Hybrid Model Based on Wavelet Decomposition for Electricity Consumption Prediction

XIA Chenxia(), WANG Zilong(), JHONY Choon Yeong Ng()

College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Abstract： The effective supply of electricity is the basis of ensuring economic development and people’s normal life. It is difficult to store electricity, as leading to the production and consumption must be completed simultaneously. Therefore, it is of great significance to accurately predict the demand for electricity consumption for the production planning of electricity and the normal operation of the society. In this paper, a hybrid model is constructed to predict the electricity consumption in China. The structural breaks test of monthly electricity consumption in China from January 2010 to December 2016 is carried out by using the structural breaks unit root test. Based on the existence of structura breaks, the electricity consumption data are decomposed into low-frequency and high-frequency components by wavelet model, and the separated low frequency signal and high frequency signal are predicted by autoregressive integrated moving average(ARIMA) and nonlinear autoregressive neural network(NAR), respectively. Therefore the wavelet-ARIMA-NAR hybrid model is constructed. In order to compare the effect of the hybrid model, the structural time series (STS) model is applied to predicting the electricity consumption. The results of prediction error test show that the hybrid model is more accurate for electricity consumption prediction.

Key words: electricity consumption; forecasting; wavelet decomposition; structural breaks; structural time series (STS) model

Introduction

Electricity is the basic energy for the development of national economy. It has extensive influence on the technology and economic development[1]. The rapid growth of electricity consumption brings development and opportunity to grid enterprises. The accurate prediction of electricity consumption can help decision-makers to get enough information to effectively balance the exuberant demand and limited resources. The electric power industry is closely related to various industries. Its healthy development is related to the smooth operation of the national economy, and the accurate prediction of the electricity consumption plays a vital role[2]. For the above reasons, the forecast of electricity consumption has attracted more and more attention from scholars.

The method of predicting electricity consumption can be divided into three methods： econometric model, machine learning, and hybrid model. At first, the econometric model was employed to predict electricity consumption in most studies. However, this kind of model is only suitable for stationary sequence that the distribution is known. As a result, this prediction method can lead to spurious regression[3]. What’s more, this method cannot capture the nonlinear and multi-variable characteristics of electricity consumption comprehensively. To sum up, the traditional forecasting method for electricity consumption is not accurate enough[4]. Because of the above reasons, the application of machine learning in the prediction of electricity consumption has made a rapid progress. Machine learning has been widely used to capture the nonlinear characteristics of electricity consumption, but the prediction results are sensitive to the initial values and have poor adaptability to the whole model in emergency situations[5]. By combining machine learning with econometric model, the hybrid model can not only improve the prediction accuracy, but also prolong the prediction time. For example, Cao and Wu combined the fruit fly optimization algorithm with seasonal index adjustment to predict the monthly electricity consumption[6]. Kheirkhahetal. constructed a hybrid model of principal component analysis, data envelopment analysis and neural networks to predict electricity consumption[7]. Gürbüzetal. developed a linear quadratic model with the artificial swarm algorithm to predict the electricity consumption of Turkey[8]. However, most of the hybrid models have some limitations on nonlinear data, such as do not suitable for uncertain data, lack of adaptability, and can not characterize the local characteristics of electricity consumption. In this paper, wavelet reconstruction is applied to obtaining useful information at different resolution levels. However, the research on hybrid models now has the following deficiencies. Firstly, annual data are applied in most of the consumption forecast literatures[9].Time series have four characteristics, including periodicity, seasonality, trend and irregularity. While, these characteristics will be unable to be observed and detected in yearly data[10]. Secondly, national economic events and energy policy changes may cause structural breaks in the process of data generation, and thus the sequence is divided into different distribution mechanisms[11]. Ignoring structural breaks in prediction will lead to a decline in prediction performance. However, in most studies of electricity consumption forecasting, there is less research on structural breaks[12]. For example, Ekonomou and Kavaklioglu forecast electricity consumption with structural breaks, but they did not take into account the impact of structural breaks on the prediction[13-15]. Dicembrino and Trovato only studied the relationship between structural breaks, price and electricity consumption[15]. Finally, the method of dealing with seasonal factors is very important in the prediction of electricity consumption, but the most commonly used method is to eliminate seasonal factors. However, an explicit seasonal change in electricity consumption is more conducive to electric power planning and construction[16-17].

