an indication that continuous technological progress is needed in taming NOx emissions. In addition to developing their own local technologies, less technologically endowed OECD countries should engage in collaboration with the more technologically endowed countries in order to facilitate increase in trans-border transfer of technology. The technologically advanced countries should also strive to continue to introduce better technologies in a bid to reduce NOx emissions. Most of the results show evidence for persistence of nitrogen oxides emissions.


Introduction
Nitrogen oxides (NO x ) are a cluster of highly reactive gases, which emerge when there is a reaction between nitrogen and oxygen during combustion (of fuels such as oil, diesel, gas and organic matter) at high temperature. It is a common designation for both nitric oxide (NO) and nitrogen dioxide (NO 2 ). NO x emissions are one of the key pollutants in the atmosphere, being a precursor to acid rain and photochemical smog. They add to ozone build-up and account for eutrophication in coastal waters, which has negative impacts on both aquatic and terrestrial ecosystems. They also have negative effects on the health of humans as a large concentration of NO x triggers numerous respiratory and cardiovascular sicknesses (including lung function impairment) and subsequently have an adverse impact on labour productivity. Huge accumulation of NO x emissions can lead to frost damage to crops, rendering them more vulnerable to diseases. Moreover, NO x damage the environment, with harmful consequences on the ecosystem and biodiversity.
Due to the significance of NO x emissions and the harmful effects that the pollutants have on society, several underlying aspects of NO x have been investigated in the existing literature including their economic determinants (Agnolucci and Arvanitopoulos 2019). There are also articles on the modelling and measurement of NO x s absorption (Nikolaeva and Khusnutdinov 2018;Liu et al. 2020). Lee and List (2004) focused on the convergence analysis of NO x emissions, while Heng, Lim, and Chi (2012) investigated the relationship between NO x emissions and trucking productivity. Erickson et al. (2020) conducted a review of the efforts made by several governments to reduce NO x emissions. The impact of NO x emissions on economic and health indicators such as labour productivity and health expenditure have been examined in the existing publications (Hansen and Selte 2000;Chen and Chen 2021). One of the aspects of NO x that is yet to be accorded sufficient attention is their persistence. The existing literature on persistence of indicators of environmental degradation is dominated by carbon dioxide emissions (Solarin, Gil-Alana, and Lafuente 2019). There are considerable differences between NO x emissions and carbon dioxide emissions. The techniques and blueprints aimed at decreasing one or other type of pollutant vary significantly. The trend that carbon dioxide emissions follows is different from the trend that the other pollutants follow over the years (Ulucak and Bilgili 2018).
There are numerous reasons why knowing the persistence of NO x emissions is vital. Firstly, the existence of persistence implies that shocks (or events that cause changes in NO x emissions) will have long-term impacts on the pollutant. There are positive shocks on NO x emissions, which arise as a result of adoption of new technologies or the introduction of laws or standards aimed at depressing the pollutant (Tiwari, Kyophilavong, and Albulescu 2016). An example of such technologies is the water injection and emulsion approach (which involves systematic addition of adding water to the device emitting NO x to reduce the temperature of combustion, leading to low NO x emissions). Another type of technology is the selective catalytic reduction approach (which involves the mixing of exhaust gas with water solution of urea, which is then channelled through the catalytic reactor of the device emitting NO x ). The other technologies include wet scrubbing, electron beam, adsorption, electrochemical reduction and nonthermal plasma (Gholami et al. 2020). The examples of standards and legislation include the Sofia Protocol in 1988 and the Gothenburg Protocol in 1999 (both of which have been revised subsequently). One of the main objectives of these two standards is to facilitate the control and reduction of NO x emissions. The revised National Emissions Ceilings Directive that came into effect on the last day of 2016 is another policy that sets new emission reduction commitments on five important pollutants, which include NO x emissions. There is also the Large Combustion Plant Directive of 2001, which aims to reduce NO x emissions from combustion plants, which have a minimum of 50-megawatt thermal capacity. There also negative shocks, which emanate from events that cause higher NO x emissions. These events include sudden spikes in emissions from power plants, buses, cars, trucks and off-road equipment, which might emanate from changes in government policies or behaviour of the citizens. On the other hand, the absence of persistence of NO x emissions infers that policy shocks to the pollutant will have temporary impacts.
