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In the present paper, different Autoregressive Integrated Moving Average (ARIMA) models were developed to model the carbon dioxide emission by using time series data of forty-four years from 1972-2015. The performance of these developed models was assessed with the help of different selection measure criteria and the model having minimum value of these criteria considered as the best forecasting model. Based on findings, it has been observed that out of different ARIMA models, ARIMA (0, 2, 1) is the best fitted model in predicting the emission of carbon dioxide in Bangladesh. Using this best fitted model, the forecasted value of carbon dioxide emission in Bangladesh, for the year 2016, 2017 and 2018 as obtained from ARIMA (0, 2, 1) was obtained as 83.94657 Metric Tons, 89.90464 Metric Tons and 96.28557 Metric Tons respectively.

Generally, emission of carbon dioxide (CO_{2}) from living animals, humans, wetlands, volcanoes, and other sources is nearly balanced by the same amount being removed from the atmosphere by plant photosynthesis and by the oceans. Human activity is disturbing this equilibrium by generating increased CO_{2} from fossil fuels like as coal, gas, and petroleum products; and combustion via electricity generation, transportation, industry, and domestic use. The results of these imbalances are believed to be greenhouse effects: global warming, melting of polar ice sheets and caps, a rise in sea levels and subsequent coastal inundations, and damage to agriculture and natural ecosystems, among others. There is an increasing trend of greenhouse gas (GHG) emissions worldwide due to human activities, which indicates a substantial increase in atmospheric concentrations of carbon dioxide (CO_{2}), methane (CH_{4}), nitrous oxide (N_{2}O), hydrofluoro- carbons (HFCs), perfluorocarbons (PFCs) and sulphur hexafluoride (SF_{6}) (EPA, 2014) [_{4}, N_{2}O and other gases contributed 14%, 8% and 1% respectively.

Climate change as a result of global warming has become one of the most important issues in the recent years. Reddy et al. (1995) shows that global mean temperature will also rise to 3˚C - 4˚C with doubling of the CO_{2} concentration [

The developed countries have a much higher share in global emissions than the developing ones. Nakicenovic (1994) [_{2} concentration due to their past consumption of fossil energy. The developed countries have a much higher share in global emissions than the developing ones. In Bangladesh, the power sector alone contributes 40% of the total CO_{2} emissions [_{2} emission found 6.7% per year which is higher than the growth of GDP and energy consumption in Bangladesh [

In the present study, time series secondary data on carbon dioxide emissions in Bangladesh were considered for the period 1972 to 2015 from Boden et al. (2016), UNFCCC (2016), BP (2016) [

ARIMA is one of the most traditional methods of non-stationary time series analysis. In contrast to the regression models, the ARIMA model allows time series to be explained by its past or lagged values and stochastic error terms. The models developed by this approach are usually called ARIMA models because they use a combination of autoregressive (AR), integration (I) - referring to the reverse process of differencing to produce the forecast and moving average (MA) operations [

The ARIMA model is denoted by ARIMA ( p , d , q ) , where “p” stands for the order of the auto regressive process, “d” is the order of the data stationary and “q” is the order of the moving average process. The general form of the ARIMA ( p , d , q ) can be written as [

Δ d y t = δ + θ 1 Δ d y t − 1 + θ 2 Δ d y t − 2 + ⋅ ⋅ ⋅ + θ p y t − p + e t − 1 α e t − 1 − α 2 e t − 2 α q e t − 2 (1)

where, Δ d denotes differencing of order d, i.e., Δ y t = y t − y t − 1 , Δ 2 y t = Δ y t − Δ y t − 1 and so forth, y t − 1 , ⋅ ⋅ ⋅ , y t − p are past observations (lags), δ , θ 1 , ⋅ ⋅ ⋅ , θ p are parameters (constant and coefficient) to be estimated similar to regression coefficients of the Auto Regressive process (AR) of order “p” denoted by AR (p) and is written as,

Y = δ + θ 1 y t − 1 + θ 2 y t − 2 + ⋅ ⋅ ⋅ + θ p y t − p + e t (2)

where, e t is forecast error, assumed to be independently distributed across time with mean θ and variance θ 2 e , e t − 1 , e t − 2 , ⋅ ⋅ ⋅ , e t − q are past forecast errors, α 1 , ⋅ ⋅ ⋅ , α q are moving average (MA) coefficient. While MA model of order q (i.e.) MA (q) can be written as,

Y t = e t − α 1 α t − 1 − α 2 e t − 2 − ⋅ ⋅ ⋅ − α q e t − q (3)

Seasonal ARIMA model is to denoted by ARIMA (p, d, q) (P, D, Q), where P denotes the number of seasonal autoregressive components, Q denotes the number of seasonal moving average terms and D denotes the number of seasonal differences required to induce stationarity [

a) Identifying a model;

b) Estimating the parameters of the model;

c) Diagnostic checking.

In the present paper, time series yearly data on emissions of carbon dioxide in Bangladesh were considered so there is no seasonal variation in the data which means non-seasonal ARIMA (p, d, q) models are applicable only. Comparison among family of different parametric combination of ARIMA (p, d, q) was done on the basis of minimum value of selection criteria which are Root mean squared error (RMSE), Mean percentage error (MPE), Mean absolute percentage error (MAPE), Mean absolute error (MAE), Maximum absolute percentage error (MAPE), Maximum absolute standard error (MASE) and Bayesian information criteria (BIC) [

In

After making the series stationary, different parametric combinations of ARIMA (p, d, q) model were tried to analyze the forty-four-year data (1972 to 2015) of carbon dioxide emission and the best fitted model is accepted on the basis of minimum value of all selection criteria as mentioned above in methodology. The results of performance of developed ARIMA (p, d, q) model is presented in

Therefore, it was concluded that the appropriate model for forecasting the carbon dioxide emission in Bangladesh during 2015 was ARIMA (0, 2, 1) having minimum value of all selection criteria as compared to remaining nineteen models.