In dealing with time series data, wavelet analysis method can combine the fluctuation of different frequencies and the time windows of different frequencies without losing the information of variables, so that the time series can be analyzed better[18]. Furthermore, the high pass filter in wavelet transform can extract the features of time series, which is very suitable to extract complex features in electricity consumption. The structural time series(STS) model also decomposes the seasonal, trend, periodicity and irregular features of the time series, so that each feature can be predicted separately. It is notable that monthly data show more complex features. Therefore, studying the features of electricity consumption by monthly data is more likely to grasp the complicated features. Most monthly time series data are characterized by seasonal, periodicity, trend and irregular factors. In other words, many unpredictable factors exist in electricity consumption data, including the seasonal, autoregressive, disturbance terms, irregular factors, and outliers. In order to understand its complex characteristics more easily, observe the change of electricity consumption with season and period, and locate the structural breaks more accurately, the monthly data of electricity consumption are applied in this paper. The first model is constructed. The electricity consumption is decomposed into low-frequency and high-frequency signals by wavelet transform, and the decomposed signals are regarded as independent time series and each signal is modeled and predicted. The low-frequency signal is predicted with autoregressive integrated moving average (ARIMA), while the high-frequency part is predicted by the nonlinear autoregressive neural network (NAR). The second model, STS model with structural breaks, is constructed to study the effect of the two models on the prediction accuracy of electricity consumption with structural breaks.

The characteristics of this study are： (1) monthly electricity consumption data are used to capture the inherent features. (2) The structural breaks of China’s electricity consumption during the sample period is located. (3) Each character of the data is decomposed into low-frequency and high-frequency components by wavelet decomposition, then ARIMA and NAR are applied to forecasting each component, respectively. (4) A STS model with structural breaks is constructed to predict electricity consumption of China.

The rest of this paper is structured as follows. section 1 describes the basic model briefly, including wavelet reconstruction, dynamic neural network and the STS model. section 2 describes the evolution of electricity consumption of China and consumption trend from January 2010 to December 2016. And then the two newly proposed models and the predicted results of electricity consumption of China are described in detail. At last, the accuracy of the two proposed models are calculated and compared. section 3 draws the conclusions and future work.

1 Methodologies

1.1 Discrete wavelet reconstruction

Wavelet decomposition is one of the two branches of modern analytical science, which is a promising multi-resolution analysis method in time domain and frequency domain. It can reveal frequency and time information in signal[19]. Wavelet decomposition is a wavelet sequence that uses the short-time Fourier transform to translate or extend a parent wavelet. The wavelet decomposition can decompose the original time series into low-frequency and high- frequency components in wavelet domain. These components exhibit better outliers and lower uncertainties, which make the original signal easy to be analyzed. The discrete wavelet decomposition developed by Mallat is based on four filters, namely decomposition low-pass, decomposition high-pass, reconstruction low-pass, and reconstruction high-passlters. Through this algorithm, the signal is decomposed continuously, and each layer is decomposed into low-frequency and high-frequency signals; on the lower layer, the low-frequency signal is decomposed again into a relatively high-frequency signal and another low-frequency signal[20]. After the signal is decomposed fornlayers by binary sampling method, the original signal will eventually be divided into a low-frequency signal andnhigh-frequency signals. Wavelet transformation includes continuous wavelet transformation and discrete wavelet transformation. Discrete wavelet transformation is applied in this paper.

Letψ(t)be a square integrable function, that is,ψ(t)∈L2(R). If the Fourier transformψ(ω) meets the condition

(1)

then,ψ(t) can be seen as a basic wavelet or mother wavelet function. In the time domain, the wavelet analysis has a compact set or an approximate compact set, and the volatility has positive and negative alternation.

The mother wavelet functionψ(t) is scaled and translated. Wavelet sequences can be obtained as

(2)

whereais a scaling factor, andτis a translating factor shifting the mother wavelet to the time domain of the signal. Wavelet transformation is that the basic wavelet functionψ(t)is shifted forτsteps. And then, in the scale ofa, the inner product function of the mother wavelet and the analyzed signalf(t) is

Wf(a,τ)=〈f(t),ψa, τ(t)〉=

(3)

(4)

Therefore, the discrete wavelet transformation can correspondingly be expressed by

(5)

where * corresponds to the complex conjugate ofψ(t).

