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Considering Multiple Factors to Forecast CO_{2} Emissions: A Hybrid Multivariable Grey Forecasting and Genetic Programming Approach

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## Abstract

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## 1. Introduction

_{2}, CH

_{4}, N

_{2}O, PFC, HFC, and SF

_{6}. In the growth of global greenhouse gas emissions, CO

_{2}is the fastest growing and accounts for 94.77% of the total. Thus, countries across the globe have been focusing on the sources of the CO

_{2}increase.

_{2}emissions include factors that affect the amount of emissions [1,2,3,4] and carbon emission amount forecasting [2,5]. Previous studies on factors that affect the amount of carbon emissions considered different factors. Zakarya et al. [1] used a panel cointegration test and Granger causality to analyze whether there is a correlation between total energy consumption, direct foreign investment, and economic growth. The major contribution in their study is the consideration of environmental pollution and the amount of carbon emissions caused by foreign investment. However, their study lacked consideration of the amount of carbon emissions caused by the population. Wu et al. [2] explored the relationship between energy consumption, urban population, the economy, and CO

_{2}emissions in the BRICS countries (i.e., Brazil, Russia, India, China, and South Africa). Their study only used the grey model coefficient to conduct the correlation analysis and did not use the grey relation interpretation. In reality, uncertainty still exists when grey action is used as the standard, and this cannot accurately determine the mutual effect and correlation between the amount of carbon emissions and other factors. Their study considered the population factor and used urban population as its representative. However, the urban population does not represent the impact of a nation’s total population on the amount of CO

_{2}emissions. Wang et al. [3] primarily explored the impact of China’s road cargo transportation on carbon emissions and used the least squares regression model and multiple linear regression analysis to build a forecast model. However, their study did not first conduct a correlation analysis between carbon emission pollution from road transportation, and only considered transportation. Thus, their study did not consider other factors that could cause and increase the amount of carbon emissions. Xu and Lin [4] primarily analyzed the carbon emissions produced by China’s transportation industry. They used panel data to analyze the impact of the number of automobiles in different areas on the amount of CO

_{2}emissions. Again, they only considered transportation, but did not consider other factors that increased the carbon emissions.

_{2}emissions. Belbute and Pereira [5] forecasted global CO

_{2}emission amount based on the ARFIMA model. They defined the amount of carbon emissions as the CO

_{2}emitted from the burning of fossil fuels (petroleum, coal, and natural gas) and the production of cement. Aydin [6] used regression t-test, F-test, and residual analysis to examine the impact of Turkey’s national population, GDP, alternative energy, nuclear power consumption, combustible renewable energy, waste energy consumption, and fossil fuel consumption on CO

_{2}emissions. Aydin also used trend analysis to forecast future growth of CO

_{2}emissions. However, all the aforementioned forecast methods required a large amount of historic data samples to be able to build an accurate forecast model. In addition, most of these models did not consider other factors in the forecast model. These forecast methods have a common drawback that the selection of samples requires an assumption of some probability distribution, e.g., a normal distribution or Poisson distribution. In addition, most previous studies speculated and built forecast models based on raw CO

_{2}data. Thus, Wu et al. [2] established a grey forecast model. The advantage of their method is that a small sample number and that the factors can be considered in the model. However, when the data has a non-linear trend, the grey forecast model can produce poorer forecast values. Although Wu et al. [2] considered energy consumption, urban population, and economy as factors, they viewed the urban population as representative of the entire population. They did not consider the problem of transportation in the forecast model, which means that they still used incomplete factors.

_{2}emissions. In addition, this study experimented with different combinations of factors in the forecast model, and scenario analysis was conducted to determine which combination of factors produced the most accurate CO

_{2}emission forecast in terms of three error performance measures (i.e., MAPE, MAE, and PE). The primary contributions of this study include the following:

- Previous studies did not consider at least three factors that affect carbon emissions. This study comprehensively considered all factors that affect carbon emissions to build a forecast model. We also conducted simulation analysis and scenario analysis to find the most suitable and accurate method to forecast carbon emissions.
- Most previous forecast methods required a large amount of historic data to conform to statistical assumptions, and did not consider factors in the forecast model. This study introduced different factors that can affect the forecast value in the multivariable grey forecasting method into the forecast model. This produced a model that conforms better to changes while retaining the advantage of only needing a small quantity of observed samples to be able to accurately make forecasts.
- The common methods for forecasting the amount of CO
_{2}emissions include regression analysis and time series. However, these forecast methods do not consider factor in the forecast model, which can result in excessive forecast errors. When the data is a non-linear, the accuracy of the forecast value is also poor. Thus, this study proposes an integrated forecast method that includes a multivariable grey forecasting method and GP. The advantage of the multivariable grey forecasting method is that it introduces factors that can affect the forecast value into the forecast model. Only four or more observation samples are needed to accurately make forecasts. The GP can automatically produce a mathematical model to effectively solve complex non-linear mathematical problems. Mutual assistance within such a mixed forecast method makes this model an effective forecast tool. - After conducting a forecast using Taiwan’s carbon emissions as an example, the experimental result showed that the best model does not need to introduce all the factors or higher grey correlation factor into the forecast model. Factor arrangement combination showed that the model with the best accuracy for 2000–2015 CO
_{2}emission amount used Taiwan population, energy consumption, and carbon emissions as factors (i.e., three factors are considered). Note that this work proposes a general forecasting model that uses multiple factors. Although the experiment results in this example show that the model performs best using three factors, the model used for other examples or applications may conclude that the model using a different number of factors performs best.

## 2. Literature Review

_{2}emissions, and then reviewed studies that focused on using statistical methods to forecast CO

_{2}emissions.

#### 2.1. Previous Studies on Factors That Affect CO_{2} Emission Amount

_{2}concentration is gradually increasing, and a lot of countries are situated in the red alert area. Excessive amounts of CO

_{2}intensify the greenhouse effects, and the direct impact on humans is reflected in climate changes and the environmental habitat. Starting from the Industrial Revolution, improvements in production technology and technology advancements have rapidly increased the global amount of CO

_{2}, and the resulting effects have been seen in recent years. The effects include reduced rain quantity, temperature increases, and more frequent appearance of extreme climate events. All these events show that man-made environmental imbalance is beginning to impact our lives. Thus, a lot of studies have been done on the correlation between the enormous energy consumption of advanced manufacturing and excessive human development (and the resulting increase in urbanization and economic indicators) and CO

_{2}concentration.

_{2}emissions. In general, the cause can be attributed to energy consumption, economic growth/depression, and other human activities. The previous studies that are more directly related to this study are listed in Table 1.

