Introduction

Global warming and the threat of climate change have become a global concern in recent decades. Climate change has devastating effects on humanity, such as deterioration of agricultural yields, thirst, and poverty in all regions of the world (World Economic Forum 2019). Scientists are aware that anthropogenic greenhouse gases (GHGs) are major contributors to climate change and the greenhouse effect (Presno et al. 2018). GHGs trap heat and make the planet warmer. Since 1750, almost all of the increase in GHG emissions has been the result of human activities (IPCC 2007).

Relentless efforts to prevent the negative effects of global warming and climate change are aimed at reducing carbon dioxide (CO2) emissions, which are the most threatening problem to human development (Alola 2019). CO2 is the most important emission, accounting for 70% of GHG emissions, and has an atmospheric lifetime of 200 years (Ahmed et al. 2017). CO2 emissions released by industrial processes and fossil fuel combustion are responsible for 78% of the increase in GHGs between 1970 and 2010 (IPCC 2014). Many scientists have found that CO2 emissions released by burning coal, oil, and gas, deforestation, and land use change positively affect the global temperature rise (Sun and Wang 1996). The increase in CO2 emissions and air temperature has negative impacts on human health and the environment (Wang et al. 2019; Ullah et al. 2020; Yilanci and Pata 2021). With increasing CO2 emissions, hospitalization and mortality rates increase, resulting in negative effects on labor productivity, industrial production, and economic development (Jacobson 2008). Without accelerated reductions in CO2 emissions, there will continue to be more than one million premature deaths per year by 2080 (Shindell et al. 2018).

Because it is important to address the economic and environmental impacts of climate change, researchers and international institutions and organizations are striving to prevent the rise of CO2. International agreements, such as Montreal Protocol in 1987, the United Nations Convention on Climate Change in 1992, the Kyoto Protocol in 1997, and Paris Climate Agreement in 2015, aim to prevent threats from CO2 emissions. In the Kyoto negotiations, it was emphasized that countries should radically reduce their CO2 emissions to 5% less than in the 1990s. Under the Paris Climate Agreement, many countries pledged to keep carbon concentrations at 450 ppm. Despite these commitments, CO2 emissions continue to rise.

Based on the above information, we focus on two fundamental questions about global CO2 emission reduction: (i) Are emission reduction policies effective? (ii) Is emission reduction possible through cooperation at the global level? Within this context, the analysis of the stochastic properties of CO2 emissions is a guide for policymakers and researchers in discussing environmental regulations. For this purpose, unit root tests are the adopted methods (Tiwari et al. 2016).

Understanding the persistence of CO2 emissions is important for the design and implementation of energy and environmental policies aimed at reducing pollution (Belbute and Pereira 2017; Fallahi 2020). The effectiveness of environmental policies varies depending on whether CO2 emissions are stationary at the national or global level. The stationarity of CO2 emissions implies that the series reverts to the long-term trend path. If CO2 emissions are stationary, environmental policies will only produce temporary effects and will not be effective for achieving emission reduction targets (Cai et al. 2018; Cai and Wu 2019). In contrast, if CO2 emissions contain a unit root, the effects of exogenous shocks on the series are persistent and CO2 emissions do not return to the long-run growth path (Zerbo and Darné 2019). Non-stationary CO2 emissions can be considered a good characteristic as positive policy shocks help to reduce emissions (Fallahi, 2020). In the unit root case, environmental policies that increase energy efficiency, change the price of energy, and promote the substitution of fossil fuels with renewables have long-lasting effects on CO2 emissions.