The wavelet reconstruction can be written as

(6)

The original time series equals to the sum of the low-frequency componentA3and the high-frequency componentsD1,D2,D3,i.e.,S=D1+D2+D3+A3.

1.2 Dynamic neural network

Dynamic neural network is a kind of neural networks considering influence of time. The NAR is a dynamic recurrent network in order to improve the auto-regressive approach[21]. A typical NAR is a feed-forward network, composing of input layer withdterms lagged, one hidden layer withnneurons, one output layer with one neuron and an input delay function. It is able to recognize time series patterns and nonlinear characteristics. Thedterms lags arey(t-1),y(t-2),…,y(t-d)[22]. The NAR model is given as

Y(t)=

f(y(t-1),y(t-2),…,y(t-d))+ε(t),

(7)

wherefis a nonlinear function,y(t) is the output,tis the time vector,dis the number of delays, andε(t) is the error term. This formula indicates that the model applies the past values to infer the current values.

Selection of excitation functions of neural network is that the hyperbolic tangent sigmoid function taken as the squashing function is used in the hidden layer of the neural network, and the linear function is used at the output layer.

The error term is assumed to be independent and identically distributed, and the minimum mean square error optimal predictor ofy(t) can be got using a conditional mean

Y(t) =E(y(t)/[y(t-1),y(t-2),…,y(t-d)])

=f(y(t-1),y(t-2),…,y(t-d)),

t≥d+1.

(8)

The predictor has mean-squared error ofσ2.

The training step is so vital in the NAR model. Data normalization, preprocessing of converting data setting to small intervals like [-1,1] or [0,1], is usually done before training a network in order to increase convergence speed. The sample data are sorted into three sets for training, validation and testing purposes. The weights of the NAR model are fitted by training set, the model variant is selected by the validation set, and the test set is used to evaluate the selection model for unknown data. Several training algorithms such as Levenberg-Marquardt, Bayesian Regularization, and Scaled Conjugate Gradient are used to calculate neurons, weights and bias. The training algorithms adjust the weight sets to get a robust mapping of outputs when certain inputs are given. In order to improve the prediction accuracy of the structure, the number of the best hidden layer neurons is determined by trial and error, which is the most important task in building the NAR model. Network training should be stopped early, since over-fitting is a common problem that usually occurs during neural network training.

A trained NAR model can only predict one-step ahead because it is in an open-loop state, through which the static neural network modeling function can be used to train the dynamic network. The back-propagation algorithm is used in this paper. Therefore, we need to use closed-loop network for multi-step ahead prediction, and change the network into parallel configuration providing the desired output back to the input to get more accuracy prediction. The output of the closed-loop network is seen as

Y(t+p)=

f(y(t-1),y(t-2),…,y(t-d))，

(9)

wherepis the number of steps to be predicted.

In the NAR modle, time-delay feedback is the time delay signal for the output, because it is based on the regression of its own data. And the NAR modle takes the output time delay signal as the input of the network, and obtains the output of the network. Through the calculation of the hidden layer and the output layer, the output of the network is obtained.

1.3 STS model

The STS model is suitable for special time series, which are composed of some unobservable factors including long-term trend, seasonal, cyclical and disturbance terms. The STS model can directly set and estimate each component model, and components prediction results can be observed clearly. The trend component usually represents the long-term development path of time series, which is often set as a smooth function of time and it can capture the non-stationary components of the time series. Regularity change in a year can be captured by seasonal components. The dynamic characteristics of the cyclical component can represent the economic cycle and associates with fluctuation cycle, which is not usually fixed. Irregularity is caused by accidental events[23]. In short, state space model is used to represent each unobservable component, and then a maximum likelihood estimation method is applied to estimating the hyperparameters and the components. At last, forecasts are made by the Kalman filter.

A univariate STS model is given by

(10)

whereμtis the trend,φtis the autoregressive component which is cyclical component,γtis the seasonal, andεtis the disturbance error.

The local level model contained a stochastic trend and an irregular component is dened as

(11)

The trend component represents the main time series by recursively setting its drift term. After increasing the slope implying the long-term change of the trend, the formula can be expressed as

(12)

A seasonal component is added in the local level model formulated as

(13)

(14)

In the trigonometric function seasonal model, each harmonic is a two state model, including an auxiliary independent part.

(15)

Consider an autoregressive component formula as

(16)

whereφp(L) is an autoregressive polynomial ofporder,θq(L) is a moving average polynomial ofqorder, andLis a hysteresis operator.