Secondly, testing of persistence NO x emissions is also necessary from the econometric viewpoint because the non-stationarity of the series has essential consequences for the environmental Kuznets curve studies that have used NO x emissions as an indicator of air pollution. 1 Few environmental Kuznets curve studies have assumed that pollutants follow stationary trends (Yilanci, Gorus, and Aydin 2019). Nevertheless, the environmental Kuznets curve publications that have used the level form of a non-stationary NO x emissions are likely to produce spurious results (Engle and Granger 1987). In other words, some econometric methods that rely on the assumption of stationarity (stability) of the series can produce spurious results if the series turn out to be nonstationary (unstable) Lafuente 2021a, 2021b).
The purpose of this study is to contribute to the literature on air pollutants in four unique ways. Firstly, we investigate the persistence of NO x emissions of 37 OECD countries during the time period 1750-2019, something which has received limited attention in the literature. Secondly, this study highlights the types of appropriate policies, which can be used to tame NO x emissions. Thirdly, we use fractional integration, a relatively recently developed technique in time series that is able to capture the long memory property of the data. Fourthly, we have used a long-span dataset. By using a dataset of 270 years, which has been extracted from Feng et al. (2020), the validity of the empirical findings is improved and the persistence of NO x emissions can be evaluated over a long-time span. We have concentrated on OECD nations for numerous reasons. The total gross domestic product in OECD nations was US$51 trillion (in 2015 prices), which amounted to more than 60 per cent of the total gross domestic product in the globe in 2019 (United Nations Statistics Division 2021). Secondly, OECD countries have experienced NO x emissions growth in most of the countries under observation. The emissions rose significantly between 1750 and 2019 in the OECD nations (Feng et al. 2020). Thirdly, OECD countries accounted for 19 per cent of global NO x emissions in 2019 (Feng et al. 2020). Fourthly, mitigation technologies for NO x emissions in OECD countries are frequently more potent than those existing in non-OECD nations.
The empirical results provide evidence for persistence of NO x emissions in most of the countries. The results also provide evidence for trends with positive coefficients in the NO x emissions, especially when the series are transformed by using logarithms. The reported result is a novelty because previous studies have failed to examine persistence of NO x emissions for such a long period of time. Therefore, the importance of the policy implications of the results is that they are able to tell us if long-term mechanisms to reduce NO x emissions are needed to tackle the pollutant (and if the past policies have been effective in taming NO x emissions).

Literature review
In the specific case of the persistence analysis of environmental and air pollution indicators, relevant articles have been published in recent years using different econometric techniques, although many of them have focused on carbon dioxide (CO 2 ) emissions. In this area and along these lines, for example, Christidou, Panagiotidis, and Sharma (2013) analyse the stationarity of CO 2 emissions per capita for 36 countries from 1870 to 2006. To do this, they use a non-linear panel unit root test and conclude that carbon dioxide emissions per capita during the last 150 years are stationary in all the countries studied. Tiwari, Kyophilavong, and Albulescu (2016) study the stationarity of CO 2 emissions per capita for 35 countries in sub-Saharan Africa for the period 1960-2009. The methodology used is non-linear time series and panel unit root tests, and the authors find stationarity in the series for all the countries analysed and reversion to the mean in 27 of them. Gil-Alana, Cunado, and Gupta (2017) analyse the behaviour of the time series of CO 2 emissions for the case of the BRICS and G7 countries. Using our methods, the results illustrate important differences in the degree of integration in the nations analysed. For most countries there are permanent effects of shocks on CO 2 emissions, except in some countries where they will be transitory as in the case of Germany, the US and the UK. In turn, they obtain evidence of non-linear behaviour for G7 member countries, such as the US, the UK, Germany and France. Gil-Alana and Trani (2019) examine the evolution of the time series of CO 2 emissions for the countries of the European Union. For this they use parametric and semi-parametric methods. The results obtained show a trend of reversion to the mean for the case of the United Kingdom. A clearly opposite trend is registered in the case of countries such as Spain, Italy, Greece or Bulgaria. They also study CO 2 emissions for the aggregate of EU countries, China and the US, finding signs of a reversion to the mean for the case of China. Zerbo and Darné (2019) analyse, using a sequential test procedure, the (non) stationary properties of CO 2 emissions per capita of 29 OECD countries plus Brazil, China, India and South Africa from 1960 to 2014. The results obtained show the non-stationarity of the emissions under study for all countries and conclude that they would be better characterised by a random walk. The foregoing publications clearly suggest that most CO 2 emissions in several countries are persistent.