_{2}emissions of BRICS countries (which are the countries that are able to maintain or even increase their economic index while facing financial crisis) from 1990 to 2012 using econometrics panel data and the Granger causality test. They mentioned green economy topics, in which green investment industry (such as energy, construction, and businesses) can create green job opportunities, and can also replace the consumption of non-renewable energy and advance humankind without economic growth. Their study also indicated that the environmental policies of developing countries are incomplete, which attracts foreign investors who are limited by policies in their own countries, resulting in more severe environmental pollution.

_{2}emission amount of each nation of BRICS countries from 2004 to 2010. Their result showed a low correlation between GDP and CO

_{2}emission amount in Brazil and Russia. In the case of Brazil, the reason is because Brazil’s industries are mainly focused on services, which produce less CO

_{2}emissions. In the case of Russia, it is because Russia possesses abundant natural gas, which is used to produce electricity and produces much less CO

_{2}than coal or petroleum. Russia’s GDP is also based primarily on the export of resources. Both of these factors do not cause an increase in the CO

_{2}emission amount. In other BRICS countries, the correlation between urbanization and CO

_{2}emission amount is significant. The case of China showed the greatest correlation between urbanization and the amount CO

_{2}of emissions. All the BRICS nations had abundant fossil fuels, and should establish long-term development plans to ensure sufficient energy use, increase market economy development, and reduce CO

_{2}emissions. China and India should make more use of renewable energy, especially hydropower, wind power, nuclear power. China and India should also focus on how to reduce the pollution caused by industrial waste gas emissions and how to achieve a balance between a rapidly growing economy as well as urbanization and environmental protection.

_{2}emission amount in Beijing. In their study, first the impact of this policy on private vehicle application quantity was analyzed. The exploration was conducted based on three different scenarios from 2011 to 2020: no policy restriction, current policy restriction, and strict policy restriction. The estimated CO

_{2}emission amounts for these three scenarios in 2020 were 230,000, 150,000 and 130,000 tons, respectively. The result of their study showed that the strict policy restriction can effectively control and curb the amount of carbon emissions.

_{2}emissions. In their study, China was divided into eastern, central, and western China. Panel data was used to analyze the effect of the number of vehicles in each region on the amount of CO

_{2}emissions in the corresponding region, respectively. Their study showed that different numbers of vehicles in different regions had different impacts on their respective CO

_{2}emissions. The effect in eastern China was more significant. Therefore, the policy drafted for each region should be appropriately adjusted according to the different regional situations to curb the amount of CO

_{2}emissions.

_{2}emissions for the correlation analysis. We also conducted correlation analysis on the factors that have more significant impact on CO

_{2}emissions during different time periods to build different models, which previous studies have rarely explored.

#### 2.2. Previous Studies on Using Statistical Methods to Forecast CO_{2} Emission Amount

_{2}emissions and to reduce uncertainties that may exist in the future. Forecasting can also be used to set up policy control and promote environmental awareness. It has been widely used to apply statistics-based forecast models using historical data. Previous studies have attempted to use different statistical methods to forecast CO

_{2}emissions.

#### 2.2.1. Regression Analysis

_{2}emissions from 1971 to 2010. Aydin [6] also used trend analysis to forecast future trends, and stated that Turkey is a country with a rapidly growing population, which is a factor that affects Turkey’s rapidly growing energy requirement and fossil fuels consumption. This increase is expected to continue to grow and can exacerbate environmental problems. A way of reducing enormous CO

_{2}emissions is to increase the use of renewable energy and nuclear power energy. These types of energy can replace fossil fuel power generation and reduce CO

_{2}emissions. Improving the efficiency of existing power plants and advanced cleaning technology can also reduce the environmental impact of Turkey’s fossil fuel consumption increase.

_{2}emission prices in the United States. It was also forecasted that crude oil price increase will significantly decrease the amount of CO

_{2}emissions. Natural gas has less impact on carbon emissions; hence, when the price of natural gas changes, it does not have a significant impact on the amount of carbon emissions. Coal and electrical power show a significant effect on carbon emissions.

_{2}emissions of six nations in southern Africa, and used the data to build an autoregressive model. Data showed that some countries’ amount of CO

_{2}emissions has a positive correlation with foreign investment, but in the other countries, the correlation was negative. Thus, each country should formulate carbon emission control policies based on the local conditions to be able to effectively curb the growth if the amount of carbon emissions.

#### 2.2.2. Time Series

_{2}emission amounts based on the United States Department of Energy’s data on the global amount of carbon emissions from 1750 to 2013. In their study, the amount of carbon emissions is defined as the amount of CO

_{2}produced by burning fossil fuels (petroleum, coal, and natural gas) and the production of cement. Their study did not consider emissions from land changes, forestry, or international shipping. The forecast value indicated that the amount of CO

_{2}emissions increased from 361.31 million tons to nearly 518.83 million tons in 2013. By 2100, the amount of carbon emissions was expected to increase by 52.9%. Bastola and Sapkota [12] used the ARDL model to forecast the CO

_{2}emission amount in Nepal, and used the Johansen cointegration test to analyze the correlation among energy consumption, economic growth, and carbon emission. The forecasted results showed that in the future the amount of carbon emissions in Nepal would continue to grow. Policy makers must look for alternative energy policy to reduce CO

_{2}emission amount.

#### 2.2.3. Econometrics Analysis

_{2}emissions of BRICS countries from 1985 to 2014. Their study found that urbanization and CO

_{2}emissions exhibit a significant relationship. Alam et al. [14] focused on the period between 1970 and 2012 in Indonesia, Brazil, China, and India, and used the environmental Kuznets curve to analyze the significance of the factors based on CO

_{2}emission amount, economic growth, population growth, and energy consumption. Based on their empirical analysis, they found that population growth in India and Brazil significantly impacted the amount of carbon emissions. India’s economic growth significantly increased its amount of carbon emissions. However, economic growth in Indonesia, Brazil, and China reduced their respective amount of carbon emissions.

_{2}emission amount of the nations in the Gulf Cooperation Council. However, the experiment showed that there was not significant correlation between economic growth and amount of carbon emissions, but energy consumption and amount of carbon emissions had a positive correlation. Tang and Bee [16] explored the correlation among CO

_{2}emission amount, energy consumption, and foreign investment in Vietnam from 1976 to 2009. Their study showed that energy consumption and foreign investment are the primary factors that influence Vietnam’s amount of carbon emissions.

