# Performance Comparison of Predictive Methodologies for Carbon Emission Credit Price in the Korea Emission Trading System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Reviews

#### 2.1. Literature Reviews Relevant to the Prediction of Carbon Emission Credit

^{2}) [16]. Hao et al. (2020) reported the good predictive effectiveness of the developed model by comparing the predictive power of the developed hybrid model with individual predictive models,: general regression neural networks (GRNN), backpropagation neural network (BPNN), and Extreme Learning Machine WRELM (Weighted Regularized Extreme Learning Machine), with carbon price time-series data through a hybrid model based on feature selection and multi-objective optimization algorithm [31]. A previous study developed a weekly price prediction model for carbon credits using oil price data and derivatives. A hybrid prediction model based on bridge regression, ANN algorithm, and a genomic algorithm was constructed to predict and confirm the improved prediction of carbon emission [21]. The carbon trading price is irregular, complex, and influenced by many microscopic factors [16]. In the case of previous studies, however, the prediction model was influenced by a simple, specific index representing the market price, such as oil price and coal price. The Certified Emission Reduction (CER) with direct correlation through EUA and swap transaction was designated as a variable [17,28]. This study compared the predicted values through the predictive model and the explanatory power of the model through MAPE, R

^{2}, and RMSE, suggesting that the proposed model is effective, robust, and can predict carbon prices more accurately [16]. On the other hand, previous studies attempting to analyze and predict carbon emission credit data using time series data or simple price indicators did not include microscopic and macroscopic factors that affect the trading prices, such as market participant behavior. They also have a limitation on the diversity of variables used in the analysis [32]. Lamphiere et al. [33] suggested quite promising trend prediction results of the European Union Emissions Trading Scheme futures market based on data of the Intercontinental Exchange from 2005 to 2019. The study developed an indicator that can explain the short-term behavior of future behavior. The Fractal Market Hypothesis has been demonstrated to deduce the likelihood of the market becoming a bear or bull trend. Therefore, the proposed study attempted to consider the factors affecting the trading price by increasing the diversity of variables used in the analysis and using multiple variables considering the behavior of market participants. Recent studies reported that generalized autoregressive conditional heteroscedasticity (GARCH) models could be effective tools for understanding the behavior of data, such as the European carbon futures prices and the three fossil energy prices (coal, natural gas, and Brent oil) [34,35]. Zhang and Sun [34] conducted a study using GARCH models and compared the effects of different markets on each other, such as the coal, carbon, and natural gas markets. Wei and Can [35] integrated Empirical Mode Decomposition (EMD) with GARCH to forecast the carbon price. Wei and Can analyzed five different pilots and employed eight simulation scenarios. They suggested an alternative interval of the carbon price benchmark within the targeted boundary of 30 yuan/tCO

_{2}to 50 yuan/tCO

_{2}in China. Zhibin and Shan [36] employed Fractional Brownian Motion (FBM) and GARCH to predict the carbon option prices in China. The study stated that GARCH models could compensate for the lack of fixed FBM volatility. The study analyzed the European Energy Exchange option contracts for price prediction and employed GARCH to determine the return volatility to be used in FBM for forecasting prices for the next 60 days. Loperfido [37] indicated the problem of outlier detection in financial time series data and achieving maximal kurtosis, which is useful for outlier detection in multivariate datasets. The study showed that in GARCH models, the problem of kurtosis maximization is simplified to an ordinary eigenvalue problem. On the other hand, it also makes it very complicated when conducting multivariate GARCH analysis due to the extremely high number of parameters. Yun et al. [38] suggested a new hybrid model, NAGARCHSK-GRU, with better accuracy and robustness for forecasting carbon price than ordinal prediction models. Those recent studies illustrate a branch of the literature using GARCH and hybrid models for analyzing correlations and predicting carbon emission prices. Future studies should employ GARCH models for KAU analysis and comparisons with the method suggested in this paper. This study performed a prediction using search volume data as a variable considering the behavior of market participants and presented a carbon trading price model with high predictive power by reflecting the time lag on the independent variable.