There are also articles that analyse the ecological footprint. For example, Solarin and Bello (2018) examine the stationarity of the ecological footprint of 128 countries between 1961 and 2013. Using tests to examine the stationarity of the series, the results obtained allow us to conclude a non-reversible mean for 96 of the countries analysed and therefore indicating a non-stationary variable. As a consequence, environmental policies would be effective for a relevant number of countries. Solarin, Gil-Alana, and Lafuente (2019) analyse the persistence of carbon footprint emissions, using a similar methodology to ours, for a group of 92 countries. The results show that only 25 of the countries studied show an average reversal. These countries present as a particularity in that the majority are of lower and lower-middle income, which in the opinion of the authors will hinder a change in trend and, if there is one due to the application of environmental policies, it will be temporary. Solarin, Gil-Alana, and Lafuente (2021b) examine the persistence of the time series of the fishing ground footprint, as a component of the ecological footprint, using fractional integration as a methodology for a set of 89 countries. Although the results obtained are very heterogeneous, the authors find that most of the series are non-stationary and not reversible at the mean. That means that in the event of a shock the series does not revert to its original level by itself. The difference is that this behaviour corresponds mostly to countries with upper-middle and upper-income levels, while countries that show a stationary pattern have the common characteristic of being low-and lower-middle income. In conclusion, Solarin, Gil-Alana, and Lafuente (2021b) suggest that countries that implement policies aimed at reducing the footprint of fishing grounds will have a high probability of being effective.
Other publications report the behaviour of particulate matter PM 10 and PM 2.5 . For example, Gil-Alana et al. (2020) analyse air quality in the 50 US states through the study of time series of particulate matter (PM 10 and PM 2.5 ). To examine the degree of persistence they use a fractionally integrated long-memory framework. In most states the results obtained show a reversion to the mean, (i.e. the shock disappearing by itself in the long run) although in a heterogeneous way given that higher degrees of persistence are registered in the western states than in the eastern ones. The same happens with another important greenhouse gas, methane. Thus, for example, Solarin and Gil-Alana (2021) used fractional integration techniques to study the persistence of methane emissions for a group of 36 OECD countries in the period 1750-2014. The results obtained indicate that the series are very persistent, with positive linear trends for almost 50 per cent of the countries under study. In conclusion, Solarin and Gil-Alana (2021) consider that policies aimed at reducing methane emissions will be effective in the long term.
Regarding the specific study of the persistence of NO x emissions, some studies should be highlighted. For example, Lee and List (2004) use time series methods to examine the temporal trajectory of US NO x emission data for the period 1900-1994.
