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Preprocessing and postprocessing strategies comparisons: case study of forecasting the carbon price in China

  • Soft Computing in Decision Making and in Modeling in Economics
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Abstract

The accurate carbon price prediction is of significance to decrease investment risks, make scientific decisions and improve production efficiency. As matters stand, most studies focusing on carbon price prediction are following the preprocessing models, while the postprocessing models based on the error correction are rarely applied. To enhance the forecasting robustness and provide a relatively comprehensive comparison between the preprocessing and postprocessing model, this research proposes a novel hybrid model KELM-VMD-KELM by combining variational mode decomposition (VMD) and the kernel-based extreme learning machine (KELM), in which the KELM is firstly employed to forecast the daily carbon price series and obtain the initial prediction results, and then the VMD-KELM is utilized to build the predicting models for the residual error series to implement the process of error correction. The particle swarm optimization (PSO) algorithm is made a use to determine the optimal parameters of KELM and VMD. The daily average carbon price from Beijing, Guangdong and Shanghai market are selected to test the validity of the model. The results indicate that there is heterogeneity of the optimal model in different datasets. Both KELM-VMD-KELM and VMD-KELM perform well in the daily carbon price prediction. The postprocessing model can guarantee a high stability in different datasets.

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Data availability

Enquiries about data availability should be directed to the authors.

Notes

  1. We omit PSO in the abbreviation of KELM-VMD-KELM model to avoid too long of the model. But in KELM-VMD-KELM, PSO is employed to learn the parameters in both KELM and VMD.

Abbreviations

VMD:

Variational mode decomposition

KELM:

Kernel-based extreme learning machine

PSO:

Particle swarm optimization

IMF:

Intrinsic mode function

MAE:

Mean absolute error

RMSE:

Root mean square error

MAPE:

Mean absolute percentage error

U1:

Theil U statistic 1

MASE:

Mean absolute scaled error

IA:

Index of agreement

D stat :

Directional statistic

BPNN:

Back propagation neural network

ELM:

Extreme learning machine

EEMD:

Ensemble empirical mode decomposition

LSTM:

Long short-term memory

PSO-KELM:

Kernel-based extreme learning machine optimized by particle swarm optimization

DM:

Diebold-Mariano

PT:

Pesaran and Timmermann

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Acknowledgements

The work was partially supported by the Fundamental Research Funds for the Central Universities (No. FRF-BR-20-04B).

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The authors have not disclosed any funding.

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Authors and Affiliations

  1. School of Economics and Management, University of Science and Technology Beijing, Beijing, 100083, China

    Kunliang Xu & Hongli Niu

Authors
  1. Kunliang Xu
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  2. Hongli Niu
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Contributions

K.X.: Writing original draft, Data curation, Methodology, Investigation. H.N.: Conceptualization, Supervision, Writing-review & editing, Methodology, Project administration.

Corresponding author

Correspondence to Hongli Niu.

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Appendices

Appendix 1

The DM test results of different models in one-step-ahead prediction (See Tables

Table 9 The DM test results of different models in one-step-ahead prediction for Beijing market
Full size table

9,

Table 10 The DM test results of different models in one-step-ahead prediction for Guangdong market
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10 and

Table 11 The DM test results of different models in one-step-ahead prediction for Shanghai market
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11).

Appendix 2

The PT test results of different models in one-step-ahead prediction (See Table

Table 12 The PT test results of different models in one-step-ahead prediction for the three markets
Full size table

12).

Appendix 3

The DM test results of different models in multi-step-ahead prediction (See Table

Table 13 The DM test results of different models in multi-step-ahead prediction for the three markets
Full size table

13).

Appendix 4

The PT test results of different models in multi-step-ahead prediction (See Table

Table 14 The PT test results of different models in multi-step-ahead prediction for the three markets
Full size table

14).

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Xu, K., Niu, H. Preprocessing and postprocessing strategies comparisons: case study of forecasting the carbon price in China. Soft Comput 27, 4891–4915 (2023). https://doi.org/10.1007/s00500-022-07690-9

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