#### 2.2. Search Queries-Based Prediction

## 3. Analysis Method

#### 3.1. Multiple Linear Regression Model

#### 3.2. Auto Regressive Integrated Moving Average

## 4. Data Collection

#### 4.1. Search Volume Data

#### 4.2. Trading Price Data

## 5. ETS Prediction Model

#### 5.1. ETS Multiple Linear Regression Model

#### 5.1.1. Variables Selection

#### 5.1.2. Model Derivation

^{2}without exceeding 10 VIF of all independent variables.

**Figure 3.**Nominal P-P plot of regression standardized residential of MRA1 (own creation): (

**a**) One-week time lag MRA model without verifying statistical significance; (

**b**) two-week time lag MRA model without verifying statistical significance; (

**c**) three-week time lag MRA model without verifying statistical significance; (

**d**) four-week time lag MRA model without verifying the statistical significance.

#### 5.2. Timeseries Analysis Using ARIMA

#### 5.2.1. Data Pre-Processing

#### 5.2.2. Time Lag for an Appropriate Prediction Model

#### 5.2.3. Model Derivation and Conformity Assessment

## 6. Results

^{2}representing the explanatory power of the derived MRA model, the prediction was attempted through the MRA model with the highest explanatory power for each analysis method, and the explanatory power of the MRA model for each time lag is shown in Table 15.

^{2}among the derived MRA models. Table 8 and Table 13 present the estimation results of each model. Table 17 lists the estimation results of the ARIMA(4,1,0) model showing the highest AIC value among the ARIMA models. Table 18 shows the results of actual trading price prediction through the ARIMA(4,1,0) model.

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**KAU trend (source: https://ets.krx.co.kr).

**Figure 4.**Nominal P-P plot of regression standardized residential of MRA2 (own creation): (

**a**) One-week time lag MRA model with statistically significant variables; (

**b**) two-week time lag MRA model with statistically significant variables; (

**c**) three-week time lag MRA model with statistically significant variables; (

**d**) four-week time lag MRA model with statistically significant variables.

**Figure 6.**ACF and PACF of the KAU data (own creation): (

**a**) Autocorrelation function of Korean Allowance Unit; (

**b**) Partial autocorrelation function of Korean Allowance Unit.

**Figure 7.**Conformity diagnosis of ARIMA model (own creation): (

**a**) Standardized residuals graph, ACF of residuals graph, significance probability graph of ARIMA(1,1,0); (

**b**) standardized residuals graph, ACF of residuals graph, significance probability graph of ARIMA(2,1,0); (

**c**) standardized residuals graph, ACF of residuals graph, significance probability graph of ARIMA(3,1,0); (

**d**) standardized residuals graph, ACF of residuals graph, significance probability graph of ARIMA(4,1,0).

Keywords | Mean | S.D | Minimum | Median | Maximum | Size |
---|---|---|---|---|---|---|