The results indicate that the series contains both a permanent and a random component and Lee and List (2004) suggest that the reduction in the emissions recorded are associated with the policies oriented to that end and that their effect was not transitory, but permanent. McKitrick (2007) analyses, using a different methodology named Vector AutoRegressive (VAR), the stationarity of different pollutants such as NO x and volatile organic compound (VOC) emissions in the US. The results indicate that the series were not stationary and the author concludes that the air quality policies adopted in 1970 increased pollution in the short term, but they gave a boost to technologies that reduced polluting gas emissions. Sidneva and Zivot (2014) analyse time series in the US regarding NO x and VOC emissions, applying unit root tests to evaluate the possible impacts of the 1970 air quality policy. The results obtained point to the non-stationarity of the series of the two pollutants. These authors (Sidneva and Zivot 2014) conclude that there is evidence of a change in trend in both NO x and VOC emissions, due to the approval and application of environmental policies. Gil-Alana and Solarin (2018) study the global and per capita emissions of NO x and VOC in the United States in order to evaluate the effectiveness of environmental policies carried out by the government during the last 50 years. Using the same techniques as used in this work and based on a concept denominated fractional integration and explained below, these authors conclude that in the series analysed there is no reversion to the mean, but the results obtained allow the authors to affirm that the policies used in the years 1965, 1967, 1970, 1977 and 1990 were effective, especially those in 1970, with regard to the extent to which they managed to reduce the volume of emissions.
Other articles have analysed the relationship between economic growth, energy use and CO 2 emissions. Along these lines, Magazzino (2015) studied this relationship in Israel for the years 1971-2006. Using tests to determine if the series were stationary or not, he concluded that all the variables examined were non-stationary, or named, integrated of order one, while the causality tests suggested that the growth of the real gross domestic product drives energy use and CO 2 emissions. In another article, the same author (Magazzino 2016a) analysed the same relationship, but for the South Caucasus area and Turkey in the period from 1992 to 2013. Using panel data techniques, the empirical results indicated that the response of CO 2 emissions energy use was negative and statistically significant in the estimated coefficients and in the impulse responses. The first CO 2 lag was also statistically significant in the real GDP equation. Magazzino (2016b) analysed for the same countries long run equilibirum relationships and found evidence of cointegration, although the results showed different causal links in the countries studied. In Magazzino (2017), 19 countries of the Asia-Pacific Economic Cooperation were studied for the time period from 1960 to 2013. Using the VAR approach mentioned above, the results showed that there is no causal relationship between real GDP and energy use. Magazzino and Cerulli (2019) analysed countries in the Middle East and North Africa from 1971 to 2013, but using a responsiveness score (RS) approach. Their results suggested that GDP per capita and energy consumption show positive RS. In turn, three-way factors analysis indicated that most countries obtain moderate negative Total Response Capacity (TRS) scores, which means that when all factors are increased together, CO 2 emissions decrease moderately. Finally, in a recent study, Magazzino, Mele, and Schneider (2021) studied the causal relationship between solar and wind energy production, coal consumption, economic growth and CO 2 emissions in China, India and the US, which are the largest energy consumers and CO 2 emitters in the world. Using Machine Learning techniques to verify predictive causal links, the authors predicted a reduction in total carbon emissions in China and the United States, mainly due to greater use of renewable energy sources, and an increase in carbon emissions for India. The conclusion they draw is that it is only possible to reduce CO 2 emissions with greater use of renewable energies and the gradual reduction of fossil resources.
As mentioned in earlier parts of this article, we investigate if the data display the property of long memory, and in particular, if fractional integration might be an appropriate alternative for modelling the series under investigation. Fractional integration means that the number of differences to be taken in the data is a fractional value. We now explain this point further. If a series is non-stationary (unstable) we cannot make statistical inference and the standard approach is to differentiate the data, i.e. instead of working with the original data, say x(t), we have to work with its first differences, i.e. x(t)x(t−1) or using the backshift operator B (Bx(t) x(t −1)), (1−B)x(t). In this case, we say that the order of integration of the series is 1 since the exponent of the polynomial (1−B) is 1. In some exceptional cases, the order of integration might be 2, requiring in this case to differentiate twice the original data, i.e. working with (1−B) 2 x(t). Fractional integration occurs when this order of integration is a fractional value.