#### 2.2.4. Genetic Programing

#### 2.2.5. Grey Forecasting

_{2}emissions and is applied in various fields. As indicated from a lot of previous literature (e.g., [7,20,21]), the grey forecasting method enjoys the following advantages: (1) this method is easily operated; (2) this method requires only a small amount of data samples to make accurate forecasts (in general, only four or more samples are required); (3) no series distribution is supposed in advance. However, it has the following flaws: (1) this method includes the least-squares method, which may produce biased forecast results when the system has a lot of noise; (2) this method is not suitable for making long-run forecasts.

_{2}emissions in Turkey in 2011 were 321.88 million tons, which account for 1.03% of the total global carbon emissions. Turkey primarily uses thermal power generation, which involves heating boilers with coal to generate steam to rotate a generator, so a large amount of CO

_{2}emissions are produced. They applied the grey forecasting method with the data from 1965 to 2012 to build a model for forecasting the amount of carbon emissions. The mean forecast error percentage for their model was less than 1, indicating that the model has high precision. Their model forecasted that by 2025 the amount of carbon emissions would reach 4.96404 billion tons. They recommended Turkey work on controlling the amount of CO

_{2}emissions, plan its energy policies, and draft a protocol to slow down climate change.

_{2}emissions in China included energy consumption and GDP. The data used was from 1953 to 2013. In terms of root mean square error and mean absolute error, their experimental results showed that the grey forecasting model has higher accuracy than the autoregressive moving average model.

_{2}emissions. Meng et al. [23] forecasted the amount of CO

_{2}emitted by energy consumption in China based on a small number of data samples. Four estimation parameters were added to their improved grey forecasting model, and the model can produce trends that conform better to carbon emission changes. Compared to regression analysis and the original grey forecasting model, their improved grey forecasting model obtained more accurate forecast results.

## 3. Methodology

_{2}emissions. First, the data of these factors are input. Then, the data is preprocessed, and then the grey relational analysis is used to calculate the grey relational degree between the primary factor (i.e., CO

_{2}emissions) and each of the other factors. After sorting the grey relational degrees, the important factors with a high degree of grey relation with CO

_{2}emissions are selected for later analysis. Then, GM(1, N) considering these selected factors is used to build the forecast model and further calculate the grey forecast value. Then, the error between the actual value and the forecast value is calculated. Then, GP is used to build the error forecast model. The final forecast value is obtained by integrating the forecast value from GM(1, N) and the error correction value from GP, to increase accuracy. The next section introduces the grey relational analysis, multivariable grey forecasting model, and GP used in the framework of the proposed method (Figure 1).

#### 3.1. Grey Relational Analysis

- When calculating the grey relation, a time series is established based on the original observed value of each period. Let ${X}_{0}(k)$ denote the primary series and ${X}_{i}(k)$, i = 1, 2, …, N denote the associated series, where k denotes the index of the period such as week, month, or year:$$\begin{array}{l}{X}_{0}=({X}_{0}(1),{X}_{0}(2),\dots ,{X}_{0}(k)),\\ {X}_{1}=({X}_{1}(1),{X}_{1}(2),\dots ,{X}_{1}(k)),\\ {X}_{2}=({X}_{2}(1),{X}_{2}(2),\dots ,{X}_{2}(k)),\\ \begin{array}{ccc}& \vdots & \end{array}\\ {X}_{N}=({X}_{N}(1),{X}_{N}(2),{X}_{N}(3),\dots ,{X}_{N}(k)),\\ \\ k=1,2,\dots ,m\end{array}$$
- The maximum difference and minimum difference between the primary series and the other associated series are calculated as follows:$${\Delta}_{\mathrm{min}}=\underset{\forall j\in i}{\mathrm{min}}\underset{\forall k}{\mathrm{min}}\left|{X}_{0}(k)-{X}_{j}(k)\right|$$$${\Delta}_{\mathrm{max}}=\underset{\forall j\in i}{\mathrm{max}}\underset{\forall k}{\mathrm{max}}\left|{X}_{0}(k)-{X}_{j}(k)\right|$$
- The grey relational coefficient $\gamma $ between the primary series and the associated series in period k is calculated as follows:$$\gamma ({X}_{0}(k),{X}_{i}(k))=\frac{{\Delta}_{\mathrm{min}}+\zeta {\Delta}_{\mathrm{max}}}{{\Delta}_{0i}(k)+\zeta {\Delta}_{\mathrm{max}}}$$
- The grey relational degree between the primary series and the associated series is the mean of all grey relational coefficients as calculated as follows:$$\gamma ({X}_{0},{X}_{i})=\frac{1}{m}{\displaystyle \sum _{k=1}^{m}\gamma ({X}_{0}(k),{X}_{i}(k))}$$

#### 3.2. Multivariable Grey Forecasting Method GM(1, N)

- After the first-order accumulation generating operation (1-AGO) on the observed series ${X}_{i}^{(0)}=({X}_{i}^{(0)}(1),{X}_{i}^{(0)}(2),\dots ,{X}_{i}^{(0)}(k))$ of each factor i, we obtain ${X}_{i}^{(1)}=({X}_{i}^{(1)}(1),{X}_{i}^{(1)}(2),\dots ,{X}_{i}^{(1)}(k))$ where:$${X}_{i}^{(1)}(k)={\displaystyle \sum _{m=1}^{k}{X}_{i}^{(0)}(m)}$$
- Similar to whitening the GM(1, 1) model to obtain the general differential equation ${X}^{(0)}(k)+a{z}^{(1)}(k)=b$, the differential equation for the GM(1, N) model is expressed as follows:$${X}_{i}^{(0)}(k)+a{z}_{1}^{(1)}(k)={\displaystyle \sum _{i=2}^{N}{b}_{i}{X}_{i}^{(1)}(k)}$$
_{i}is the grey action coefficient corresponding to the associated series i; and the mean series is obtained as follows:$${z}_{i}^{(1)}=0.5\cdot {x}_{i}^{(1)}(k)+0.5\cdot {x}_{i}^{(1)}(k-1),\text{}k\ge 2$$ - Transform Equation (6) into the following matrix form:$$\left[\begin{array}{c}{X}_{1}^{(0)}(2)\\ {X}_{1}^{(0)}(3)\\ \vdots \\ {X}_{1}^{(0)}(m)\end{array}\right]=\left[\begin{array}{cccc}-{z}_{1}^{(1)}(2)& {X}_{2}^{(1)}(2)& \dots & {X}_{N}^{(1)}(2)\\ -{z}_{1}^{(1)}(3)& {X}_{2}^{(1)}(3)& \dots & {X}_{N}^{(1)}(3)\\ \vdots & \vdots & & \vdots \\ -{z}_{1}^{(1)}(m)& {X}_{2}^{(1)}(m)& \dots & {X}_{N}^{(1)}(m)\end{array}\right]\left[\begin{array}{c}a\\ {b}_{2}\\ \vdots \\ {b}_{n}\end{array}\right]$$The above matrix is solved by the least-squares method to obtain coefficient a and coefficient b
_{i}. Then, $\widehat{\alpha}={\left[\begin{array}{cccc}a& {b}_{2}& \cdot \cdot \cdot & {b}_{N}\end{array}\right]}^{T}={({B}^{T}B)}^{-1}{B}^{T}Y$ where:$$Y=\left[\begin{array}{c}{X}_{1}^{(0)}(2)\\ {X}_{1}^{(0)}(3)\\ \vdots \\ {X}_{1}^{(0)}(m)\end{array}\right]\text{}\mathrm{and}\text{}B=\left[\begin{array}{cccc}-{z}_{1}^{(1)}(2)& {X}_{2}^{(1)}(2)& \dots & {X}_{N}^{(1)}(2)\\ -{z}_{1}^{(1)}(3)& {X}_{2}^{(1)}(3)& \dots & {X}_{N}^{(1)}(3)\\ \vdots & \vdots & & \vdots \\ -{z}_{1}^{(1)}(m)& {X}_{2}^{(1)}(m)& \dots & {X}_{N}^{(1)}(m)\end{array}\right]$$ - We substitute coefficients a and b
_{i}into Equation (6) to obtain the following series:$${\widehat{X}}_{1}^{(1)}(k+1)=[{X}_{1}^{(0)}(1)-{\displaystyle \sum _{i=2}^{N}\frac{{b}_{i}}{a}{X}_{i}^{(1)}(k+1)}]{e}^{-ak}+{\displaystyle \sum _{i=2}^{N}\frac{{b}_{i}}{a}{X}_{i}^{(1)}(k+1)}$$ - Conduct inverse accumulation generation to obtain the forecast value:$${\widehat{X}}_{1}^{(0)}(k+1)={\widehat{X}}_{1}^{(1)}(k+1)-{\widehat{X}}_{1}^{(1)}(k)$$