CET * | 108.7 | 41.0 | 38.5 | 109.1 | 198.9 | 37 |

FOOSUNG | 23,663.7 | 7092.7 | 11,293.8 | 22,554.5 | 45,426.4 | 37 |

CETS ** | 369.2 | 155.2 | 120.4 | 360.2 | 733.4 | 37 |

EAGON | 11,542.5 | 8320.6 | 3555.1 | 9609.5 | 42,022.2 | 37 |

Price of CERs | 54.0 | 44.5 | 0.0 | 43.8 | 213.6 | 37 |

HH *** | 11,809.8 | 5206.7 | 5330.9 | 10,853.0 | 27,770.4 | 37 |

UNISON | 16,969.4 | 4586.8 | 7856.3 | 16,120.1 | 34,258.3 | 37 |

HOMEDECO | 1176.7 | 218.6 | 863.2 | 1155.3 | 1935.6 | 37 |

HUCHEMS | 4862.7 | 1144.5 | 2336.9 | 4692.9 | 7703.0 | 37 |

productive | 1675.0 | 520.4 | 973.7 | 1470.6 | 2869.6 | 37 |

productivity | 1425.9 | 342.9 | 798.2 | 1370.5 | 2507.4 | 37 |

compare | 1820.6 | 436.7 | 1285.7 | 1771.3 | 3289.3 | 37 |

excavator | 855.6 | 80.4 | 709.1 | 861.1 | 1083.3 | 37 |

emissions | 766.4 | 194.6 | 445.2 | 750.6 | 1201.0 | 37 |

CO_{2} emissions | 14.0 | 13.5 | 0.0 | 9.6 | 55.7 | 37 |

GW **** | 280.1 | 53.5 | 155.4 | 287.7 | 370.5 | 37 |

NOx | 4087.3 | 755.7 | 3007.9 | 3991.2 | 6967.7 | 37 |

PEMS | 168.9 | 163.1 | 0.0 | 122.3 | 914.0 | 37 |

durable | 2100.4 | 475.3 | 1150.9 | 2075.8 | 3443.7 | 37 |

furniture | 3026.7 | 536.9 | 1906.2 | 2902.2 | 4546.0 | 37 |

wakefulness | 83.7 | 51.2 | 12.6 | 70.7 | 222.1 | 37 |

**Table 2.**KAU data basic statistics (source: https://ets.krx.co.kr).

Data | Mean | Standard Deviation | Minimum | Median | Maximum | Size |
---|---|---|---|---|---|---|

KAU | 23,931.081 | 1770.136 | 21,600 | 24,000 | 27,050 | 37 |

Variable | Week 1 | Week 2 | Week 3 | Week 4 |
---|---|---|---|---|

CET * | −0.149 | −0.211 | −0.247 | −0.363 |

FOOSUNG | −0.39 | −0.417 | −0.493 | −0.532 |

CETS ** | −0.317 | −0.316 | −0.341 | −0.384 |

EAGON | −0.368 | −0.346 | −0.359 | −0.374 |

Price of CER | −0.313 | −0.356 | −0.465 | −0.507 |

HANSOLHOMEDECO | −0.469 | −0.419 | −0.433 | −0.456 |

UNISON | −0.191 | −0.146 | −0.213 | −0.223 |

HOMEDECO | 0.578 | 0.623 | 0.666 | 0.702 |

HUCHEMS | 0.166 | 0.183 | 0.066 | 0.075 |

productive | 0.656 | 0.671 | 0.663 | 0.635 |

productivity | 0.399 | 0.458 | 0.47 | 0.462 |

Compare | 0.536 | 0.503 | 0.459 | 0.464 |

Excavator | −0.444 | −0.218 | −0.215 | −0.319 |

emissions | 0.468 | 0.537 | 0.529 | 0.548 |

CO_{2} emissions | 0.14 | 0.112 | 0.097 | −0.022 |

global warming | −0.161 | −0.101 | −0.067 | 0.02 |

NOx | −0.08 | 0.025 | 0.102 | 0.168 |

PEMS | −0.089 | −0.017 | −0.037 | −0.02 |

durable | 0.513 | 0.499 | 0.464 | 0.387 |

furniture | 0.285 | 0.314 | 0.334 | 0.348 |

wakefulness | 0.582 | 0.543 | 0.5 | 0.482 |

Time Gap | Search Queries |
---|---|

Week 1 | HOMEDECO, productive, compare, durable, wakefulness |

Week 2 | HOMEDECO, productive, compare, emissions, wakefulness |

Week 3 | HOMEDECO, productive, emissions, wakefulness |

Week 4 | FOOSUNG, price of CER, HOMEDECO, productive, emissions |

Variable | Coefficient | S.E | t | Pr | VIF | adj-R^{2} | D.W. | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

HOMEDECO | 2.934 | 0.363 | 0.728 | 4.028 | 0.000 | 1.125 | 0.740 | 1.395 |

productive | 2.113 | 0.622 | 0.418 | 5.057 | 0.000 | 2.092 | ||

compare | 1.960 | 0.475 | 0.645 | 3.036 | 0.005 | 3.386 | ||

durable | −1.693 | −0.453 | 0.688 | −2.461 | 0.020 | 4.687 | ||

wakefulness | 8.256 | 0.233 | 3.892 | 2.121 | 0.042 | 1.671 | ||

(Constant) | 16,306.254 | - | 1062.465 | 15.348 | 0.000 | - |

^{2}: adjusted R

^{2}; D.W.: Durbin Watson.

