Electricity Price Prediction by Enhanced
Combination of Autoregression Moving
Average and Kernal Extreme
Sahibzada Muhammad Shuja1, Nadeem Javaid1(B
), Sajjad Khan1,
Umair Sarfraz1, Syed Hamza Ali2, Muhammad Taha2, and Tahir Mehmood3
1COMSATS University Islamabad, Islamabad 44000, Pakistan
2COMSATS University Islamabad, Wah Campus, Wah Cantonment 47040, Pakistan
3Bahria University Islamabad, Islamabad 44000, Pakistan
Abstract. In electricity market, electricity price has some complicated
features like high volatility, non-linearity and non-stationarity that make
very diﬃcult to predict the accurate price. However, it is necessary for
markets and companies to predict accurate electricity price. In this paper,
we enhanced the forecasting accuracy by combined approaches of Kernel
Extreme Learning Machine (KELM) and Autoregression Moving Aver-
age (ARMA) along with unique and enhanced features of both models.
Wavelet transform is applied on prices series to decompose them, after-
ward test has performed on decomposed series for providing stationary
series to AMRA-model and non-stationary series to KELM-model. At
the end series are tuned with our combine approach of enhanced price
prediction. The performance of our enhanced combined method is evalu-
ated by electricity price dataset of New South Wales (NSW), Australian
market. The simulation results show that combined method has more
accurate prediction than individual methods.
Keywords: Predictions of electricity price ·ARMA ·KELM ·
Wavelet transform ·Enhanced combined price prediction
In the past decade of electricity market, the volatile electricity prices became a
complicated phenomenon along with few characteristics and important concep-
tion. Market’s managers have to ensure the stability of forecasting for the power
market. In power, money contribution decisions and transmission inﬂation, pre-
dictions of electricity price play an important role. However, it is a complicated
task to predict accurate price of electricity because of many segregated fea-
tures, like as high volatility, nonlinearity, multiple seasonality, etc. In past few of
Springer Nature Switzerland AG 2019
L. Barolli et al. (Eds.): WAINA 2019, AISC 927, pp. 1145–1156, 2019.
1146 S. M. Shuja et al.
researches, many authors have presented diﬀerent prediction techniques to pre-
dict the price for electricity. Those techniques are majorly classiﬁed into three
categories, which are artiﬁcial intelligences, classical and data driven based pre-
diction techniques. With the intelligent feature and self-training process, neural
network as an artiﬁcial intelligence technique are best in performance over other
techniques. Some of the recent work is presented in .
In , forecasting techniques is summarized in the ﬁve diﬀerent types: sta-
tistical models, multi-agent models, fundamental models, reduced-form models
and computational-intelligence model techniques. Statistical and computational
models are two widely used techniques among given ﬁve techniques. Statistical-
model techniques like Auto Regression (AR), Moving Average (MA), Autore-
gression Moving Average (ARMA) and Autoregression Integrated Moving Aver-
age (ARIMA), while some other ARMA-based models such as Exogenous vari-
able (ARMAX) and Generalization Autoregression Conditional Heteroskedastic
(GARCH) predict the current electricity price from historical data of price. How-
ever, statistical-model techniques are basically limited to capture the non-linear
and the rapid change behavior of electricity price signal .
The authors have proposed the recent learning technique in , which is
Extreme Learning Machine (ELM) relay on Single-hidden Layer Feed-forward
Neural-network (SLFN). This technique randomly produces the connection
weight among input, hidden layer and threshold of neurons in the hidden layer,
and they do not need the adjustment of parameters during the training process.
A framework for modeling for prediction of electricity price has been presented
in . They proposed four diﬀerent models of deep learning for electricity price
forecasting. The machine learning models outperform than statistical models.
However, their hybrid model was not capable to outperform in results.
Motivated by increasing the performance of forecasting in the market of elec-
tricity, two diﬀerent methods of electricity price prediction are presented . To
calculate the importance of features, a novel feature selection algorithm is used
for the prediction accuracy being improved from 15% to 12% Mean Average Per-
centage Error (MAPE). However, they have not expanded their experiment for
the European markets. With Singapores weekly forecasting price of electricity
is presented in . They make use of ARIMA and complemented with GARCH
models for electricity price prediction. Results depict that their models consid-
erably match the price patterns based on out of univariate forecasted samples.
However, results conﬂict with multivariate data to be used in their models.
