(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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