The multivariate time series can be expressed as the STS model in the state-space form which is determined as

Observed equation：

yt=Ztαt+εt,εt～NID(0,Ht),

(17)

State equation：

αt+1=Ttαt+Rtηt,ηt～NID(0,Qt),

(18)

where,αtis a vector of unobserved components, called state vector;Ttis the state system matrices;Ztconnects the unobservable factors and the regression coefficients of the state system to the observation vectors. The observation perturbations are assumed to be zero mean and unknown variance-covariance structure, expressed byHt;Rtis the error system matrix;HtandQtare the variance matrices.

2 Empirical Results

Compared with developed countries, power generation technology and power infrastructure in developing countries started late and developed rapidly. It is easy to be influenced by economy, market and environment in the process of development[24]. Therefore, the characteristics of electricity consumption data in developing countries are complex. Because the two models are based on the complex features of time series, we choose the monthly electricity consumption data of China as the research sample. The sample length is from January 2010 to December 2016. Because of the freezing disaster and the Wenchuan earthquake in 2008, the power distribution system in the South has been damaged. These events led to inaccurate data for 2008-2009, which could result in variance changes. In order to avoid this situation and ensure that our research results can keep pace with the time, we use the data after 2010. Time series dataset on the electricity consumption employed in this paper was sourced from Wind database. Figure 1 shows the evolution of China’s electricity consumption.

Fig.1 Evolution of China’s electricity consumption

As shown in Fig.1, the trend of monthly electricity consumption of China obviously shows two characteristics： the first one is that the main long-term trend is an upward one; and the second is cyclical fluctuation, that is, monthly electricity consumption presents different cycles and amplitude fluctuations.

2.1 Testing for structural breaks

In the process of economic activity and environment changes, the influence and adjustment of some events can easily lead to changes of economic structure. Structural breaks usually occur when an uncontemplated shift in the level or volatility of a time series appears between regimes[25]. Standard unit root tests such as the Augmented Dickey-Fuller (ADF) and Phillips-Perron tests cannot reject unit root null hypothesis, which will provide false results when structural breaks occur during the data generation process. That is, the presence of structural breaks within a data series might make traditional standard unit root tests less effective in examining the stationary properties of data series[26]. To construct a STS model, we need to test the stationary of the electricity consumption series. The degenerate stationary process with structural breaks is often misjudged as a sequence containing unit root. On this account, this study opts Zivot and Andrews unit root test with one structural break to confirm the order of integration of variables. The number of structural breaks are measured by Bai and Perron method[27]. The results of Zivot and Andrews unit root test is reported in Table 1.

Table 1 Zivot and Andrews test

Note：*significant at 1% level of significance

As presented in Table 1, electricity consumption rejects the null hypothesis at a significant level of 1%, that is, the electricity consumption contains structural breaks. Since Zivot and Andrews can only detect one structural break, Bai and Perron method is used to detect multiple structural breaks. Bai and Perron have carried out a thorough study of the structural breaks, and put forward a method of endogenous structural breaks test[27]. This method does not need to presuppose the number and location of structural break, and overcomes the limitation that only one or two structural breaks can be detected. Bai proves that this method has better detection level and test efficiency in small sample cases. It is a more accurate and objective method at present[28]. The results of Bai and Perron applied to detecting the multiple structural breaks are reported in Table 2.

Table 2 Bai and Perron test of electricity consumption

Note：*significant at 1% level of significance

As shown in Table 2, theUDmaxandWDmaxare found to be 41.84 and 57.15, respectively. Compared with their respective critical value, they are significant at 1% level. The sequential test SupFT(l+1/l) and the test statistic values are obtained as 20.77 and 5.59. 20.77 is significant at 1% level. The number of breaks is two, which is identified by the sequential approach, the Bayesian information criterion (BIC), and the modified Schwarz’ criteria (LWZ), and the structural breaks are December 2010 and February 2015.

2.2 Wavelet-ARIMA-NAR based forecasting

2.2.1Waveletreconstruction

In the wavelet prediction method, the problem of how to determine the level of decomposition is presented. The characteristic of wavelet decomposition is that the finer the frequency of the signal is divided, the better the smoothness and wavelength of the signals are decomposed. However, if there are too many decomposition layers, the error in wavelet reconstruction will be larger, so the ideal decomposition layer number is 3-5 layers[29]. For the sake of obtaining the optimum level of decomposition, Daubechines 5 selected as mother wavelet with five-level of decomposition was applied. A data pre-processing method is adopted to decompose the electricity consumption time series into discrete wavelet coefcients.