#### 3.3. Genetic Programing

_{i}(1), e

_{i}(2), …, e

_{i}(k)}. The function set is {+, −, ×, /, log, sin, cos, exp}. The fitness function is defined as $\mathrm{min}\left|{\widehat{e}}_{i}-{e}_{i}\right|,$ for i = 1, 2, …, N. That is, the difference between the error estimation value produced by GP and the error obtained from the GM(1, N) model is used to evaluate fitness. The parameters used in GP include the population size, evolution size, the maximal depth for the evolutionary tree, crossover rate, and mutation rate. These parameter values are set through repeated experiments and exploration. The final forecast value is obtained by summing the forecast value ${\widehat{x}}_{i}(k)$ obtained by GM(1, N) and the forecast error value ${\widehat{e}}_{i}(k)$ obtained by GP, as calculated as follows:

## 4. Results

_{2}emissions in Taiwan, and considered the factors that affect the amount of CO

_{2}emissions. Among the factors that affect the amount of CO

_{2}emissions mentioned in the literature review in Section 2 [1,2,3,4], the factors that had a higher correlation with the amount of emissions include population, GDP per capita, total energy consumption, number of registered motor vehicles, and foreign investment.

_{2}emissions from 2000 to 2015 shows that in 2009 the amount of carbon emissions significantly decreased. From the historic events, the cause of the CO

_{2}emission decrease during that year may be the financial crisis caused by the American subprime mortgage crisis at the end of 2007. At that time, the global stock market reached a new low, and banks in different countries faced collapse. This had a significant impact on Taiwan’s economy. Affected by the financial crisis, economic development encountered obstructions, and factories were closed.

_{2}emissions data and the factors from 2006 to 2011 (the year before Taiwan faced the financial crisis) for the grey relational analysis, as well as compared forecasts from different GM(1, N) models. We also found that growth of the amount of carbon emissions from 2010 to 2014 was gentle. Data showed that Taiwan’s investment in China increased. As manufacturers moved out from Taiwan, this study attempts to investigate whether this movement slowed down the carbon emission growth in Taiwan. This study analyzed and explored carbon emissions during this period. Data on the amount of CO

_{2}emissions and the factors in Taiwan for the period from 2010 to 2014 (the year when a large number of Taiwan businessmen moved factories to China) were compiled for grey relational analysis. Forecasts of different GM(1, N) models were compared.

_{2}emissions and the factor data for the period from 2000 to 2015 for the grey relational analysis. Then, we further consider two periods. The second subsection analyzed the period from 2006 to 2011 (when Taiwan faced the financial crisis), and the third subsection analyzed the period from 2009 to 2015 (when a large number of Taiwan businessmen moved their factories to China). For the grey forecasting model, N = 2, 3, 4, 5, 6 was substituted to compare different GM(1, N) models.

#### 4.1. Forecast and Analysis of the CO_{2} Emission Amount in Taiwan

_{2}emissions, we collected data on Taiwan’s population, GDP per capita, total energy consumption, number of registered motor vehicles, and the amount invested in China for the period from 2000–2015, as shown in Table 2. We then applied the grey relational analysis to understand the importance ordering of the factors and the correlation(s) between them. The key to the analysis lay in the correlation coefficient between the factors.

_{2}emissions and the factors is shown in Table 3, in which the highest correlation of the amount of CO

_{2}emissions is with the number of registered motor vehicles. The second highest correlation is with the GDP per capita, followed by population, total energy consumption, and amount invested in China. The relational degree between each pair of factors is not significant. The key to the analysis is the correlation ordering between the factors.

_{k}is the forecast value of period k, and o

_{k}is the original actual value of period k. This method divided the accuracy rate into four levels, as shown in Table 5.

_{2}emissions established with the simulation value and forecast value of the five types of forecast models from Table 6. Figure 3 is the bar chart built from the PE values of the five forecast models in Table 6. It can be observed that compared with other forecast models, the method proposed by this study had better accuracy for forecasting the amount of CO

_{2}emissions.

#### 4.2. Analysis of the Amount of CO_{2} Emissions in Taiwan during the Financial Crisis

_{2}emissions during the financial crisis, we collected data on population, GDP per capita, total energy consumption, number of registered motor vehicles, and the amount invested in China for the period from 2006–2011, as shown in Table 4. We then applied the grey relational analysis to understand the importance of factors and the relational degrees of factors. The key to the analysis is the relational degrees of factors.

_{2}emissions, followed by total energy consumption, the number of registered motor vehicles, GDP per capita, and the amount invested in China.

