【免费】一种创新的基于随机森林的非线性集成范式，用于碳价格预测的改进特征提取和深度学习1

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An innovative random forest-based nonlinear ensemble paradigm of

improved feature extraction and deep learning for carbon

price forecasting

Jujie Wang

a,b,

⁎

,XinSun

,QianCheng

,QuanCui

School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China

HIGHLIGHTS

• Propose a new model based on nonsta-

tionary and nonlinear data: CEEMDAN-

SE-LATM-RF

• The efﬁcacy was tested in different car-

bon trading markets in China.

• Proposed model outperformed the

other 4 benchmark methods.

• Improved feature extraction heightens

the forecast accuracy.

• Nonlinear ensemble model repre-

sents better generalization ability for

robustness.

GRAPHICAL ABSTRACT

abstractarticle info

Article history:

Received 19 July 2020

Received in revised form 4 October 2020

Accepted 11 October 2020

Available online 16 October 2020

Editor: Kuishuang Feng

Keywords:

Carbon price prediction

Hybrid model

Improved feature extraction

Long short-term memory network

Nonlinear ensemble algorithm

Random forest

Carbon price is the basis of developing a low carbon economy. The accurate carbon price forecast can not only

stimulate the actions of enterprises and families, but also encourage the study and development of low carbon

technology. However, as the original carbon price series is non-stationary and nonlinear, traditional methods

are less robust to predict it. In this study, an innovative nonlinear ensemble paradigm of improved feature extrac-

tion and deep learning algorithm is proposed for carbon price forecasting, which includes complete ensemble

empirical mode decomposition (CEEMDAN), sample entropy (SE), long short-term memory (LSTM) and random

forest (RF). As the core of the proposed model, LSTM enhanced from the recurrent neural network is utilized to

establish appropriate prediction models by extracting memory features of the long and short term. Improved fea-

ture extraction, as assistant data preprocessing, represents its unique advantage for improving calculating efﬁ-

ciency and accuracy. Removing irrelevant features from original time series through CEEMDAN lets learning

easier and it's even better for using SE to recombine similar-complexity modes. Furthermore, compared with

simple linear ensemble learning, RF increases the generalization ability for robustness to achieve the ﬁnal nonlin-

ear output results. Two markets' real data of carbon trading in china are as the experiment cases to test the effec-

tiveness of the above model. The ﬁnal simulation results indicate that the proposed model performs better than

Science of the Total Environment 762 (2021) 143099

Abbreviations: ADF, Augmented Dickey-Fuller; AE, Approximate entropy; ANN, Artiﬁcial neural network; ARIMA, Autoregressive integrated moving average; BDS, Brock-Decher-

Scheikman; BPNN, Back propagation neural network; CEEMD, Complete ensemble empirical mode decomposition; CEEMDAN, Complete ensemble empirical mode decomposition

with adaptive noise; EMD, Empirical mode decomposition; EEMD, Ensemble empirical mode decomposition; EWT, Empirical wavelet transform; GARCH, Generalized autoregressive con-

ditional heteroscedasticity; GPR, Gaussian process regression; GRU, Gated recurrent unit; IMF, Intrinsic mode function; KNN, K-nearest neighbor; LSSVM, Least squares support vector ma-

chine; LSTM, Long short-term memory; MAE, Mean absolute error; MAPE, Mean absolute percentage error; RF, Random forest; RMSE, Root mean square error; RNN, Recurrent neural

network; SE, Sample entropy; SVM, Support vector machine; VAR, Vector auto regression; VARIMA, Vector autoregressive integrated with moving average; WT, Wavelet transform;

XGboost, Extreme gradient boosting.

⁎ Corresponding author at: School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China.

E-mail address: jujiewang@126.com (J. Wang).

https://doi.org/10.1016/j.scitotenv.2020.143099

Contents lists available at ScienceDirect

Science of the Total Environment

journal homepage: www.elsevier.com/locate/scitotenv

the other four benchmark methods reﬂected by the smaller statistical errors. Overall, the developed approach

provides an effective method for predicting carbon price.

1. Introduction

From a global perspective, climate changes and natural disasters

caused by greenhouse gas emissions are more and more serious in re-

cent years (Huang and He, 2020). This phenomenon has much to do

with the continuous economic activities of humans, but it is inevitable.