Researchers have extensively tested the convergence of CO2 emissions (Yavuz and Yilanci 2013; Acaravci and Erdogan 2016; Ahmed et al. 2017; Presno et al. 2018; Rios and Gianmoena 2018; Cai and Wu 2019; Morales-Lage et al. 2019; Solarin 2019; Erdogan and Acaravci 2019; Apergis and Payne 2020; Payne and Apergis 2020; Erdogan and Solarin 2021; Tiwari et al. 2021; Nazlioglu et al. 2021). Relatively few studies have looked at the (non) stationarity of CO2 emissions (Heil and Selden 1999; Lanne and Liski 2004; Christidou et al. 2013; Tiwari et al. 2016; Gil-Alana et al. 2017; Gil-Alana and Trani 2019; Zerbo and Darné 2019; Churchill et al. 2020). These studies have generally analyzed countries or groups of countries and there is no consensus on the stationarity of CO2 emissions. To our knowledge, only three studies have examined whether the effects of shocks on global CO2 emissions are temporary or permanent (Barros et al. 2016; Belbute and Pereira 2017; Fallahi 2020).

Among the studies that have examined the stationary of global CO2 emissions, Barros et al. (2016) used annual data from 1760 to 2009, Belbute and Pereira (2017) from 1751 to 2014, and Fallahi (2020) from 1865 to 2013. None of these studies considered the frequency-domain properties of the series in their analysis and performed tests with data of up to 250 years. In this context, there is a gap in the literature that we aim to fill.

The contribution of this study to the existing literature is twofold. First, this study uses the most comprehensive data set on CO2 emissions. As noted by Churchill et al. (2020), using a longer time period can provide additional insights and information. For this reason, we aim to make accurate inferences about the stationarity of CO2 emissions by using annual data spanning more than 2000 years. Second, this work employs several unit root tests as well as a more powerful unit root test based on the Fourier and wavelet transformation. The Industrial Revolution, the Oil Crisis in 1973, the global economic crisis in 2008, and many important structural changes can affect the shape of the series. Neglecting these structural breaks in unit root analysis can lead to a false rejection of the null of the unit root (Perron 1989; Vaona 2012; Kula et al. 2012; Adedoyin et al. 2020). It is not easy to determine how many structural changes have occurred in a 2000-year series. The Fourier approximation allows smooth shifts to be included in the analysis whose time, structure, and number are not predetermined. Moreover, conventional unit root tests deal only with the time dimension of the series and neglect the frequency dimension. Conventional methods may not reflect the true picture of the stochastic properties of the analyzed series, since the behavior of the series may change across different frequencies (Ahmed et al. 2017). To address this issue, wavelet transforms enable an analysis that incorporates both the time and frequency properties, helping to exploit all the information about the series. Therefore, we apply the Fourier wavelet ADF unit root test developed by Aydin and Pata (2020), which considers both frequency components and smooth shifts in the series.

The remainder of the work is organized as follows. The “Literature review” section reviews the literature examining the stochastic properties of CO2 emissions. The “Data and methodology” section introduces the dataset and method used in this study. The “Empirical results and discussion” section reports and discusses the empirical findings. The “Conclusion” section concludes the study.

Literature review

Modeling the dynamic behavior of CO2 has become one of the most interesting research areas, because CO2 has some important implications for policymakers and researchers. Depending on whether the shocks to CO2 emissions are temporary or permanent, inferences can be drawn about the effectiveness of emission reduction policies. The persistence of the effects of shocks is usually determined using unit root or stationarity tests. Because of this importance, there has been an increased interest in studying the stochastic properties of CO2 emissions. Table 1 provides an overview of the literature on the stationarity properties of CO2.

Table 1 Empirical studies on stationarity properties of CO2
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The foregoing review of the literature shows that there is no consensus on the dynamic behavior of CO2 emissions because of using different samples, time spans, and econometric approaches. Environmental problems have recently begun to seriously threaten all countries in the world, whether developed or underdeveloped. Therefore, this study employs historical data on global CO2 emissions to get more robust results. In addition, a comparative analysis using traditional and new structural break unit root tests is conducted to analyze the stationarity properties of global CO2 emissions.

Data and methodology

The CO2 data (parts per million) employed in this study cover the period from 0 to 2014 and were compiled by Institute for Atmospheric and Climate Science (CO2.earth 2021). Since the size and power properties of econometric methods become stronger with increasing time dimension (Enders and Lee 2012), we aim to empirically analyze CO2 emissions for the first time in the literature with more than 2000 observations. Following Gil-Alana et al. (2017), we examine total CO2 emissions. Since we focus on emissions around the world and do not make country comparisons, we aim to use aggregate values to analyze whether the effects of policies to address emissions at the global level are permanent.