_{2}emission amount trend produced from the simulation value and forecast value of the five forecast models in Table 9 for the financial crisis period. Figure 5 is the bar chart that compares the PE values from the five forecast model from Table 9. The original actual value in the data and chart clearly shows that after the financial crisis occurred in 2008, the amount of CO

_{2}emissions decreased significantly. CO

_{2}emissions gradually rose with the revival of the economy. Compared with other forecast models, the proposed model has superior fitness and variability, and is more accurate in forecasting CO

_{2}emission amount.

#### 4.3. The Impact of Taiwan Businessmen Moving Overseas on Taiwan’s CO_{2} Emission Amount

_{2}emissions in Taiwan during the period that Taiwan businessmen were moving overseas. We collected data on population, GDP per capita, total energy consumption, number of registered motor vehicles, and amount invested in China for the period between 2010 and 2014. We then applied grey relational analysis to understand the importance of factors and the relational degree between factors. The key to the analysis is the relational degree between factors. The grey relational degrees of all factors was sorted from large to small. Table 10 shows that Taiwan’s energy consumption has the highest correlation with the amount of CO

_{2}emissions, followed by population, the number of registered motor vehicles, GDP per capita, and the amount invested in China.

_{2}emissions produced with the simulation value and forecast value of the five forecast model in Table 12 for the period when Taiwan businessmen were moving overseas. Figure 7 is the bar chart that compares the PE values from the five forecast models in Table 12. The original actual value in the data and chart clearly shows that the amount of CO

_{2}emissions in 2010 dropped after Taiwan businessmen moved overseas. Compared with other forecast models, the proposed model has superior fitness and variability, and is more accurate in forecasting the amount of CO

_{2}emissions.

## 5. Discussion

_{2}emissions, the scale of the relational degree of factors does not have a significant influence on forecast accuracy. Hence, by repeatedly experimenting with different combinations of factors, we were able to determine the combination with the highest accuracy. The difference between the proposed forecast model and the classical GM(1, 1) or other conventional forecast methods is that the proposed forecast model not only considers the time change in the original data, but also considers the factors that are reflected on the actual value. We also used GP to conduct error value correction to avoid only considering changes in original data. This is because when drastic change occurs to a factor, it could result in an excessive forecast error.

_{2}emissions during the financial crisis period and when Taiwan businessmen moved overseas) for comparison. The experiment results show that the method proposed in this study has higher accuracy rate and better adaption to different environmental changes compared to other methods. The main experiment conclusions are as follows:

- Our experimental results showed that the amount of carbon emissions began to drop significantly after 2006. Therefore, the forecast error for those few years also increased significantly. From previous history and news, at that time, global stock markets were at historic lows, and banks in different countries faced bankruptcy. Taiwan was affected by the financial crisis caused by the American subprime mortgage crisis. The experiment scenario was focused on the carbon emission forecast and analysis for Taiwan during the financial crisis period. The most accurate model for forecasting Taiwan’s CO
_{2}emission amount during this period considered the following factors: population, total energy consumption, number of registered motor vehicles, and the amount invested in China. - The experiments also found that the growth of the amount of carbon emissions from 2010 to 2014 was gentle. Data shows that when Taiwan’s investment in China grew and manufacturers moved overseas, there is a possibility that this slowed down carbon emissions in Taiwan. Therefore, we analyzed and explored that period. For the period from 2010 to 2014, the most accurate Taiwan amount of CO
_{2}emission forecast model considered the following factors: Taiwan’s population, number of registered motor vehicles, and the amount invested in China.

## 6. Conclusions

_{2}emissions in some year, the data that year may have a large drop. However, those regulations and methods may not be effective or stable in the following years, and hence the data of these years may demonstrate great vibration. Most forecasting methods suffer from this kind of noisy data.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Comparison of forecast values of the five forecast models trained with the data from 2000–2013 and tested with the data from 2014–2015.

**Figure 3.**Comparison of PE values of the five forecast models trained with the data from 2000–2013 and tested with the data from 2014–2015.

**Figure 4.**Comparison of the five forecast models trained with the data from 2007–2010 and tested with the data in 2011.

**Figure 5.**Comparison of PE values of the five forecast models trained with the data from 2007–2010 and tested with the data in 2011.

**Figure 6.**Comparison of forecast values of the five forecast models trained with the data from 2011–2013 and tested with the data in 2014.

**Figure 7.**Comparison of PE values of the five forecast models trained with the data from 2011–2013 and tested with the data in 2014.

Reference | Study Area | Study Period | Energy Consumption | Economic Growth/Depression | Other Human Activities |
---|---|---|---|---|---|

[1] | BRICS countries | 1990~2012 | v | v | |

[2] | BRICS countries | 2004~2010 | v | v | v (urban population) |

[3] | Beijing | 2011~2020 | v (number of vehicles) | ||

[4] | China | 2000~2012 | v (number of vehicles) | ||

[8] | Southeast Asian Nations countries | 1980~2009 | v | v (urbanization) |

Year | Carbon Emission Amount (Gg CO_{2}-Equivalent) | Taiwan’s Population (People) | GDP per Capita (NT$) | Total Energy Consumption (1000 kiloliter of Oil Equivalent) | Number of Registered Motor Vehicles | Amount Invested in China (1000 USD) |
---|---|---|---|---|---|---|

2000 | 20,936 | 22,276,672 | 466,598 | 101,788.10 | 16,981,890 | 2,607,142 |

2001 | 21,304 | 22,405,568 | 454,687 | 106,381.60 | 17,422,491 | 2,784,147 |

2002 | 22,109 | 22,520,776 | 475,484 | 111,424.17 | 17,861,379 | 6,723,058 |

2003 | 23,068 | 22,604,550 | 486,018 | 119,583.41 | 18,452,827 | 7,698,784 |

2004 | 23,851 | 22,689,122 | 514,405 | 132,607.81 | 19,132,734 | 6,939,912 |

2005 | 24,520 | 22,770,383 | 532,001 | 133,679.26 | 19,809,106 | 6,002,029 |

2006 | 25,207 | 22,876,527 | 553,851 | 136,520.00 | 20,251,086 | 7,375,197 |

2007 | 25,587 | 22,958,360 | 585,016 | 144,192.32 | 20,652,231 | 9,961,542 |

2008 | 24,463 | 23,037,031 | 571,838 | 139,161.90 | 21,029,329 | 10,691,390 |

2009 | 23,218 | 23,119,772 | 561,636 | 136,267.54 | 21,306,396 | 7,142,593 |

2010 | 24,828 | 23,162,123 | 610,140 | 142,501.32 | 21,650,247 | 14,617,872 |

2011 | 25,345 | 23,224,912 | 617,078 | 138,236.51 | 22,150,801 | 14,376,624 |

2012 | 24,864 | 23,315,822 | 631,142 | 140,768.47 | 22,265,065 | 12,792,077 |

2013 | 24,911 | 23,373,517 | 652,429 | 143,135.84 | 21,477,473 | 9,190,090 |

2014 | 25,104 | 23,433,753 | 687,816 | 147,453.21 | 21,198,831 | 10,276,570 |

2015 | 26,463 | 23,483,793 | 711,310 | 145,084.20 | 21,400,897 | 9,896,793 |

Population | GDP per Capita | Total Energy Consumption | Number of Registered Motor Vehicles | Amount Invested in China | |
---|---|---|---|---|---|