Variable | Coefficient | S.E | t | Pr | VIF | adj-R^{2} | D.W. | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

HOMEDECO | 3.505 | 0.435 | 0.832 | 4.211 | 0.000 | 1.271 | 0.698 | 1.281 |

productive | 1.545 | 0.455 | 0.380 | 4.064 | 0.000 | 1.491 | ||

emissions | −0.035 | −0.004 | 1.074 | −0.033 | 0.974 | 1.665 | ||

compare | 0.821 | 0.184 | 0.491 | 1.672 | 0.105 | 1.446 | ||

wakefulness | 5.259 | 0.135 | 4.412 | 1.192 | 0.242 | 1.522 | ||

(Constant) | 15,428.686 | - | 1124.782 | 13.717 | 0.000 | - |

^{2}: adjusted R

^{2}; D.W.: Durbin Watson.

Variable | Coefficient | S.E | t | Pr | VIF | adj-R^{2} | D.W. | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

HOMEDECO | 3.958 | 0.492 | 0.854 | 4.635 | 0.000 | 1.306 | 0.698 | 1.281 |

productive | 1.658 | 0.489 | 0.381 | 4.350 | 0.000 | 1.465 | ||

emissions | 0.138 | 0.015 | 1.075 | 0.129 | 0.898 | 1.620 | ||

wakefulness | 5.254 | 0.128 | 4.362 | 1.205 | 0.237 | 1.310 | ||

(Constant) | 16,093.189 | - | 980.468 | 16.414 | 0.000 | - |

^{2}: adjusted R

^{2}; D.W.: Durbin Watson.

Variable | Coefficient | S.E | t | Pr | VIF | adj-R^{2} | D.W. | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

HOMEDECO | 2.415 | 0.302 | 4.068 | −0.797 | 0.434 | 2.322 | 0.822 | 1.561 |

productive | 1.758 | 0.508 | 0.030 | −2.867 | 0.009 | 4.460 | ||

emissions | 1.210 | 0.133 | 1.756 | −0.298 | 0.769 | 6.302 | ||

FOOSUNG | −0.085 | −0.408 | 0.018 | 1.150 | 0.261 | 1.963 | ||

price of CER | −1.441 | 0.043 | 4.353 | 0.194 | 0.848 | 3.613 | ||

(Constant) | 19,590.524 | - | 1098.553 | 17.833 | 0.000 | - |

^{2}: adjusted ${\mathrm{R}}^{2}$; D.W.: Durbin Watson.

Time Gap | Search Queries |
---|---|

Week 1 | productive, HOMEDECO, wakefulness |

Week 2 | productive, HOMEDECO, compare |

Week 3 | HOMDECO, productive |

Week 4 | HOMEDECO, productive, FOOSUNG |

Variable | Coefficient | S.E | t | Pr | VIF | $\mathbf{adj}-{\mathbf{R}}^{2}$ | D.W. | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

productive | 1.562 | 0.460 | 0.344 | 4.543 | 0.000 | 1.158 | 0.682 | 1.262 |

HOMEDECO | 3.098 | 0.384 | 0.800 | 3.874 | 0.000 | 1.109 | ||

wakefulness | 11.264 | 0.318 | 3.631 | 3.102 | 0.004 | 1.189 | ||

(Constant) | 16,774.013 | - | 972.621 | 17.246 | 0.000 | - |

Variable | Coefficient | S.E | t | Pr | VIF | $\mathbf{adj}-{\mathbf{R}}^{2}$ | D.W. | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

HOMEDECO | 2.658 | 0.333 | 0.689 | 3.861 | 0.000 | 1.499 | 0.703 | 1.281 |

productive | 2.030 | 0.587 | 0.264 | 7.696 | 0.000 | 1.174 | ||

FOOSUNG | −0.090 | −0.434 | 0.017 | −5.211 | 0.000 | 1.398 | ||

(Constant) | 19,825.066 | - | 1023.652 | 19.367 | 0.000 | - |

Variable | Coefficient | S.E | t | Pr | VIF | $\mathbf{adj}-{\mathbf{R}}^{2}$ | D.W | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