After decomposition, wavelets were reconstructed with all sub-series at different frequency levels. Reconstructed wavelet is reflected inRoriginalabout its periodicity and uptrend. Low-frequency in the wavelet reconstruction reected by theRapproxshows the general trend in the variable. High-frequency components (Rcd1,Rcd2,Rcd3,Rcd4,Rcd5) replicate details of the series, and every significant pattern is derived from wavelet decomposition[30]. The wavelet reconstruction is presented in Fig.2.

Fig.2 Wavelet reconstruction

Figure 2 illustrates that the electricity consumption data are decomposed into four parts, a stable long-term uptrend component, components affected by seasonal and cyclical factors, random fluctuation components, and its corresponding approximation mode. As the time window increases, the time resolution is reduced; as the frequency domain window becomes small, the frequency resolution is significantly enhanced. And also the time resolution decreases with the increase of the time window, and the frequency resolution increases with the frequency domain window becoming smaller. The calculation results show that the error between the original signal and the reconstructed signal is 1.8438×10-8. The value indicates that reconstructed wavelet can be used to do forecasting. The regularity of high-frequency coefficients in the fourth and fifth layers are not obvious, so these two layers are regarded as random fluctuation time series that have low correlation to the original data. Therefore, they are deleted during the prediction process[31]. The low-frequency and high-frequency components are forecasted by the ARIMA and dynamic neural network time series-NAR, respectively.

2.2.2ARIMAbasedforecasting

The data ofRapproxfrom January 2010 to December 2013 are viewed as in-sample data to estimate the stationary. Firstly, the unit root test of in-sample data is carried out, and it is found that the low-frequency part is integrated of order 1. The first order differences series is found to be significant in 10% confidence interval. Therefore, it is appropriate to use ARIMA model to predict low-frequency component. Two models are built according to the correlation as well as autocorrelation graph, and the Akaike information criterion (AIC) and Schwarz Criterion (SC) values are used to select the optimal model. It turns out that the ARIMA (1, 1, 1) model obtains the minimum values of AIC and SC, and the largest values of R-squared (0.977) and Adjusted R-squared (0.977). In addition, the residuals of ARIMA(1,1,1) show that the residuals are white noise, that is, there is no significant correlation of autocorrelation residuals at 1% confidence intervals. Therefore, the model ARIMA (1,1,1) is selected. This model is applied to predicting electricity consumption between 2014 and 2016. The value of the Theil Inequality Coefficient is 0.000 698, which means that this model is suitable for prediction of low-frequency (Rapprox).

2.2.3Dynamicneuralnetworkbasedforecasting

NAR is used to predict the high-frequency part between January 2010 and December 2013. It is sufficient to use one hidden layer[32]. The high-frequency part (Rcd1) from January 2010 to December 2013 was normalized at first to eliminate singular samples for obtaining faster convergence rates. The samples are considered as a target data randomly and divided into three parts, namely, training data (70%), validation data (15%) and testing data (15%). The network is trained by the Levenberg-Marquardt algorithm, which typically requires less time and it can eliminate the over-fitting to a certain extent[33]. The result shows that the usage of three lags with two neurons in the hidden layer is the right choice for forecasting purpose with the fastest convergence and the smallest forecasting error. After getting the prediction results, we need to anti-normalize the forecasted data to get the final prediction result. Figure 3 shows the autocorrelation of error and regression plot.

Fig.3 Network’s performance and regression plot

From Fig.3, it is evident that the value of the mean squared error equals to 0.032 at epoch 3. In consideration of error distribution, all samples are reconstructed at high accuracy. TheRvalue in the regression graph is greater than 0.8, showing a good regression value between the target value and the network output[34]. This indicates that

network output does not deviate from the target value, and there is a high correlation between the two values. The same training method and algorithm are used forRcd2andRcd3, and the optimal architectures are acquired. The number of hidden neurons, the number of lags, and the percentage of training validation are presented in Table 3.