The main strategy for estimating past atmospheric CO2 data is to combine proxy records such as microfossils and sediments in the oceans to model past environmental conditions. For instance, Hönisch et al. (2009) modeled CO2 levels by examining the shells of the single-celled plankton found along the African coast of the Atlantic Ocean. By dating the shells and examining their boron isotope ratios, they were able to estimate what the atmospheric CO2 levels were when the plankton were alive. This strategy allowed them to go back further than the precise records in polar ice cores, which go back only 800,000 years. (Sciencedaily 2009). The Scripps CO2 Program (2022) traces CO2 levels back to 13.3 CE using multiple studies. Lüthi et al. (2008) extended earlier records from Antarctica from 650,000 years ago to 800,000 years ago. These records are integrated with observations of the present-day Earth system to model past atmospheric conditions. As a well-organized data source, we utilized data from 0 to 2014. The used data were converted into logarithmic values by taking the natural logarithm, and missing data for the year 158 was interpolated using the Eviews 10 software.

The descriptive statistics of global carbon emissions are shown in Table 2. To determine whether the Industrial Revolution had an impact on the CO2 data, we divided the historical CO2 data into two parts: 0–1711 and 1712–2014. The choice of 1712 as the division point is appropriate because the steam engine was invented in 1712 and the descriptive statistics indicate that emissions were higher after the Industrial Revolution than during the entire period. A sharp increase in the mean of the data was caused by the Industrial Revolution, and a peak in the observation occurred afterward. This situation can also be seen in Fig. 1.

Table 2 Descriptive statistics
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Fig. 1
figure 1

Source: CO2.earth (2021)

Global CO2 emissions from 0 to 2014 (ppm).

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We began our analysis by employing widely known unit root and stationarity tests such as augmented Dickey and Fuller (ADF) (1981), Phillips and Perron (PP) (1988), and Kwiatkowski et al. (1992) (KPSS). Afterward, to avoid biased estimates as suggested by Perron (1989), we then implemented unit root tests with structural shifts developed by Lee and Strazicich (2003), Fourier Lagrange Multiplier (Enders and Lee 2012), and Fourier wavelet ADF (Aydin and Pata 2020).

The unit root test of Lee and Strazicich (2003) examines the stationarity of the series under the assumption of the existence of two sharp structural changes. The data generation process (DGP) of the test could be defined as follows:

$${\Delta y}_{t}={\delta }^{^{\prime}}{\Delta Z}_{t}+{\varepsilon }_{1t},$$
(1)

where \({\varepsilon }_{1t}={\beta \varepsilon }_{1t-1}+{e}_{t},{e}_{t}\sim iid\left(N,{\sigma }^{2}\right)\) \({Z}_{t}\) denotes the set of exogenous variables. If the stationarity property of the data is investigated for the model A with two breaks in level, \({Z}_{t}\) can be defined as \({Z}_{t}={\left[1,t,{D}_{1t},{D}_{2t}\right]}^{^{\prime}}\), and \({D}_{jt}\) is \({D}_{jt}=1\) \(t\ge {T}_{Bj}+1,J=\mathrm{1,2},\) and otherwise, 0. Moreover, \({T}_{Bj}\) denotes the break date. If the stationarity property of the data is investigated for the model with constant and trend, \({Z}_{t}\) can be defined as \({Z}_{t}={\left[1,t,{D}_{1t},{D}_{2t},{DT}_{1t},{DT}_{2t}\right]}^{^{\prime}}\), and \({DT}_{jt}=t-{T}_{Bj}\) \(t\ge {T}_{Bj}+1,J=\mathrm{1,2},\) otherwise, 0. Ultimately Lagrange Multiplier of Lee and Strazicich test can be estimated as follows:

$${\Delta y}_{t}={\delta }^{^{\prime}}{\Delta Z}_{t}+{\gamma \overline{S} }_{t-1}+{\varepsilon }_{3t},$$
(2)

where \({\overline S}_t=r_t-{\overset{}\Psi}_x-Z_t{\overset{}\delta}_t\), \({\overset{}\Psi}_x=r_t-Z_t\delta\), \(\overset{}\delta\) shows coefficients, and \(\overline{LM}=1/N{\textstyle\sum_{i=1}^N}{LM}_i^\tau\) (Aslan and Kum 2011). Lee and Strazicich (2003) adopt the null hypothesis of the unit root “(\(\gamma =0\))” against the alternative of trend stationarity “\(\gamma =0\).”

Enders and Lee (2012) extended the standard ADF test by including Fourier functions. Hence, the ADF specification was modified to consider structural shifts as smooth and gradual. The extended Fourier form of the ADF test can be defined as follows:

$$d\left(t\right)=\alpha_0+{\textstyle\sum_{k=1}^n}\alpha_k\sin\left(2\pi kt/T\right)+{\textstyle\sum_{k=1}^n}\beta_k\cos\left(2\pi kt/T\right);n\leq T/2,$$
(3)

where \(d\left(t\right)\) is a deterministic function of t, n is the number of cumulative frequencies, k is a particular frequency, and T is the number of observations. Enders and Lee (2012) note that a small number of frequency components can replicate the types of breaks commonly occur in economic data. Therefore, they begin by considering a Fourier approximation using a single frequency component as follows:

$$d\left(t\right)\cong {\alpha }_{0}+{\alpha }_{k}\mathrm{sin}\left(2\pi kt/T\right)+{\beta }_{k}\left(2\pi kt/T\right),$$
(4)

where k is the single frequency, \({\alpha }_{k}\) its amplitude, and \({\beta }_{k}\) is the displacement of the sinusoidal component of the deterministic term.

We also employed the wavelet and Fourier based ADF unit root test developed by Aydin and Pata (2020). Following Yazgan and Özkan (2015), they extended the wavelet ADF test by adding structural changes to the data generation process:

$${y}_{t}=\mu \left(t\right)+{\varepsilon }_{t},$$
(5)

where \({y}_{t}\) is related time series evolve by following the process shown in Eq. (4) and, \(\mu \left(t\right)\) includes the structural changes of \({y}_{t}\) at unknown dates. Yazgan and Özkan (2015) utilize Eq. (5) to estimate the unknown deterministic factor:

$$\mu\left(t\right)\cong\alpha{\textstyle\sum_{i=1}^n}\left\{\left(2i-1\right)^{-1}\sin\left[2\pi\left(2i-1\right)kt/T\right]\right\},$$
(6)

where i = 0,1,…,n + 1, and n, k are the frequency of the deterministic factor and frequency of the Fourier, and term \(\alpha\) indicates their size (amplitude), respectively. Moreover, T is the number of observations. Aydin and Pata (2020) presume n = 1 and use Eq. (6) to obtain the FWADF estimation:

$${\Delta V}_{1,t}={\textstyle\sum_{j=1}^p}\rho_j{\Delta V}_{1,t-j}+{\delta V}_{1,t-1}+\beta\sin\left(2\pi kt/T\right)+\varepsilon_t,$$
(7)

where \(\beta\) is the coefficient associated with the Fourier function. The FWADF method follows a two-step procedure. In the first step, Eq. (7) is estimated for \(1\le k\le 5,\) and the model, having the minimum residual squares, is chosen. In the second step, the validity of the nonlinearity is decided using the traditional t-test. If the Fourier term is statistically significant, the FWADF can be employed.

Empirical results and discussion

We began the empirical analysis by utilizing standard unit root and stationarity methods. Table 3 presents the results of traditional unit root tests. According to the ADF and PP tests, the null hypothesis of unit root cannot be rejected. The KPSS findings reveal that the null hypothesis of stationarity is rejected. It can be said that the results of the traditional unit root tests support the existence of a unit root in the global CO2 data.