$\gamma ({X}_{0},{X}_{i})$ | 0.9486 | 0.9592 | 0.9377 | 0.9807 | 0.5533 |

Combination of Factors | Simulation Error | Forecast Error | Average Error | Average Accuracy |
---|---|---|---|---|

GM(1, 3) with P, EC | 4.45% | 2.28% | 3.37% | 96.63% |

GM(1, 4) with G, NV, I | 5.29% | 1.59% | 3.44% | 96.56% |

GM(1, 2) with NV | 4.67% | 2.23% | 3.45% | 96.55% |

GM(1, 4) with P, EC, I | 4.13% | 2.93% | 3.53% | 96.47% |

GM(1, 4) with P, EC, NV | 3.91% | 3.26% | 3.59% | 96.41% |

GM(1, 5) with P, G, EC, I | 4.52% | 2.69% | 3.61% | 96.40% |

GM(1, 5) with P, G, EC, NV | 4.10% | 3.14% | 3.62% | 96.38% |

GM(1, 4) with P, G, EC | 4.41% | 2.86% | 3.63% | 96.37% |

GM(1, 6) with P, G, EC, NV, I | 4.08% | 3.24% | 3.66% | 96.34% |

GM(1, 5) with P, EC, NV, I | 3.92% | 3.41% | 3.66% | 96.34% |

GM(1, 3) with NV, I | 5.29% | 2.27% | 3.78% | 96.22% |

GM(1, 4) with G, NV, I | 4.34% | 3.22% | 3.78% | 96.22% |

GM(1, 3) with P, G | 5.29% | 2.48% | 3.88% | 96.12% |

GM(1, 3) with EC, I | 4.38% | 3.42% | 3.90% | 96.10% |

GM(1, 5) with P, G, NV, I | 5.67% | 2.18% | 3.93% | 96.07% |

GM(1, 4) with P, G, I | 5.74% | 2.20% | 3.97% | 96.03% |

GM(1, 4) with P, NV, I | 5.52% | 2.48% | 4.00% | 96.00% |

GM(1, 4) with P, G, NV | 5.70% | 2.40% | 4.05% | 95.95% |

GM(1, 3) with P, NV | 5.54% | 2.58% | 4.06% | 95.94% |

GM(1, 2) with EC | 4.73% | 3.58% | 4.15% | 95.85% |

GM(1, 3) with G, EC | 4.97% | 3.38% | 4.17% | 95.83% |

GM(1, 3) with P, I | 5.77% | 2.60% | 4.18% | 95.82% |

GM(1, 2) with P | 5.77% | 2.60% | 4.19% | 95.82% |

GM(1, 4) with EC, NV, I | 6.09% | 2.91% | 4.50% | 95.50% |

GM(1, 5) with G, EC, NV, I | 7.70% | 1.45% | 4.58% | 95.42% |

GM(1, 4) with G, EC, NV | 4.29% | 7.65% | 5.97% | 94.03% |

GM(1, 3) with EC, NV | 9.52% | 6.60% | 8.06% | 91.94% |

GM(1, 3) with G, NV | 5.85% | 11.22% | 8.53% | 91.47% |

GM(1, 3) with G, I | 25.50% | 36.38% | 30.94% | 69.06% |

GM(1, 2) with G | 79.85% | 61.76% | 70.81% | 29.19% |

GM(1, 2) with I | 88.72% | 73.91% | 81.32% | 18.68% |

≤ 10% | 10%~20% | 20%~50% | > 50% | |
---|---|---|---|---|

Accuracy level | Highly accurate | Good | Reasonable | Inaccurate |

**Table 6.**Comparison of five forecast models trained with the data from 2000–2013 and tested with the data from 2014–2015.

Year | Real Value | Regression Forecast | Time Series Forecast | GP | Hybrid GM(1, 1) | Hybrid GM(1, 3) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Simulation | PE | Simulation | PE | Simulation | PE | Simulation | PE | Simulation | PE | ||

2001 | 21,304 | 22,350.4 | 4.91% | 22,907 | 7.52% | 18,842.86 | 13.06% | 21,726.23 | 4.6% | 19,046.65 | 4.5% |

2002 | 22,109 | 22,621.3 | 2.32% | 21,672 | 1.98% | 26,202.04 | 15.62% | 21,979.24 | 4.3% | 26,365.75 | 4.5% |

2003 | 23,068 | 22,892.2 | 0.76% | 22,040 | 4.46% | 25,144.92 | 8.26% | 22,757.94 | 1.7% | 25,305.06 | 4.0% |

2004 | 23,851 | 23,163.0 | 2.88% | 22,408 | 6.05% | 24,723.45 | 3.53% | 23,737.88 | 1.5% | 24,844.14 | 3.7% |

2005 | 24,520 | 23,433.9 | 4.43% | 22,776 | 7.11% | 24,437.15 | 0.34% | 24,370.46 | 3.1% | 24,519.58 | 0.0% |

2006 | 25,207 | 23,704.8 | 5.96% | 23,144 | 8.18% | 24,515.35 | 2.82% | 24,535.62 | 2.8% | 24,853.90 | 1.4% |

2007 | 25,587 | 23,975.7 | 6.30% | 23,512 | 8.11% | 24,867.04 | 2.90% | 25,125.12 | 4.1% | 25,425.72 | 0.6% |

2008 | 24,463 | 24,246.6 | 0.88% | 23,880 | 2.38% | 24,708.94 | 1.00% | 24,871.53 | 2.3% | 24,948.51 | 2.0% |

2009 | 23,218 | 24,517.4 | 5.60% | 24,248 | 4.44% | 24,651.85 | 5.82% | 23,615.23 | 4.0% | 25,195.36 | 2.5% |

2010 | 24,828 | 24,788.3 | 0.16% | 24,616 | 0.85% | 24,948.26 | 0.48% | 25,043.91 | 1.1% | 25,079.83 | 1.0% |