The best approach at present is the market-based policy formul ation

of pricing for carbon emissions, which can calculate the cost of emis-

sions by directly considering the economic efﬁciency (Sun and Wang,

2020; Song et al., 2019). Therefore, recent years have seen the trading

system of carbon emissions gaining global popularity (Wu and Liu,

2020). Looking at the international market, it admits of no doubt that

the European Union Emissions Trading System (EU-ETS) is the largest,

most liquid and most inﬂuential greenhou se gas emission reduction

mechanism in the world, which has provided an effective operating par-

adigm for carbon emissions trading around the world and accumulated

a wealth of data and experience (Zhang and Wei, 2010). Afterwards, as

one of the major contributors in reducing global carbon emissions,

China has successively established eight carbon markets in the pilot cit-

ies including Beijing (2013 ), Shan ghai (2013), Chongqing (2014),

Guangdong (2013), Tianjin (2013), Shenzhen (2013), Hubei (2014)

and Fujian (Song et al., 2018). Moreover, in 2017, the national develop-

ment and reform commission ofﬁ cially announced that China will

launch carbon trading market pilots and put this project on a vital posi-

tion in the 13th ﬁve-year plan, which indicates our ﬁrm conﬁdence in

developing a green economy. In light of this, enhancing carbon price

forecasting precision can not only assist in policy implementation for

manufacturing processes and investment decisions, but also create an

effective and stable carbon pricing mechanism (Zhu et al., 2019). How-

ever, as a burgeoning policy-setting market created by artiﬁcial regula-

tion, the price series of carbon have the characteristics of nonstationary

and nonlinear, which are caused by internal market mechanisms as well

as external environmental uncertainties (Yang and Liang, 2017; Yang

et al., 2020). Therefore, it is a great challenge to predict carbon prices

and more researchers get involved in this research issue.

Numerous studies show that the carbon price is, to some extent, pre-

dictable only if use some certain methods, which are essentially the time-

series prediction technology. This technology is broadly divided into two

classes: statistical and economics models and artiﬁcial intelligence

models. Among them, statistical and economics models are relatively tra-

ditional, including autoregressive moving integrated moving average

(ARIMA), vector autoregression (VAR), generalized autoregressive condi-

tional heteroscedasticity (GARCH) and the like. Byun and Cho (2013) pre-

dicted the volatility of carbon price through GARCH-type models and K-

nearest neighbor model (KNN). It can be found that an improved

GARCH model obtained the most accurate result in all of the selected

models. García-Martos et al. (2013) veriﬁed that the approach of vector

autoregressive integrated with moving average (VARIMA) gave better re-

sults for very short forecasting horizons (one-day-ahead forecasts) in the

case of nonstationary and nonlinear price series. Benz and Truck (2009)

predicted the carbon spot price and volatility in the different phases of

returns with the Markov-switching method and a standard AR-GARCH

model. Although these statistical and economics methods are able to

achieve effective prediction results and possess good theoretical descrip-

tion based on statistical logic, their implementations are rooted on the lin-

ear hypothesis and mainly for very short forecasting span, which don't

have adequate ability to catch the nonlinear characteristics hidden in

the time-series. For the sake of solving this problem, artiﬁcial intelligence

models sprung up and were applied to predict time-series, which are the

data-driving method (Sun et al., 2020). Artiﬁcial intelligence models

mainly cover artiﬁcial neural network (ANN) and support vector machine

(SVM). Fan et al. (2015) applied ANN with a multi-layer perceptron

model for carbon price forecasting, which proved prediction accuracy

and ﬁtting capacity are higher than many single and variant models.

Zhu et al. (2016) developed an ensemble paradigm of forecasting energy

price with the feature of nonstationary and nonlinear through the least

squares SVM (LSSVM) model and the ﬁnal research result also showed

the superiority over the models such as ARIMA and ANN. Patel et al.

(2015) combined ANN with SVM as the hybrid model, which resulted

in the best overall prediction performance. Also, the hybrid model incor-

porating the artiﬁci al intelligen ce model and statistical model can repre-

sent relatively better performance. Zhu and Wei (2013) then made a

combination between LSSVM and ARIMA, which proved better carbon

price prediction results compared by simple statistical models. Further-

more, for the reason that time series prediction is relative not only to

the current data but also to the data at a passed time, whose information

will be lost if only applying the latest data, the recurrent neural network

(RNN) connecting with hidden units was established for enabling the net-

work to keep the memory of recent information, which is unlike tradi-

tional ANNs (Lin et al., 1998). It has been widely used in many ﬁelds,

especially for nonstationary and nonlinear series. Rather et al. (2015)

found that according to the prediction error and correlation between

the original data and output data, RNN generates much better prediction

results. Chen et al. (2013) developed an enhanced RNN for multi-step-

ahead ﬂood forecasting with the feature of nonstationary and nonlinear,

representing that RNN could deal with the association between the past

and future data by the memory features. Meanwhile, in the time series

forecast ﬁeld, the long short-term memory (LSTM) as an enhanced special

RNN has a wide use. The “gate” mechanism is the core of the algorithm,

which can selectively ﬁlter the input information and more important his-

torical data information will be extracted for the following prediction (Li,

2020). Huang et al. (2019a) established the LSTM prediction model for

carbon emissions in China and the emulation result showed that the pre-

diction accuracy is higher compared with back propagation neural net-

work (BPNN) and Gaussian process regression (GPR). Krishan et al.