In , considering PJM and Spanish markets by authors to propose a com-
bination for hybrid method consist of current day-based forecaster, correlation
and Wavelet Transform (WT) analysis for preprocessing stage. Afterward, their
method results revealed positive prediction as compared with other respective
methods. An optimization scheme is proposed in , to minimize the price of
electricity. They have scheduled the usage pattern of residential appliances by
their scheme candidate solution updation algorithm. However, user comfort is
not considered to fulﬁll the consumer’s side waiting time for appliances usage in
Enhanced Combined Price Prediction 1147
Using publicly available data in , a forecasting method is proposed for
real time Ontario’s market of electricity. Their method uses data as input of
two diﬀerent hourly based forecasted model. The model is capable to detect the
serious outrage and spikes in the electricity price. A model of functional additive
attributes for electricity price forecasting is presented in . The proposed the
point wise prediction of information from the Spanish electricity market. Dataset
of the same paper is compared with other functional, regression models, which
makes better prediction result for load and price forecasting. A neural network
based training algorithm is presented in . They have extended Kalman ﬁlter
and used energy price forecasted. One-step and n-step ahead of Kalman ﬁlter
veriﬁed better result of price prediction from European electricity system.
The authors presented a forecasting model for load predictions through
hybrid neural network . In their work, they veriﬁed their simulations on
USA based datasets. The results of their method in comparison from two exist-
ing models outperform with respect of execution time, forecasting accuracy and
scalability. In , unique and new short-term forecasting method is presented
by using aﬃnity propagation and a ﬁreﬂy heuristic algorithm for the system.
This technique improves various priority indexes to select similar days. Simula-
tions compared with the existing techniques for accuracy and operational cost,
which shows their system outperform and also minimized the error through error
Electricity price data in the real world have some unusual pattern, due to
which they are non-stationary and non-linear. Therefore, both of the non-linear
and linear prediction of electricity of price is needed for the eﬀective purpose
of price prediction models. In this paper, proposed a combined price prediction
model have some enhanced feature of existing models KELM and ARMA. The
original series of electricity price is decomposed into more stable variants of
volatile and stationary series by WT. The ARMA-model is used for the predic-
tion of a stationary series because of its eﬃciency and robustness, whereas due to
best generalization of KELM-model performed forecasting on the volatile series
of price. To generate the ﬁnal forecasted values of electricity price, proposed
method for model integrate the combination unique features from KELM and
ARMA. Dataset of New South Wales (NSW) is used to illustrate the forecasting
ability of our proposed method to compare the results with individual prediction
of KELM and ARMA on original price series.
2 Proposed System Model
In this section of the paper, we describe in detail proposed system model for
method develop to forecast the electricity price and is shown in Fig.1.Itisvery
diﬃcult to forecast the accurate electricity price, because of many circumstances
including weather, load and previous predicted prices. In addition, balance is
required between demand and supply as electricity cannot be stored due to the
inelastic nature of electricity shorter comes and unstable nature of generation
, complexity is produced in the behavior of electricity price. In this paper, we
1148 S. M. Shuja et al.
capture diﬀerent pattern of electricity price series to produce an accurate price
prediction. Generally, electricity price series presents irregular behavior due to
high ﬂuctuation. In our proposed model, irregular pattern of price series are
change into a regular pattern of the essential series by WT and more accurate
results of prediction produced by decomposed series than direct price prediction
from forecasting model. However, wavelet decomposition series cannot reﬂect
the information received by individual model. Therefore, the performance might
not be fulﬁlled by single model prediction for WT as an input.
Fig. 1. Proposed system model
Enhanced Combined Price Prediction 1149
We used Enhanced Combined Prediction (ECP) of electricity price that can
perform on the basis of the unique characteristic of each model to get information
from decomposed price series. Our ECP method generates the better the predic-
tion output. In the ECP method, ARMA-model and KELM-model is used for
selection and training data. The ARMA-model is generally solved the problem
of linear time series; its performance for stationary series is quite satisfactory.
The positive feature of KELM-model is its fast speed of learning for non-linear
prediction. Hence, our new ECP method comprises of WT, ARMA and KELM
is proposed to forecast the price.
The performance steps in the ECP price model of prediction for electricity
price mentioned as follows:
•Preparation of dataset: Date of price is divided into training and testing
portion of the series. The data are trained for developing models and tested
for executing model.