Note that most of the earlier studies focus on integer degrees of differentiation, i.e. 0 in case of stationary series and 1 for non-stationary ones, in the latter case requiring first differentiation to achieve stationarity I(0). In the following section we present a model that allows the order of integration of the series to be a fractional value. Thus, it might be smaller than 0, 0, a value constrained between 0 and 1, 1 or even above 1. In doing so, we allow a much richer degree of flexibility in the dynamic specification of the data, allowing even for non-stationary mean reverting processes, if the differencing parameter is constrained between 0 and 1.

Methods and model application
The first thing we want to investigate in this article is whether the data display a long memory pattern, and for this purpose, we use a modelling approach based on fractional integration. This means that the number of differences that have to be taken in the data to render them short memory or I(0) may be a fractional value. In this context, long memory takes place if the differencing parameter (also named order of integration) is positive. The framework of this article is based on the concept of stationarity of the series. The stationarity of a series implies that such series is mean reverting. In such case, any shock on the series will have a transitory impact on the series. The non-stationarity of a series suggests that the series is persistent. In such case, any shock on the series will have a permanent impact on it.
Given a second-order stationary process x(t), we say it is integrated of order d if it can be represented as: where B refers to the backshift operator, i.e. B k x(t) x(t−k) and where u(t) is a short memory process. Then, in order to examine the potential presence of trends, we suppose x(t) are the regression errors in the following regression model, where y(t) is the observed time series and α and β are unknown coefficients representing an intercept and a time trend respectively. Note that if d = 0 in (1), α and β can be estimated by standard least squared methods, but if d is positive, x(t) is long memory and the previous estimation can be biased producing erroneous results. Thus, we jointly estimate the deterministic terms along with the differencing parameter in the following model, allowing for different assumptions for the error term u(t) in (3). First, we will assume non-correlation, though, later, weak autocorrelation (e.g. AutoRegressive Moving Average, ARMA) will be permitted. The estimation will be based on the Whittle function using a frequency domain approach. We use a testing approach developed in Robinson (1994) that is very convenient in the context of the present data based on their non-stationary nature. In fact, Robinson's (1994) method tests the null hypothesis.
in Equation (3) for any real value d o , including thus those outside from the stationary region (i.e. d ≥ 0.5). Due to this, it does not require preliminary differentiation when dealing with non-stationary data, and the limit distribution of his testing procedure is standard normal, allowing the computation of confidence bands for the non-rejection values of d. Alternative parametric methods like Sowell's (1992) maximum likelihood in the time domain and Beran's (1995) approach produced almost identical results to those reported in this work.
In the results displayed below, we will report the estimated values of d (and their associated 95 per cent confidence bands) in Equation (3) under various assumptions on u(t) and for the three classical scenarios in the unit root literature: (1) including no deterministic terms, i.e. assuming that α = β = 0 in (3) (2nd column); (2) including an intercept, i.e. with β = 0 (3rd column) and (3) with a constant and a linear time trend (column 4th in Table 2). To select the most appropriate specification we look at the tvalues of these coefficients (α and β) in the joint representation of the two equalities in (3) wherẽ and noting that u(t) is I(0) by assumption, standard t-tests apply in (4). The values in bold in the tables refer to the selected specification for each series.

Data
We obtained the NO x emissions datasets (in kilotons) of the 37 OECD nations for the period 1750-2019, from Feng et al. (2020). Contrary to other datasets of NO x emissions, the data available in Feng et al. (2020) is free of estimation process ambiguity as well as inadequacy of time-based resolution (Feng et al. 2020). The preparation of the data entails the use of factors of emissions, inventories of emissions and driver/activity data to compute annual national emissions, and numerous sub-stages are involved in the computation stage. The descriptive statistics of NO x emissions data across 37 OECD countries are summarised in Table 1. Specifically, Table 1 displays the mean, standard deviation, minimum value, maximum value, kurtosis, skewness and Jarque-Bera statistics of NO x emissions data across 37 OECD countries. US is the largest emitter among the OECD countries, responsible for an average of 5793.48 kilotons of NO x per year. These statistics are not surprising given the large sizes of the US economy and population. The other countries with large amounts of NO x emissions are Japan, Germany, France and Canada. Iceland is the smallest emitter among the OECD countries, with an average of 84 kilotons of NO x /year. The country also has the lowest emissions variation and the standard deviation of NO x of Iceland is the smallest among the OECD countries. The other countries with small amounts of NO x emissions are Slovakia, Slovenia, Latvia, Estonia and Luxembourg. The NO x emissions appear to be platykurtic (which implies that the series do not follow normally distribution) as the kurtosis statistics are less than three in most of the countries. Jarque-Bera statistics are reported to test for normality in the series. The null hypothesis of NO x emissions following a normal distribution is rejected in all cases. Hence, we have added the logged form of the series in the subsequent analyses. Logarithmic transformation is often considered as one of the means to address the non-normality issue in time series (Changyong et al. 2014).