(2019) used LSTM on the ﬁeld of air quality, which referred to the carbon

emission and results showed that LSTM did have a good capacity to cap-

ture complicated features in the nonstationary and nonlinear series. Liu

and Shen (2019) also established an improved LSTM model for obtaining

higher carbon price forecasting accuracy to some extent. These

extinguished results encouraged us to explore the possibilities of

predicting carbon prices in China via LSTM. Nonetheless, given a large

ﬂuctuationtowardstheoriginalcarbonpriceseries,theeffectthrougha

single AI technique is not very outstanding.

And except for single AI technique, data preprocessing plays an im-

portant role in the time-series prediction, among which feature extrac-

tion is exactly vital. On the one hand, feature extraction can reduce the

feature numbers and dimensions to prevent the emergence of an

overﬁtting problem. On the other hand, it can remove irrelevant fea-

tures and let learning easier. Generally, the methods of feature extrac-

tion are broadly divided into wrapper methods and ﬁlter methods.

Wrapper methods usually cost highly and have a slow learning rate be-

cause of many times' learner training, whereas ﬁlter methods are relied

on original data and have a faster calculating rate than wrapper

methods (Wang a nd Li, 2018). Hence, considering the convenience

and speed case, researchers may prefer the later. Zhu et al. (2013) man-

ifested that the exploitation of various internal logic and necessary fea-

tures implied at different frequencies can be made possible through

decomposing methods. Wavelet transform (WT) is one of the decompo-

sition method s widely utilized in the area of prediction. Chevallier

J. Wang, X. Sun, Q. Cheng et al. Science of the Total Environment 762 (2021) 143099

(2011) applied the wavelet packet transforms into carbon price fore-

casting, which represented a good performance. Sun et al. (2018) also

used WT as the basis decomposing model in the research of China

Emiss ions-Trading Scheme. But these representations of effectivity

mainly depend on the wavelet basis function selected by researchers'

subjectivity without a speciﬁc theory foundation. Empirical mode de-

composition (EMD) is an adaptive method overcoming the drawback

of reliance on the subjective experience of setting a basis function previ-

ously. Zhu et al. (2017) proved that using EMD can well capture several

components with different features. Gao and Jian (2014) proposed a hy-

brid model comprising particle swarm optimization (PSO), SVM and

EMD. In the EMD part, several stationary intrinsic mode functions

(IMFs) and a residual series will be put into a neural network for train-

ing. For the sake of innovation, Gilles (2013) built a new self-adaptive

signal decomposition method named empirica l wavelet transform

(EWT) by combing EMD with WT, whose ﬁnal result showed a better

performance. However, the process of decomposition through EMD is

easy to emerge modal mixing problem and its physical meaning is lack-

ing (Tian and Hao, 2020). To tackle the problem, Wu and Huang (2009)

carried out a study and improved EMD, which was named as ensemble

empirical mode decomposition (EEMD). Qin et al. (2015) utilized EEMD

as a data preprocessing method for improving the prediction effect of

the carbon price. Wu et al. (2019) also combined EEMD with LSTM to

predict the spot price of west texas intermediate crude oil. It can be

found that EEMD is an enhanced EMD, which can improve the phenom-

enon of modal mixing effectively by offsetting and restraining the ef-

fects of noises in man y times' experiences. Despite robustness and

effectiveness of forecasting based on EEMD, there is still a drawback to-

wards it. Increasing the times of integration can reduce the error of re-

construction, whereas it expands the scale of calculation and remains

residual noises to a certain amplitude. Besides, Wu and Huang (2009)

said that the problem of modal splitting may occur. To overcome this

defect, complete ensemble empirical mode decomposition (CEEMD)

as an improved method of EEMD is applied. Zhang et al. (2018) proved

that complete ensemble empirical mode decomposition with adaptive

noise (CEEMDAN) as a signal processing technology can not only solve

the modal aliasing problem, but also lessen the white noise interference

and save the computing time. What's more, Cao et al. (2019) combined

CEEMDAN with LSTM, indicating that CEEMDAN can exploit more hid-

den information than EMD and the hybrid model surpasses the single

one. Therefore, CEEMDAN can be seen as a relatively progressive de-

composition method at present and utilized by this paper for the reason

that its error of reconstruction is nearly zero by adding adaptive white

noise into each phase.