Table 3 Traditional unit root and stationarity test results
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It is common knowledge that economic data is often subject to structural changes. Ignoring structural changes in economic data can cause biased statistical inferences (Nazlioglu and Karul 2017; Pata 2018; Erdogan and Acaravci 2019; Erdogan et al. 2020). Therefore, we utilized unit root tests with sharp and smooth structural shifts and reported the results in Table 4. On the one hand, Lee and Strazicich (2003) unit root test with sharp changes indicates that the null hypothesis of unit root cannot be rejected. Moreover, the first and second structural changes in the global CO2 emissions occurred in 1558 and 1714, respectively. On the other hand, the unit root test with smooth changes (Enders and Lee 2012) revealed that the null hypothesis of unit root cannot be rejected. Finally, the wavelet-based unit root test with smooth changes revealed that the Fourier term is statistically significant. Therefore, the FWADF test can be utilized. The results of the FWADF test show that the null hypothesis of unit root cannot be rejected. The findings of all unit root and stationarity tests prove that the historical global CO2 data follow a unit root process. Therefore, the effects of possible shocks on global CO2 are permanent, and global CO2 cannot revert to its mean and trend path without exogenous intervention.

Table 4 Unit root test results with structural shifts
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Another important point is the occurrence times of structural breaks, which were determined utilizing the Lee and Strazicich (2003) test. The first structural change occurred in 1558. This could be related to the influenza pandemic that broke out in the spring of 1557. Influenza pandemic first emerged in Asia and rapidly spread to Africa, Europe, and eventually the Americas. The pandemic spread so quickly that it affected all of Europe before the fall of 1557, even though it emerged in Asia in the spring of 1557. Unlike previous pandemic experiences, the death toll was so high. Children were especially susceptible the flu, which is why the death rate among them was high. The influenza flu of 1557 lasted for more than two years and took lives all over the world (Alibrandi 2018). This led to a decline in the global population. Cole and Neumayer (2004) reported that the increase in population was closely related to the increase in CO2 emissions. It could be inferred that a decrease in population may lead to a slowdown in economic activities and a decrease in global CO2 emissions. This is also evident from Fig. 1 as well, and global CO2 emissions began to decline from about the 1550 s until the early 1700s.

The second structural change occurred in 1714. This may be related to the invention of the steam engine by Thomas Newcomen in 1712. The early form of the steam engine provided nearly 4 kW of energy per minute. Later, it was modified to provide 56 kW of energy per minute. The provision of such manpower led to the replacement of human and animal power with machine power. Therefore, the steam engine was enthusiastically adopted in industrial production (Lovland 2007). Especially in coal mining, the steam engine was used extensively. This provided the required energy supply for mass production, leading to a huge increase in industrial production, which became known as Industrial Revolution. Moreover, James Watt modified the steam engine again in 1763. This made the steam engine a more powerful machine that operated at a lower cost. As the cost of the steam engine was reduced, it quickly spread to other industries. As a result, production levels increased, which in turn increased wealth and consumption. This led to an increase in population (Komlos 1990). These facts inevitably led to an increase in resource consumption and anthropogenic CO2 emissions. From Fig. 1, it can be seen that the trend of global CO2 emissions has been increasing since the beginning in 1700. Moreover, Fig. 2 shows that the Fourier approximation of the global CO2 data successfully gives the signals of the change in economic data.