The sum of NO x emissions (in kilotons) in the OECD countries is displayed in Figure 1. The figure shows that the series increased over many years. Thus, the emissions spiked in the 1930s and the increase continued until the 1970s. This was a period of rapid economic expansion in many OECD countries. The decline of the emissions starts from 1970s in OECD countries, which can be partly attributed to the concerted efforts by the US and few other countries to contain emissions. For instance, the US initiated the Clean Air Act in the 1960s to reduce emissions. Table 2 displays the estimates of d under the assumption that u(t) is a white noise process. 2 The first thing we observe is that the time trend coefficient is found to be significant in only three cases: Colombia, Finland and Israel; the intercept is required in the case of New Zealand, and, for the remaining series both deterministic terms are found to be statistically insignificant. As there are significant differences in terms of the level of development in these countries and also in their geographical locations, this might indicate that persistence of the pollutant does not depend on the level of development and geographical locations of countries. However, what is common in these countries is the introduction of   The time trend coefficients are positive for the three countries. The fact that for the rest of the countries the time trend is insignificantly different from zero is good news in the sense that we do not observe a systematic increase in the number of the emissions except for the three countries mentioned above. Looking at the values of d, we observe that only Finland displays mean reversion, i.e. an estimate of d significantly below 1; for seven countries, the unit root null (i.e. d = 1) cannot statistically be rejected: Israel (d = 0.95); Iceland and Slovenia (0.97); Slovakia (1.03); Austria and Ireland (1.07) and Norway (1.08). For the remaining cases, the estimated values of d are significantly higher than 1. This high level of persistence observed in all countries implies that exogenous shocks in the series are expected to be permanent in all countries except Finland. This is not good or bad per se, depending clearly on the nature of the shock. Thus, for example, if there is a negative shock reducing the emissions, based on the permanent nature of the shocks we will not have the necessity of imposing strong environmental policies since that new level will maintain by itself. On the contrary, if the shock increases the number of emissions, strong measures should then be adopted to recover previous levels of emissions. We next replicate the experiment but this time using the logged transformed data. Results are displayed across Tables 3 (and A2 in the supplementary data). Surprisingly the time trend is now required in 25 out of the 37 countries examined; the intercept is required in 10 cases, and neither intercept nor trend in only two cases (Table A2 in the supplementary data). In the cases where the trend is required, it is found to be positive in all cases, the highest value being obtained in the case of Australia. This is clearly not good news since it indicates that the number of emissions continues growing in a number of countries. Focusing now on estimated coefficients for d, we see that mean reversion occurs in the cases of Poland (d = 0.75), Belgium (0.80) and Ireland (0.90). In the rest of the cases, d is found to be statistically equal to or higher than 1, implying permanency of shocks, which is consistent with the results obtained in the previous table based on the original data for the majority of countries in the sample.

Results
The results displayed above are based on the strong assumption that u(t) in (3) is a white noise process. In what follows, we allow for a richer structure allowing for weak autocorrelation in the error term. In other words, the errors are related across time. However, as against imposing a parametric model, e.g. an AutoRegressive Moving Average (ARMA) modelling context, we use here a non-parametric method that is attributable to Bloomfield (1973) that approximates AR structures in a very simple way throughout the spectral density function. 3 This approach has been widely used in the context of fractional integration (Gil-Alana and Robinson 1997;Gil-Alana 2004;Robinson and Velasco 2015;etc.).