HOMEDECO | 4.318 | 0.537 | 0.765 | 5.643 | 0.000 | 1.063 | 0.694 | 1.064 |

productive | 1.806 | 0.533 | 0.322 | 5.602 | 0.000 | 1.063 | ||

(Constant) | 15,901.400 | - | 938.182 | 16.949 | 0.000 | - |

Variable | Coefficient | S.E | t | Pr | VIF | $\mathbf{adj}-{\mathbf{R}}^{2}$ | D.W | |
---|---|---|---|---|---|---|---|---|

U | S | |||||||

HOMEDECO | 2.658 | 0.333 | 0.689 | 3.861 | 0.000 | 1.499 | 0.822 | 1.608 |

productive | 2.030 | 0.587 | 0.264 | 7.696 | 0.000 | 1.174 | ||

FOOSUNG | −0.090 | −0.434 | 0.017 | −5.211 | 0.000 | 1.398 | ||

(Constant) | 19,825.066 | - | 1023.652 | 19.367 | 0.000 | - |

Dependent Variable | Variable | First Difference | ||
---|---|---|---|---|

t-Statistic | Pr | t-Statistic | Pr | |

KAU | –2.9167 | 0.2158 | –3.8459 | 0.02834 |

Model | Week 1 | Week 2 | Week 3 | Week 4 |
---|---|---|---|---|

MRA 1 | 0.740 | 0.698 | 0.689 | 0.822 |

MRA 2 | 0.682 | 0.703 | 0.694 | 0.822 |

Model | ARIMA(1,1,0) | ARIMA(2,1,0) | ARIMA(3,1,0) | ARIMA(4,1,0) |
---|---|---|---|---|

AIC | −183.93 | −182.11 | −183.2 | −184.09 |

Variable | Coefficient | Standard Error | z | Pr |
---|---|---|---|---|

(Constant) | 0.0007 | 0.0063 | 0.1144 | 0.9089 |

AR(1) | −0.5192 | 0.1560 | −3.3269 | 0.0008 |

AR(2) | 0.2080 | 0.1731 | 1.2018 | 0.2294 |

AR(3) | 0.5824 | 0.1857 | 3.1358 | 0.0017 |

AR(4) | 0.3191 | 0.1725 | 1.8498 | 0.0643 |

AIC | −184.09 | |||

Log-likelihood | 98.05 |

Dependent Variable | MRA | Time Series | |
---|---|---|---|

Time Lag: Week 4 (MRA1) | Time Lag: Week 4 (MRA2) | ARIMA(4,1,0) | |

Predicted Price (KRW/ton) | 25,702.69 | 25,819.75 | 26,579.88 |

Actual Price (KRW/ton) | 26,550 | 26,550 | 26,550 |

MAPE | 3.19 | 2.75 | 0.11 |

MAE | 847.31 | 730.25 | 29.88 |

Time Lag: Week 4 (MRA1) | Time Lag: Week 4 (MRA2) | ARIMA(4,1,0) | |
---|---|---|---|

MAPE | 7.31 | 7.14 | 0.99 |

Inbound | Outbound | |||||
---|---|---|---|---|---|---|

MRA1 | MRA2 | ARIMA(4,1,0) | MRA1 | MRA2 | ARIMA(4,1,0) | |

MAPE | 2.11 | 2.39 | 1.07 | 6.49 | 7.14 | 0.99 |

MAE | 509.37 | 583.89 | 261.27 | 1756.25 | 1927.99 | 269.07 |

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## Share and Cite

**MDPI and ACS Style**

Kim, H.; Kim, Y.; Ko, Y.; Han, S.
Performance Comparison of Predictive Methodologies for Carbon Emission Credit Price in the Korea Emission Trading System. *Sustainability* **2022**, *14*, 8177.
https://doi.org/10.3390/su14138177

**AMA Style**

Kim H, Kim Y, Ko Y, Han S.
Performance Comparison of Predictive Methodologies for Carbon Emission Credit Price in the Korea Emission Trading System. *Sustainability*. 2022; 14(13):8177.
https://doi.org/10.3390/su14138177

**Chicago/Turabian Style**

Kim, Hyeonho, Yujin Kim, Yongho Ko, and Seungwoo Han.
2022. "Performance Comparison of Predictive Methodologies for Carbon Emission Credit Price in the Korea Emission Trading System" *Sustainability* 14, no. 13: 8177.
https://doi.org/10.3390/su14138177