•Applying wavelet transform: In this paper, Daubechine 5 is used as mother
wavelet and 5 levels of decomposition series. WT is used to decompose elec-
tricity price series into 5 levels, among them one is approximate series A and
others are detail series D1, D2, D3 and D4.
•Stationarity check of each series: We performed Augmented Dicky Fuller
(ADF)-test on decompose series for the check of stationarity. The ADF-test
results consist of ADF-statistic and three critical level values of 1%, 5% and
10%. If an ADF-statistic value less than critical level values than series are
stationary otherwise non-stationary.
•We used ARMA-model for processing of stationary series and KELM-model
for non-stationary series because of their construction.
•Combined and enhanced the forecasting of the individual result of KELM
and ARMA for the ﬁnal prediction of electricity price.
2.1 Error Measures for Predictions
The performance ability of prediction of our proposed model is veriﬁed by dif-
ferent error measures. Most of the used measures are the Root Mean Square
Error (RMSE), Mean Square Error (MSE) and Mean Absolute Percentage Error
(MAPE). When error measures are computed at low values, its mean there is a
good performance of predictions. Lots of out range’s peaks for a price series of
electricity can numerously aﬀect the prediction of price. In our proposed model,
MAPE outperform from other techniques ARMA and KELM.
3 Existing and Proposed Techniques
In this section, we discuss the techniques used for the predictions of electricity
1150 S. M. Shuja et al.
3.1 Kernel Extreme Learning Machine (KELM)
This model is used in many areas of researches with respect of simple ELM and
ELM comes out of SFLN. Its responsiveness behavior toward non-stationary and
volatile series is due to fast learning and forecasting ability in price. In ELM,
hidden layer’s parameters do not need tuning. In , Huang proposed the kernel
based ELM. Kernel matrix in ELM is used, when feature mapping is unknown
for the user. The user has not speciﬁed hidden nodes and the hidden layer feature
mapping. In the stable kernel function is changing the randomness of ELM that
why KELM is better in generalization.
Algorithm 1. Kernel Extreme Learning Machine
Require: Input: [Original Electricity Price Series;]
1: Train electricity series data;
2: Applying elmregressor to prepare model;
3: Applying ﬁtter function;
4: Applying predict function;
3.2 Autoregression Moving Average (ARMA)
This is the model based on random time series used for predictive analysis .
Prediction analysis of time series values consist of three types: AR, MA and
ARMA. The ARMA model implementation is based on following steps:
•Adf-Test: for stationarity analysis.
•Identiﬁcation of model feature and structure.
•Estimate the parameters and development of the model.
•Model testing for the noise.
•Predict the future values of cost.
Algorithm 2. Autoregression Moving Average
Require: Input: [Original Electricity Price Series;]
1: Train electricity series data;
2: Applying AR and MA coeﬃcient parameters;
3: Combine both of parameters to prepare model;
4: Applying predict function;
Enhanced Combined Price Prediction 1151
3.3 Enhanced Combined Price Prediction (ECPP)
In the ECPP, to select a particular single model is an important part. The
ARMA-model is a quantitative model in which correlation function is used to
compare the data between current and historical activities. The ARMA-model
is generally used for prediction of stationary series. The dominance of KELM
is its capability for fast learning and generalizing, that’s why we use it for non-
stationary and volatile series. Performance of KELM-model is aﬀected by penalty
factor and kernel parameters. With the help of few unique features from both
KELM and ARMA, we made our proposed technique of ECPP method.
Algorithm 3. Enhanced Combined Price Predictions
Require: Input: [Original Electricity Price Series;]
1: Applying Wavelet Transform to decompose series;
2: Two series Approximate and Detailed Series;
3: Applying stationarity adf-test on decomposed series;
4: Find local best solution;
5: if adf statitic < critical value then
6: Price Series= Stationary Series;
7: Applying ARMA on Price Series;
9: Price Series= Non Stationary Series;
10: Applying KELM on Price Series;
11: end if
12: Combine Output of both model;
13: Final Forecasting of Electricity Price;
4 Case Results and Reasoning
In this section of the paper, case of Australian Electricity Market (AEM) is
used to demonstrate the forecasting performance of the proposed method. Our
proposed method is tested on price prediction of AEM. We put a daily forecasted
price in our method from New South Wales (NSW) dataset for the month of
January of the year 2018. Each day of the month is used to verify the production
of our proposed method, although the training set of data comprised of 30 days
taken from the start of the test days. NSW dataset is taken from the website
4.1 Analysis of Case for Proposed Method
Applying wavelet decomposition, the two series are produced approximate-series
and detail-series. This series illustrates the low-frequency and high-frequency
components of the main series. We justify the simulation from our proposed
method in two steps.