Starting with the original data (Tables 4, and A3 in the supplementary data) we observe that Chile and Israel are the only two countries with a positive significant time trend, while the remaining countries show no need of deterministic terms, and Finland is the only country with significant evidence of mean reversion, with an estimated value of d about 0.72. Thus, as in the previous cases, shocks are expected to be permanent in all countries except in Finland where they are transitory though with long lasting effects.
Looking at the log-transformed data (Tables 5 and Supplementary Table A4) the time trend is required in 23 countries, and only the intercept in 11. The highest time trend coefficient corresponds to Australia (0.0884), followed by Israel (0.0327), Chile (0.0289) and Canada (0.0278), and mean reversion is not found in any single case. Thus, the results are similar to those based on white noise errors, finding evidence of positive trends in many countries, which is a worrying issue and which the authorities of these countries need to consider.
We can summarise the results presented in terms of the two parameters of interest, i.e. the time trend coefficient, β, and the measure of persistence, d. Starting with the time trend, the summary results are reported in Table 6. We observe that Israel along with Chile appears in the top positions in three out of the four cases considered. Colombia also appears in three cases, while Australia appears at the top with the logged values and Slovenia and Canada also display high values of β. For these countries authorities should take action to try to remove these trends. Note: The model is based on the logged data and assumes white noise errors. The values in bold correspond to the estimates of d (and 95 per cent confidence interval) for the selected model in relation to the deterministic terms. Table 7 displays a summary of the results in terms of the differencing parameter d. We observe that Japan appears as the country with the highest level of persistence under no autocorrelation, and also appears in the 4th place with autocorrelation and using the original data. Countries such as Latvia, Italy and Czech Republic also display high levels of persistence in the four cases, while Korea is in the 3rd position with autocorrelated errors in both cases with the original and the logged transformed data. Looking now at the countries with the lowest degrees of persistence we notice that Slovenia and Iceland are among the countries with the lowest values of d, while Israel and Finland on the one hand, and Ireland and Poland on the other, also present low values for white noise and autocorrelated errors respectively. Evidence of mean reversion is found only for Finland, Ireland, Belgium and Poland. Thus, for all these countries with low levels of persistence, if there are exogenous shocks increasing the number of emissions, the authorities should not be as worried as in the other countries with high levels of persistence since the series will revert to their original levels by themselves sometime in the future. Comparing these results with previous works, the closest to ours are Sidneva and Zivot (2014) and Gil-Alana and Solarin (2018), the first authors using unit root methods and the latter employing fractional methods, in both cases with US data and supporting the hypothesis of nonstationarity and lack of mean reversion.