Extant studies have shown that the AI prediction models with

the feature extraction part can not only achieve the effects of data

preprocessing and improv e the calcul ating efﬁciency, but also es-

tablish an appropriate prediction model for the time series. But

several major drawbacks still remain. First of all, after

decomposing the carbon price series, each sub-sequence has been

put into a prediction model for the output results, which didn't

consider the similar complexity and correlation among them so

as to lower efﬁciency and accuracy. Secondly, the predicti on

model for each sub-sequence is the same without the realization

that each mode is different for its unique feature and frequency,

so the respectiv e establishment of mo dels with more prope r pa-

rameters is of vital importa nce (Che, 2015). Thirdly, after achieving

the prediction results of each sub-sequence, existing ﬁnal ensem-

ble models mainly limit to the linear form such as obtaining the

ﬁnal forecast result t hrough combining the prediction values of

all the decomposed modes (Zhu et al., 2018). For the reason that

it is not usually applicabl e for all the cases, a line ar ensemble ap-

proach may affect the accuracy of predicting (Liao and Tsao,

2006

). There are two main ty pes of nonlinear integration methods.

One o f them is serialization methods with strong dependencies

among individual learners and the o ther is paralleliz ation met hods

generated simultaneously without strong dependencies among in-

dividual learners. Representative of the former i s boost ing and the

latter is bagging, which develop the extre me gradient boosting

(XGboost) and the random forest (RF) respectively. By comparing

these two methods, we can ﬁnd that the XGb oost is more se nsitive

to overﬁtting if the data is noisy and it is often takes longer for

being built in sequence (Fan et al., 2020). What's more, RF is

more adjustable.

In order to solve these existing problems towards carbon price

forecast, a novel hybr id model incorporat ing CEEMDAN, Sample

entropy (SE), LSTM and Random forest (RF) is put forward. From

the perspectiv e of meth odology, it develops an innov ative r andom

forest-based nonlinear ensemble paradigm of improved feature

extraction and deep learning algorithm for higher accuracy in the

case of nonst ationary and nonl inear carbon pr ice forecast. Firstly,

the original carbon price series is decomposed into several simple

stationary modes with the application of CEEMDAN algorithm.

Then, the obtained simple modes with similar co mplexity are

recombined according to the SE algorithm, so as to boost calculat-

ing efﬁciency and accuracy. Considering that different modes

have their own frequency and characteristic, LSTM can then be ap-

plied t o set an appropriate prediction model for each reconstructed

component because of i ts strong long and shor t term memory. At

last, after forecast results of reconstructed components have been

achieved through the deep learning algorithm, RF as a nonlinear

ensemble bagging learning model is utilized to aggregate the ﬁnal

carbon price forecast result for the further improved predictio n

accuracy.

From the above, the main innovations and contributions of this re-

search compared to the ﬁndings in the literature are shown in the fol-

lowing four points:

a. Considering the neglect of similar complexity and correlation among

decomposed modes, an improved feature extraction incorporating

CEEMDAN and SE is adopted for screening different features effec-

tively from the original carbon price series so as to the higher efﬁ-

ciency and accuracy.

b. With the realization that respective establishment of models is of

vital importance and in order to capture more complicated features,

LSTM replaces RNN as the crucial prediction model.

c. For the reason that nonlinear ensemble learning can get smaller er-

rors and more stability than a linear approach, this research applies

RF as integrated algorithm to improve the forecast accuracy.

d. The novel hybrid model for carbon price forecast setting as an adap-

tive nonlinear ensemble learning paradigm is ﬁrstly proposed,

which excels single model and represents its unique robustness.

The structure of the rest of this paper is as follows: the methodologies

and brief proposed model structure are outlined in Section 2. The case

study with data collecting, preprocessing and relative measurement indi-

ces are elaborated in Section 3. Section 4 describes the forecast results as

well as discussions in more detail. At last, Section 5 draw a conclusion.

2. Methodology

2.1. Complete ensemble empirical mode decomposition (CEEMDAN)

EMD proposed b y Huang et al. (1998) has been widely utilized in

many ﬁelds, which is an adaptive si gnal decomposition met hod

without any assumptions about data. However, the problem of

modal aliasing causes the decomposed intrinsic functions affecting

each other, which deprives the physical meaning of t he IMF. To

solve this probl em, Wu and Huang (2009) proposed EEMD, which

can offset the effects of noise during the procession of decomposition

by making several times' experiments. U nfortunately, there is resid-

ual noise in the components, which lowers efﬁciency. Ove rall,

J. Wang, X. Sun, Q. Cheng et al. Science of the Total Environment 762 (2021) 143099

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