1152 S. M. Shuja et al.
First, stationarity analysis is performed through the ADF test in the wavelet
decomposition series of NSW data. The ADF test results show that the ADF-
statistic values of detail series, D1, D2, D3 and D4 are smaller than 1% critical
level, thus their unit root hypothesis is rejected. However, ADF-statistic value
of an approximate series A greater than 10% critical level, thus its unit root
hypothesis is not rejected. Stationarity analysis indicates that A is identiﬁed as
non-stationary series and other detail series are stationary series.
Second, we applied ARMA-model on stationary series contain four detail
series and KELM-model of non-stationary series having one approximate series.
After that, we enhanced the results for both of the models along with the sum
of their predicted price values.
4.2 Discussion and Comparison
To elaborate the eﬃciency of our proposed method for prediction, data from
NSW is tested for January month of the year 2018 and the three type errors
MAPE, MSE and RMSE are calculated. We compare the results of our enhanced
proposed scheme with ARMA-model and KELM-model for errors. NSW electric-
ity price forecasted data is predicted by ARMA-model is shown in Fig.2.The
peak of predicted values depicts the accuracy of single ARMA-model.
The prediction of enhanced combined prediction for NSW data of electricity
price is depicted in the Fig. 4. Peaks of graphs show that when ARMA and KELM
for were used separately and were not combined, then the accuracy value price
prediction was less than the proposed scheme. Complex price feature cannot be
resolved by single KELM and ARMA. ARMA is not capable to solve the non-
linear issues, because its forecasted values are not more accurate than KELM.
In Fig. 3, single KELM-model based electricity forecasting of price is shown.
Fig. 2. ARMA-model base electricity price forecasting
Enhanced Combined Price Prediction 1153
Fig. 3. KELM-model base electricity price forecasting
MAPE error estimation is performed in Fig. 5. Our proposed enhanced
method is compared with other methods ARMA and KELM. The results show
that our proposed method has an eﬃcient and better performance with respect
of other method. We have achieved signiﬁcant reduction of error for MAPE by
8.67% in ARMA-model, 15.07% in KELM-model and 3.06% in our proposed
Fig. 4. Enhanced combined electricity price forecasting
However, according to the analysis of our proposed method performance
is not satisfactory for error calculation by MSE and RMSE in Figs. 6and 7.
Our proposed method achieves less accurate values for MSE and RMSE error
and encountered with more error rate as compared ARMA and KELM models
1154 S. M. Shuja et al.
Fig. 5. MAPE error in percentage comparison of our enhanced combined prediction
with ARMA and KELM
Table 1. Comparison of error measures
Methods(s) MAPE MSE RMSE
ARMA 8.67% 56.48% 56.48%
KELM 15.07% 5.36% 2.32%
ECPP 3.06% 11.44% 14.54%
Fig. 6. MSE error in percentage comparison of our enhanced combined prediction with
ARMA and KELM
Enhanced Combined Price Prediction 1155
Fig. 7. RMSE error in percentage comparison of our enhanced combined prediction
with ARMA and KELM
Due to uncontrolled electricity market, predicting the price of electricity has
become essential to power users and supplier. Implementing an eﬃcient and an
accurate prediction model has become a very important role in the electricity
scope. In this paper, a new enhanced method for prediction of electricity price
combining KELM and ARMA forecasted output is proposed. Electricity dereg-
ulated price series is transformed and decomposed into diﬀerent series by WT,
the KELM-model forecast the non-stationary part of decomposed price, while
ARMA-model is used to predict the stationary part of the price. Final forecasting
of electricity price is the combination of KELM-model and ARMA-model. NSW
market data is used to verify the forecasting ability of our proposed enhanced
combine method. This paper is completed depends on the improvement of fore-
casting accuracy through enhanced method. Although some prices patterns of a
speciﬁc time period are not matched, the proposed method improved the match-
ing feature for prediction of electricity price. In future, load and weather should
be considered for the prediction accuracy through our proposed method.
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