Table 3Architecture of NAR models for high-frequency components

Because the training samples are normalized before the network training, the predicted data need to be anti-normalized, and then, the prediction results of the high-frequency part (Rcd1,Rcd2,Rcd3) are obtained. The final prediction results require the combination of low-frequency data (Rapprox) and high-frequency data (Rcd1,Rcd2,Rcd3).

2.3 STS model based forecasting

The time series data from January 2010 to December 2013 were logarithmically transformed to reduce heteroscedasticity. According to the Bai and Perron test, there exists a structural break, so the time series is modeled with a dummy variable to capture intervention effects. The whole model for the observed time series data can be described by the following equation[35].

where,wtδtis the dummy variable. Andwt=0,t<2010M12,wt=1,t≥2010M12.

After 61 iterations, the model converges strongly and is stable. The log-likelihood is 125.677. Meanwhile, the prediction error variance is 3.255 81×10-5. Std.error is 0.006. The heteroscedasticity testH(10) is 0.94, larger than the critical value of 0.5. Durbin-Watson statistics is 1.66, which implies no sequence correlation existing in residuals.Q(24,18), the Box-LjungQ-statisticstest, is the result of autocorrelation. The result is 18.80, which is greater than the critical value of 0.1.R2representing the determination’s coefficient is 0.96. Modified Schwarz’ criteria is -9.54. Moreover, Bayesian information criterion is -8.80. The coefficients of auto regressive AR (2) arec1=0.721 andc2=-0.09, and sincec1+c2<1, the model is steady[36].

The above statistics show model passed the entire diagnostic test. Therefore, the model is the best fit for the data. The variances of disturbance terms are listed in Table 4.

Table 4 Variances of disturbance terms

2.4 Forecasting performance criteria

The evaluation of prediction effect is a very important part in forecasting research. In order to evaluate the prediction effect of the above model, the average absolute error percentage (MAPE) and relative error estimation (RE) were used to compare the predicted data with the actual data.

MAPEis a measure of accuracy as a percentage and is defined as

(19)

REcan be expressed by

(20)

In this paper, the hybrid model and STS model are used to forecast China’s electricity consumption from January 2010 to December 2016. The predicted results are shown in Fig. 4 and Table 5.

Fig.4 Forecasting results of proposed models

Figure 4 shows the comparison between the predicted value and the original value, and the predicted results of the hybrid model are closer to the original one. The error value is shown in Table 5.

Table 5 Error values of the hybrid model and STS model

In measuring forecasting performance, a smallerMAPEorREindicates better performance of forecasting model. As shown in Fig.4 and Table 5, the results ofMAPEandREof the hybrid model are 7.97% and 0.012, respectively. The wavelet-ARIMA-NAR model shows lower values both inMAPEandREcompared to STS model, meaning a better performance of the wavelet-ARIMA-NAR model.

3 Conclusions

Due to the complex characteristics of the monthly time series of electricity consumption and the impact of economic policies and natural disasters, there may have structural breaks. In order to improve the prediction accuracy of the model, a hybrid model (wavelet-ARIMA-NAR) and a STS model with structural breaks are constructed to predict the electricity consumption. The empirical results show that the performance of hybrid model is better than that of the STS model.

(1) In the sample period, China’s electricity consumption has structural breaks. The Bai-Perron method for detecting multiple structural breaks can be used to test the sample sequence. The results show that there are two structural breaks in the whole sample period.

(2) The main factors of electricity consumption in China are seasonal and trend. According to the results of disturbance term, the main influencing factors of electricity consumption are level and seasonal because of the same order of magnitude. The influence of observation disturbance error is the next, while the slope and autoregressive have little effects on electricity consumption of China.

(3) The performance of hybrid model on the forecast of China’s electricity consumption is better than that of the STS model. The time series are decomposed into low-frequency and high-frequency parts by wavelet analysis, which represent periodicity, seasonal, trend and irregular components. Then, the ARIMA model is used to predict the low-frequency part, and the NAR model predicts the high-frequency part. TheMAPEandREvalues of the wavelet-ARIMA-NAR model are 7.97% and 0.012, respectively. The prediction ability of hybrid model is much better than that of the STS model for electricity consumption with structural breaks, which indicates that wavelet decomposition model has better prediction ability for variables with complex features and structural breaks. This conclusion is the same as that result of Aussem[38]. The fluctuation of each feature and its contribution to the original data can be accurately idenfied by this model, and it can be applied to other economic variables in the future, and also its prediction performance can be studied.