2011 | 25,345 | 25,059.2 | 1.13% | 24,984 | 1.42% | 24,819.81 | 2.12% | 25,435.47 | 1.7% | 24,892.17 | 1.8% |

2012 | 24,864 | 25,330.1 | 1.87% | 25,352 | 1.96% | 25,000.76 | 0.55% | 25,096.56 | 0.7% | 25,042.46 | 0.7% |

2013 | 24,911 | 25,601.0 | 2.77% | 25,720 | 3.25% | 25,147.65 | 0.94% | 24,901.87 | 2.4% | 25,188.18 | 1.1% |

MAPE | |||||||||||

(01-13) | 3.07% | 4.44% | 4.42% | 2.64% | 2.14% | ||||||

MAE | |||||||||||

(01-13) | 768.78 | 1067.38 | 1079.89 | 248.67 | 457.40 | ||||||

2014 | 25,104 | 25,871.8 | 3.06% | 26,088 | 3.92% | 25,378.75 | 1.08% | 25,050.47 | 2.8% | 25,453.16 | 1.4% |

2015 | 26,463 | 26,142.7 | 1.21% | 26,456 | 0.03% | 25,319.91 | 4.51% | 26,293.30 | 1.1% | 26,573.95 | 0.4% |

MAPE | |||||||||||

(14, 15) | 2.13% | 1.97% | 2.80% | 2.65% | 0.91% | ||||||

MAE | |||||||||||

(14, 15) | 544.54 | 1061.42 | 708.921 | 205.09 | 119.10 |

Population | GDP per Capita | Total Energy Consumption | Number of Registered Motor Vehicles | Amount Invested in China | |
---|---|---|---|---|---|

$\gamma \left({X}_{0},{X}_{i}\right)$ | 0.9476 | 0.8812 | 0.9303 | 0.8946 | 0.6166 |

**Table 8.**The mean error and accuracy rate of GM(1, N) model during the financial crisis (i.e., trained with the data from 2007–2010 and tested with the data in 2011).

Combination of Factors | Simulation Error | Forecast Error | Average Error | Average Accuracy |
---|---|---|---|---|

GM(1, 5) with P, EC, NV, I | 5.44% | 0.26% | 2.85% | 97.15% |

GM(1, 2) G | 4.84% | 1.02% | 2.93% | 97.07% |

GM(1, 3) G, NV | 5.27% | 0.61% | 2.94% | 97.06% |

GM(1, 3) G, I | 5.11% | 0.92% | 3.01% | 96.99% |

GM(1, 3) NV, I | 5.54% | 0.81% | 3.18% | 96.82% |

GM(1, 2) NV | 5.64% | 0.93% | 3.29% | 96.71% |

GM(1, 5) P, G, EC, NV | 6.20% | 0.49% | 3.34% | 96.66% |

GM(1, 3) P, G | 5.30% | 1.48% | 3.39% | 96.61% |

GM(1, 4) P, EC, I | 5.41% | 1.61% | 3.51% | 96.49% |

GM(1, 3) P, I | 5.43% | 1.67% | 3.55% | 96.45% |

GM(1, 4) P, G, EC | 5.52% | 1.98% | 3.75% | 96.25% |

GM(1, 5) P, G, EC, I | 6.95% | 0.57% | 3.76% | 96.24% |

GM(1, 3) P, NV | 5.98% | 1.74% | 3.86% | 96.14% |

GM(1, 4) P, G, I | 5.67% | 2.06% | 3.87% | 96.13% |

GM(1, 3) G, EC | 5.64% | 2.21% | 3.93% | 96.07% |

GM(1, 4) G, EC, I | 5.65% | 2.24% | 3.95% | 96.05% |

GM(1, 4) P, NV, I | 5.72% | 2.18% | 3.95% | 96.05% |

GM(1, 4) P, G, NV | 6.01% | 2.18% | 4.10% | 95.90% |

GM(1, 4) EC, NV, I | 5.75% | 2.47% | 4.11% | 95.89% |

GM(1, 4) G, EC, NV | 5.79% | 2.44% | 4.12% | 95.89% |

GM(1, 3) EC, NV | 5.86% | 2.53% | 4.19% | 95.81% |

GM(1, 4) P, EC, NV | 5.81% | 2.73% | 4.27% | 95.73% |

GM(1, 3) EC, I | 6.05% | 3.01% | 4.53% | 95.47% |

GM(1, 6) P, G, EC, NV, I | 6.98% | 2.83% | 4.90% | 95.10% |

GM(1, 2) P | 6.91% | 3.44% | 5.17% | 94.83% |

GM(1, 2) EC | 6.78% | 4.41% | 5.59% | 94.41% |

GM(1, 3) P, EC | 6.96% | 4.71% | 5.83% | 94.17% |

GM(1, 4) G, NV, I | 21.27% | 19.15% | 20.21% | 79.79% |

GM(1, 2) I | 34.1% | 36.51% | 35.31% | 64.69% |

GM(1, 5)G, EC, NV, I | 56.72% | 44.52% | 50.62% | 49.38% |

GM(1, 5) P, G, NV, I | 67.22% | 48.57% | 57.9% | 42.1% |

**Table 9.**Comprehensive comparison of forecast model trained with the data from 2007–2010 and tested with the data in 2011.

Year | Real Value | Regression Forecast | Time Series Forecast | GP | Hybrid GM(1, 1) | Hybrid GM(1, 5) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Simulation | PE | Simulation | PE | Simulation | PE | Simulation | PE | Simulation | PE | ||

2007 | 25,587 | 24,896.0 | 2.70% | 25,207 | 1.49% | 23,053.83 | 9.90% | 25,383.70 | 2.72% | 24,052.30 | 6.00% |

2008 | 24,463 | 24,815.1 | 1.44% | 25,967 | 6.15% | 22,609.25 | 7.58% | 24,609.06 | 0.37% | 23,354.61 | 4.53% |

2009 | 23,218 | 24,734.2 | 6.53% | 26,347 | 13.48% | 23,247.98 | 0.13% | 23,999.04 | 2.79% | 23,085.06 | 0.57% |

2010 | 24,828 | 24,653.3 | 0.70% | 26,727 | 7.65% | 25,085.03 | 1.04% | 24,943.91 | 1.09% | 24,927.84 | 0.40% |

MAPE | 2.84% | 7.19% | 4.66% | 1.74% | 2.88% | ||||||

(07-10) | |||||||||||

MAE | 592.80 | 1728.00 | 1168.48 | 250.25 | 602.46 | ||||||

(07-10) | |||||||||||

2011 | 25,345 | 24,572.4 | 3.05% | 27,107 | 6.95% | 25,437.31 | 0.36% | 25,614.84 | 3.86% | 25,350.54 | 0.02% |

MAPE | 3.05% | 6.95% | 0.36% | 3.86% | 0.02% | ||||||

MAE | 592.80 | 1762 | 92.31 | 951.03 | 5.54 |

Population | GDP per Capita | Energy Consumption | Number of Registered Motor Vehicles | Amount Invested in China | |
---|---|---|---|---|---|

$\gamma \left({X}_{0},{X}_{i}\right)$ | 0.9122 | 0.8052 | 0.9266 | 0.8847 | 0.5093 |

**Table 11.**Mean error and accuracy rate of the GM(1, N) model during the period when Taiwan businessmen were moving overseas (i.e., trained with the data from 2011–2013 and tested with the data in 2014).