Fig. 2
figure 2

Fourier approximations

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We used six different unit root tests in this study. We applied traditional unit root tests (ADF and PP) and the KPSS stationarity test to compare the results with current unit root tests. We performed the Lee and Strazicich (2003) test to obtain sharp breaks and found that CO2 emissions contain a unit root. However, in this study, which we conducted with more than 2000 observations, there may be more structural breaks for the relevant period. In this context, we employed the Fourier ADF and Fourier wavelet ADF unit root tests, which allow more than two smooth structural breaks with an unknown date and number. Using the wavelet transform, we considered both the frequency domain and time domain properties of the series. Time-domain based analysis can lead to loss of information about the series and thus to discrepant results (Aydin et al. 2021). The use of Fourier approximation alone does not ensure that the time and frequency domain properties are considered together. Unit root tests based on the wavelet transform allow simultaneous consideration of the time and frequency domain properties of the series and help gather more information about the series and obtain robust results (Aydin and Pata 2020). For this reason, we also use a wavelet-based unit root test. Thus, we have taken into account many aspects that should be considered when studying the stochastic properties of a time series, and thus we have obtained robust results. The results of our study show that historical CO2 emissions worldwide have a unit root when structural breaks and properties in the time and frequency domains are taken into account. For this reason, our study emphasizes that policies to reduce CO2 emissions in the fight against climate change and global warming can have long lasting effects worldwide.

Conclusion

In recent times, environmental concerns are gradually becoming one of the foremost issues of deliberations among policy makers and global leaders. This is mainly due to the global warming and climate change being witnessed in numerous regions of the world. Anthropogenic emissions of carbon dioxide being the dominant greenhouse gas contributes to global warming and climate change. Hence, it is necessary to examine several dimensions of carbon dioxide emissions including the persistence of carbon dioxide emissions. The examination of persistence of carbon dioxide emissions will show how effective are emission reduction policies. Moreover, persistence can also reveal the possibility of emission reduction through cooperation at the global level, if a global-level dataset is analysed.

The aim of this study is to examine the persistence of shocks to global carbon dioxide emissions using a dataset of more than 2000 years. With the use of long time span of data, the reliability of the results is enhanced and the persistence of carbon dioxide emissions can be evaluated over a long span horizon. Whether the shocks to CO2 emissions are temporary or permanent can be analyzed by unit root tests or fractional integration techniques. Several researchers have used fractional integration techniques to test the persistence of CO2 emissions (see, e.g., Barassi et al. 2011; Barros et al. 2016; Gil-Alana et al. 2016; Belbute and Pereira 2017). In the fractional integration approach, fractional values rather than 0 or 1 values can be used to determine whether a series is stationary or not (Gil-Alana et al. 2015). This approach provides the possibility that the series can be fractional I(d) instead of I(0) or I(1). For this reason, more accurate predictions of the time trend coefficients can be made by estimating d (Gil-Alana et al. 2016). However, some of the studies that use the fractional integration approach neglect the structural breaks and this approach does not take into account the properties of the time series in the frequency domain. Therefore, in our work, we use a variety of traditional and new unit root tests that take into account sharp and smooth structural shifts in addition to the frequency domain properties of the series.

The results show that global carbon dioxide emissions contain a unit root. Furthermore, structural breaks were observed which coincided with the influenza pandemic of 1557 and the invention of the steam engine in 1712. The implication of the results is that global carbon dioxide emissions do not exhibit mean-reverting behavior. In other words, global carbon dioxide emissions will not move back to their original mean after experiencing an economic or natural shock. Thus, policy makers and global environmental institutions need to concentrate on the long-term trends of carbon dioxide emissions instead of focussing on short-run targets.

Long run instruments including investments in carbon dioxide emission reduction technologies, emission trading, and grants will be more effective than short-term instruments such as short-term energy and carbon tax incentives. Another implication of the results is that a reduction in global carbon dioxide emissions is possible if effective energy environmental and policies linked to existing international agreements meetings such as Rio Conference, Kyoto Protocol Paris Agreement, and the United Nations Sustainable Development Summit are properly implemented. This is because most of the policies in these agreements have long-term outlooks.

The results also imply that any shocks that induced carbon dioxide emissions such as a sudden increase in the use of a persistent fossil fuel will have a permanent impact on carbon dioxide emissions if relevant policies are not introduced to combat carbon dioxide emissions. As the developed nations seem to possess superior policies and technologies (such as the capture and storage of biogenic carbon dioxide, electrification of vehicles, and fossil-free technology) for combating carbon dioxide emissions, the developing countries can adapt (and if possible, acquire) some of these technologies in order to reduce the global CO2 emissions level.