Precise prediction of carbon prices is not only of significance for policy formulation and investment decisions, but also helpful to the carbon finance market development. Considering the non-stationary and nonlinearity characteristics inherent in the carbon price, this study proposed a novel hybrid model named ICEEMDAN-TGARCH/LSTM(CS)-LSTM(CS), in which the ICEEMDAN (improved complete ensemble empirical mode decomposition with adaptive noise) is applied to decompose the carbon price original series into several subcomponents, then the subcomponents are identified according to comprehensive contribution index (CCI) and divided into short-term, long-term and trend components. TGARCH(threshold generalized auto-regressive conditional heteroscedasticity) is chosen for the short-term components forecasting, while LSTM (long-short term memory) neural network model with hyper-parameters optimized by cuckoo search (CS) algorithm is selected to forecast other components and combine all the forecasting sequences. The empirical results Hubei carbon emission trading market indicated that the proposed model outperformed other benchmark models with the lowest prediction error, meaning that the hybrid model proposed by us can be an effective and accurate tool for carbon price forecasting. It provides effective information for regulatory authorities and enterprises to make decisions.
表3 MR2分量和R分量的输入变量 Table 3 Input variables of the component MR2 and R
表4非线性集成方法预测的4个评价指标 Table 4 Four evaluation indicators of nonlinear ensemble method
MAPE/%
RMSE
MAE
TIC/%
0.715 71
0.264 33
0.212 53
0.444 47
表4 非线性集成方法预测的4个评价指标 Table 4 Four evaluation indicators of nonlinear ensemble method
图7 非线性集成方法的碳价格预测结果 Fig.7 Carbon price forecasting result of nonlinear ensemble method
表5模型预测效果对比 Table 5 Four evaluation criteria of the various methods
比较项目
MAPE/%
RMSE
MAE
TIC/%
(1) BP
3.344 47
1.466 44
1.028 19
2.467 27
(2) RNN
2.946 66
1.439 96
0.895 82
2.423 77
(3) GRU
2.882 17
1.431 47
0.895 95
2.414 7
(4) LSTM
2.837 34
1.405 34
0.885 17
2.375 87
(5) LSTM(CS)
1.777 82
0.618 99
0.534 24
1.052 37
(6) ICEEMDAN-TGARCH/ LSTM(CS)-LSTM(CS)
0.715 71
0.264 33
0.212 53
0.444 47
(7) ICEEMDAN-GARCH/ LSTM(CS)-LSTM(CS)
0.822 8
0.332 66
0.250 2
0.563 1
(8) ICEEMDAN-LSTM(CS)-LSTM(CS)
0.907 64
0.447 56
0.279 85
0.756 01
(9) ICEEMDAN-TGARCH/ LSTM(CS)-
0.764 95
0.328 79
0.235 56
0.555 44
(10) ICEEMDAN-GARCH/ LSTM(CS)-
0.810 07
0.352 45
0.249 48
0.595 39
(11) ICEEMDAN-LSTM(CS)-
1.118 44
0.460 01
0.336 09
0.774 52
(12) EMD-LSTM(CS)-
1.294 15
0.636 41
0.401 09
1.073 85
(13) EEMD-LSTM(CS)-
1.205 28
0.495 24
0.367 72
0.838 74
(14) CEEMDAN-LSTM(CS)-
1.131 39
0.464 66
0.343 09
0.787 24
(15) ICEEMDAN-TGARCH/LSTM-LSTM
0.802 61
0.320 23
0.244 33
0.539 69
(16) ICEEMDAN-GARCH/LSTM-LSTM
0.832 55
0.342 38
0.254 2
0.577 09
(17) ICEEMDAN-LSTM-LSTM
1.706 82
0.621 73
0.508 34
1.044 1
表5 模型预测效果对比 Table 5 Four evaluation criteria of the various methods
图8 各种方法的预测结果 Fig.8 Forecasting results of the various methods
图9 采用不同方法的预测模型的4个评价指标结果(MAPE、RMSE、MAE、TIC) Fig.9 Four different evaluation criteria of different methods
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