ARIMA (0, 2, 1) was obtained as 83.94657 Metric Tons, 89.90464 Metric Tons and 96.28557 Metric Tons with Upper emission limit (UEL) and Lower emission limit (LEL) are 92.21431 Metric Tons and 75.96045 Metric Tons, 98.72545 Metric Tons and 81.13923 Metric Tons, 105.90164 Metric Tons and 87.02782 Metric Tons respectively.

Models | Model Selection Criteria | ||||||
---|---|---|---|---|---|---|---|

RMSE | MAE | MPE | MAPE | MASE | AIC | BIC | |

ARIMA (0, 1, 0) | 2.3425 | 1.7402 | 6.6104 | 7.1229 | 0.9773 | 198.22 | 199.98 |

ARIMA (0, 1, 1) | 1.9891 | 1.4639 | 4.7313 | 6.5207 | 0.8221 | 186.35 | 189.88 |

ARIMA (0, 1, 2) | 1.5460 | 1.1544 | 3.1398 | 5.6675 | 0.6483 | 168.01 | 173.29 |

ARIMA (0, 1, 3) | 1.4824 | 1.1296 | 2.5420 | 5.6682 | 0.6344 | 166.91 | 173.96 |

ARIMA (1, 1, 0) | 1.5956 | 1.2749 | 1.8421 | 6.2357 | 0.7159 | 168.03 | 171.55 |

ARIMA (1, 1, 2) | 1.4660 | 1.14591 | 2.1419 | 5.8150 | 0.6435 | 165.74 | 171.55 |

ARIMA (2, 1, 0) | 1.4060 | 1.1035 | 1.1014 | 5.4728 | 0.6197 | 159.71 | 164.99 |

ARIMA (2, 1, 1) | 1.4021 | 1.1024 | 1.1528 | 5.5165 | 0.6191 | 161.5 | 168.55 |

ARIMA (2, 1, 2) | 1.3333 | 0.9679 | 1.0146 | 4.8551 | 0.5436 | 159.86 | 168.67 |

ARIMA (2, 1, 3) | 1.2603 | 0.9817 | 0.8985 | 5.1329 | 0.5513 | 157.32 | 167.88 |

ARIMA (0, 2, 0) | 1.6744 | 1.3174 | -0.0317 | 6.3415 | 0.7398 | 166.44 | 168.18 |

ARIMA (0, 2, 1) | 1.3216 | 0.9600 | 0.4590 | 4.6932 | 0.5391 | 149.42 | 152.9 |

ARIMA (0, 2, 2) | 1.3212 | 0.9558 | 0.4602 | 4.6698 | 0.5368 | 151.41 | 156.62 |

ARIMA (0, 2, 3) | 1.2666 | 1.0051 | 0.3100 | 5.1614 | 0.5644 | 150.1 | 157.05 |

ARIMA (1, 2, 0) | 1.4139 | 1.1248 | 0.0158 | 5.4194 | 0.6317 | 154.57 | 158.05 |

ARIMA (1, 2, 1) | 1.3211 | 0.9547 | 0.4604 | 4.6638 | 0.5361 | 151.41 | 156.62 |

ARIMA (1, 2, 2) | 1.3079 | 0.9478 | 0.4499 | 4.5701 | 0.5323 | 152.59 | 159.54 |

ARIMA (1, 2, 3) | 1.2481 | 0.9741 | 0.3619 | 4.9698 | 0.5470 | 150.78 | 159.47 |

ARIMA (2, 2, 1) | 1.3140 | 0.9719 | 0.4336 | 4.7371 | 0.5458 | 152.9 | 159.85 |

ARIMA (2, 2, 3) | 1.1497 | 0.9081 | 0.3649 | 4.6018 | 0.5101 | 149.43 | 159.85 |

Year | Forecast | LEL* | UEL* |
---|---|---|---|

2016 | 83.94657 | 75.96045 | 92.21432 |

2017 | 89.90464 | 81.13923 | 98.72545 |

2018 | 96.28557 | 87.02782 | 105.90164 |

*95% confidence interval.

This paper aimed to model the emission of carbon dioxide during 2015 in Bangladesh, by Autoregressive Integrated Moving Average (ARIMA) approach. On basis of results obtained, it is concluded that ARIMA (0, 2, 1) model having minimum value of all measures of selection criteria was found to be the appropriate model amongst all for predicting the carbon dioxide emission in Bangladesh. The model showed a good performance in case of explaining variability in the data series and, it’s predicting ability. Using the model ARIMA (0, 2, 1) we obtained the emission as 83.94657 Metric Tons, 89.90464 Metric Tons and 96.28557 Metric Tons in the year 2016, 2017 and 2018. However, the forecasting of carbon dioxide can help the government of Bangladesh and world leaders as well as the policy makers for taking the appropriate plan for reducing the future emission of carbon dioxide in Bangladesh.

We would like to acknowledge Md. Ahmed Kabir Chowdhury, Professor, Department of Statistics, Shahjalal University of Science & Technology, Sylhet, Bangladesh.

The authors declare no conflict of interest.

Rahman, A. and Hasan, M.M. (2017) Modeling and Forecasting of Carbon Dioxide Emissions in Bangladesh Using Autoregressive Integrated Moving Average (ARIMA) Models. Open Journal of Statistics, 7, 560-566. https://doi.org/10.4236/ojs.2017.74038