Conclusions
In order to advance wide-ranging plans to tackle the increasing climate change concerns, there is a need to comprehend the underlying features of different pollutants such as the time series characteristics of pollutants. Nonetheless, the greatest proportion of the current studies on pollution indicators persistence has focussed on the CO 2 emissions stationarity. In this article we have looked at the persistence of NO x emissions in 37 OECD countries. We were interested in looking at the degree of persistence of the series along with the potential presence of time trends in the data. Both features were examined in the context of fractional integration. The orders of integration were significantly positive in all cases, supporting the hypothesis of long memory behaviour and implying high dependence between the observations across time. This is consistent with previous works in other environmental series (Solarin, Gil-Alana, and Lafuente 2019; Solarin, Gil-Alana, and Lafuente 2021a, 2021b). However, the results were very heterogenous across countries depending on the data examined (original versus logged versions) and the way of modelling the I(0) disturbance term (white noise versus autocorrelation). Thus, for example, the time trend only appears significant in very few cases if we work with the original data (Colombia, Israel and Finland with white noise errors, and Chile and Israel under autocorrelation) but significant trends are found in 25 (white noise) and 23 (autocorrelation) countries with the logged transformed data. Removing these trends must be an objective for the authorities in the future. On the other hand, evidence of mean reversion and thus transitory shocks are only obtained in the case of Finland under the assumption of white noise errors (for both original and logged data) and for Ireland, Belgium and Poland with autocorrelation and the original data; for all these countries shocks in the series might have a transitory nature. However, in the majority of the cases, shocks are expected to be permanent. As a general conclusion, there is evidence of persistence of NO x emissions in the OECD countries. The implication of the empirical findings is that shocks (which might emanate from policy interventions) to the NO x emissions in the majority of the OECD countries will be permanent. In other words, NO x emissions are not likely to move back to their initial mean after experiencing a policy shock in most of these nations. Thus, there is a need to incorporate more mechanisms that focus on the long-term reduction of NO x in the overall environmental policy of these countries, instead of short-term and unsustained interventions. The national policies include National Ambient Air Quality Standards (NAAQS) in the US and Environmental Protection Policy in Japan. The results also mean that blueprints aimed at reducing NO x emissions in these countries will be effective. An example of such blueprints is the National Emission Ceilings Regulations which entails the reduction of UK NO x emissions by 73 per cent relative to the emissions level in 2005, by 2030. Moreover, international environmental regulations need to concentrate on the longterm trends in NO x emissions instead of focusing on short-run targets. Subsequent revisions or amendments of international blueprints including the convention on long range transboundary air pollution (CLRTAP), Sofia Protocol of 1988, Gothenburg Protocol of 1999 and the National Emissions Ceilings Directive should focus more on long-term targets in order to continuously decrease the NO x emissions in these OECD countries.
The empirical results also imply that there is a need for proactive measures on the part of the OECD governments to combat NO x emissions if a negative shock occurs with regard to the pollutant, although NO x emission duration in the atmosphere might be not as long-lasting as other pollutants. In other words, attempts to decrease NO x emissions are needed when there is (negative shock or) a rise in the pollutant due to different economic activities including vehicular activities, biological decay processes and lightning and high-temperature operations in industries. A policy action in this direction is the fostering of technological innovations that can lead to the design of new and processes materials, which reduces the use of NO x emission-prone materials. Similarly, the governments can introduce regulatory instruments including policies and laws that discourage or ban the use of unsustainable materials, which are consistent with the reduction of NO x emission. These activities can be augmented by the introduction of more markets for climate-friendly activities and facilitating access to untapped low-emitting energy sources at affordable prices.
The promotion of scientific and technological collaborations towards the reduction of NO x emission is another viable policy action. Collaborations involving energy and nonenergy sectors, non-profit organisations, local and foreign entities can lead to the development and transfer of technologies. This would particularly lead to transfer of latest NO x emission-reducing technologies to less technologically endowed regions within a country. Collaborations can also lead to trans-border transfer of technology to the less technologically endowed countries (including Slovakia, Slovenia, Chile and Colombia) from the more technologically endowed countries (including Japan, UK, Germany, France and Canada).
Following this line of research, future studies should continue to focus on the methodology used in this article and based on fractional integration. However, noting that for many countries the estimate of the differencing parameter is significantly higher than 1 this may be a consequence of a potential presence of structural breaks in the data. Many authors have shown that not taking this into account may produce spurious evidence of long memory, increasing the value of the differencing parameter. Thus, the possibility of structural (and other non-linear structures) are areas that should be investigated in these and in other data. Notes 1. In plain words, nonstationarity means that the series is not stable across time, with the mean and the variance among other things changing with time. Environmental Kuznets curve hypothesis suggests nations will generate less pollution as they grow. The hypothesis is based on the assumption that as countries experience economic expansion, they will develop technologies that will ensure lower pollution levels are generated from economic activities. 2. A white noise process is a pure random process, that is characterised by having a zero mean, a constant variance and zero values for the autocorrelations. 3. The spectral density function is the counterpart of the autocorrelations (time dependence) in the frequency domain.

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