Combination of Factors | Simulation Error | Forecast Error | Average Error | Average Accuracy |
---|---|---|---|---|

GM(1, 4) with P, NV, I | 3.77% | 0.49% | 2.13% | 97.87% |

GM(1, 4) with G, EC, I | 5.98% | 0.65% | 3.31% | 96.69% |

GM(1, 4) with P, EC, I | 6.58% | 0.63% | 3.60% | 96.40% |

GM(1, 3) with G, I | 6.34% | 1.04% | 3.69% | 96.31% |

GM(1, 4) with EC, NV, I | 5.77% | 1.88% | 3.82% | 96.18% |

GM(1, 3) with NV, I | 5.95% | 2.44% | 4.19% | 95.81% |

GM(1, 3) with P, I | 7.05% | 1.41% | 4.23% | 95.77% |

GM(1, 4) with G, NV, I | 6.18% | 2.40% | 4.29% | 95.71% |

GM(1, 2) with G | 6.11% | 2.61% | 4.36% | 95.64% |

GM(1, 5) with P, G, EC, I | 6.92% | 1.88% | 4.40% | 95.60% |

GM(1, 3) with EC, NV | 6.95% | 2.43% | 4.69% | 95.31% |

GM(1, 6) with P, G, EC, NV, I | 6.04% | 3.70% | 4.87% | 95.13% |

GM(1, 2) with P | 7.64% | 2.68% | 5.16% | 94.84% |

GM(1, 3) with P, EC | 7.62% | 2.71% | 5.17% | 94.83% |

GM(1, 2) with EC | 7.79% | 2.54% | 5.17% | 94.83% |

GM(1, 3) with G, NV | 7.90% | 2.89% | 5.39% | 94.61% |

GM(1, 3) with P, NV | 8.09% | 2.86% | 5.47% | 94.53% |

GM(1, 3) with EC, I | 8.01% | 2.99% | 5.50% | 94.50% |

GM(1, 2) with NV | 5.43% | 6.41% | 5.92% | 94.08% |

GM(1, 3) with G, EC | 5.52% | 7.96% | 6.74% | 93.26% |

GM(1, 4) with G, EC, NV | 11.52% | 5.43% | 8.47% | 91.53% |

GM(1, 3) with P, G | 11.76% | 5.74% | 8.75% | 91.25% |

GM(1, 4) with P, G, NV | 12.01% | 6.11% | 9.06% | 90.94% |

GM(1, 4) with P, G, EC | 12.63% | 6.41% | 9.52% | 90.48% |

GM(1, 4) with P, EC, NV | 13.26% | 7.96% | 10.61% | 89.39% |

GM(1, 4) with P, G, I | 19.80% | 23.29% | 21.54% | 78.46% |

GM(1, 5) with P, G, EC, NV | 30.91% | 25.59% | 28.25% | 71.75% |

GM(1, 5) with G, EC, NV, I | 22.65% | 42.80% | 32.73% | 67.27% |

GM(1, 5) with P, EC, NV, I | 55.70% | 91.88% | 73.79% | 26.21% |

GM(1, 5) with P, G, NV, I | 65.72% | 89.3% | 77.51% | 22.49% |

GM(1, 2) with I | 67.21% | 90.96% | 79.09% | 20.91% |

**Table 12.**Comprehensive comparison of forecast model trained with the data from 2011–2013 and tested with the data in 2014.

Year | Real Value | Regression Forecast | Time Series Forecast | GP | Hybrid GM(1, 1) | Hybrid GM(1, 4) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

Simulation | PE | Simulation | PE | Simulation | PE | Simulation | PE | Simulation | PE | ||

2011 | 25,345 | 25,286.8 | 1.85% | 25,011 | 0.74% | 23,783.27 | 6.16% | 25,512.63 | 2.9% | 24,626.80 | 2.8% |

2012 | 24,864 | 24,698.6 | 2.55% | 26,071 | 2.86% | 24,234.79 | 2.53% | 26,115.29 | 2.3% | 24,690.29 | 0.7% |

2013 | 24,911 | 25,510.4 | 2.60% | 25,862 | 4.01% | 25,559.53 | 2.60% | 25,441.51 | 0.9% | 25,893.21 | 3.9% |

MAPE | |||||||||||

(11-13) | 2.24% | 3.38% | 3.77% | 2.03% | 2.49% | ||||||

MAE | |||||||||||

(11-13) | 560.1 | 843.75 | 946.49 | 511.5 | 408.90 | ||||||

2014 | 25,104 | 25,934.0 | 3.31% | 26,896 | 7.14% | 25,227.71 | 0.49% | 26,588.1 | 2.3% | 25,257.58 | 0.6% |

MAPE | 3.31% | 7.14% | 0.49% | 2.3% | 0.61% | ||||||

MAE | 830 | 1792 | 123.71 | 598.43 | 153.58 |

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## Share and Cite

**MDPI and ACS Style**

Lin, C.-C.; He, R.-X.; Liu, W.-Y.
Considering Multiple Factors to Forecast CO_{2} Emissions: A Hybrid Multivariable Grey Forecasting and Genetic Programming Approach. *Energies* **2018**, *11*, 3432.
https://doi.org/10.3390/en11123432

**AMA Style**

Lin C-C, He R-X, Liu W-Y.
Considering Multiple Factors to Forecast CO_{2} Emissions: A Hybrid Multivariable Grey Forecasting and Genetic Programming Approach. *Energies*. 2018; 11(12):3432.
https://doi.org/10.3390/en11123432

**Chicago/Turabian Style**

Lin, Chun-Cheng, Rou-Xuan He, and Wan-Yu Liu.
2018. "Considering Multiple Factors to Forecast CO_{2} Emissions: A Hybrid Multivariable Grey Forecasting and Genetic Programming Approach" *Energies* 11, no. 12: 3432.
https://doi.org/10.3390/en11123432