CN104268408A

CN104268408A - Energy consumption data macro-forecast method based on wavelet coefficient ARMA model

Info

Publication number: CN104268408A
Application number: CN201410507466.0A
Authority: CN
Inventors: 于凤芹; 於敏
Original assignee: Jiangnan University
Current assignee: Jiangnan University
Priority date: 2014-09-28
Filing date: 2014-09-28
Publication date: 2015-01-07

Abstract

The invention belongs to a method in the field of macro prediction of energy consumption data. Since wavelet multi-scale analysis can well represent the essential characteristics of data and obtain more detailed information, energy consumption data has multi-scale characteristics due to its randomness and noise fluctuation. Using wavelet analysis to perform multi-scale decomposition and wavelet denoising processing on energy consumption data, and combined with ARMA model to make macro prediction on energy consumption data. The present invention first performs wavelet multi-scale decomposition on energy consumption data, and after obtaining wavelet coefficients at different scales, removes wavelet coefficients belonging to noise and retains wavelet coefficients of useful signals to achieve the purpose of denoising energy consumption data. Then, an ARMA model that can reflect its essential law is established for the wavelet coefficients of each scale after denoising, and the wavelet coefficients of each scale are predicted with the built model. Finally, the prediction result is obtained by using the idea of wavelet reconstruction to obtain the final prediction result. The accuracy of energy consumption data prediction is improved by denoising and predicting processing of wavelet coefficients at each scale of energy consumption data.

Description

A Macroscopic Prediction Method of Energy Consumption Data Based on Wavelet Coefficient ARMA Model

技术领域 technical field

本发明属于能耗数据宏观预测领域的一种方法。运用小波分析对能耗数据进行多尺度分解和小波去噪，并结合ARMA模型对能耗数据进行预测。首先对数据进行小波去噪处理，然后对处理后的小波系数建立ARMA模型进行预测，最后运用小波重构得到最终的预测结果。通过小波分析的方法可以对能耗数据进行小波分解后去噪处理，达到对能耗数据去噪的目的。本发明利用小波的多尺度的理论从细节更准确的预测能耗数据，提高预测数据的精确性。 The invention belongs to a method in the field of macro prediction of energy consumption data. Using wavelet analysis to perform multi-scale decomposition and wavelet denoising on energy consumption data, and combined with ARMA model to predict energy consumption data. Firstly, wavelet denoising is performed on the data, then an ARMA model is built on the processed wavelet coefficients for prediction, and finally the final prediction result is obtained by wavelet reconstruction. Through the method of wavelet analysis, the energy consumption data can be de-noised after wavelet decomposition, so as to achieve the purpose of de-noising the energy consumption data. The invention utilizes the multi-scale theory of wavelet to more accurately predict energy consumption data from details, and improves the accuracy of prediction data. the

背景技术 Background technique

能源是经济增长的动力，能源主要包括原煤、原油、天然气、水电、核电等。能耗数据就是指对具体能源消耗的数据。能耗预测是通过能源消耗的历史和现状，预测未来的能源消耗的状况。 Energy is the driving force of economic growth, and energy mainly includes raw coal, crude oil, natural gas, hydropower, nuclear power, etc. Energy consumption data refers to the data on specific energy consumption. Energy consumption prediction is to predict the future energy consumption situation through the history and current situation of energy consumption. the

能耗预测的理论研究开始于20世纪中叶，这个时期的预测方法主要以经典预测为主。方法有：比例法、单耗法、弹性系数方法、比例系数增长法等，用这些简单方法预测得到的结果不够准确，精度较差，所以预测效果不好。随着能耗预测理论研究的丰富与发展，用于能耗预测的方法越来越，多如回归方法、经济计量模型法、灰色模型法、时间序列法、小波分析预测法、人工神经网络法等。 Theoretical research on energy consumption forecasting began in the middle of the 20th century, and the forecasting methods in this period were mainly classical forecasting. Methods include: proportional method, unit consumption method, elastic coefficient method, proportional coefficient growth method, etc. The prediction results obtained by these simple methods are not accurate enough and the precision is poor, so the prediction effect is not good. With the enrichment and development of theoretical research on energy consumption prediction, there are more and more methods for energy consumption prediction, such as regression method, econometric model method, gray model method, time series method, wavelet analysis and prediction method, artificial neural network method wait. the

时间序列分析法是以时间角度来分析数据序列的变化趋势，是一种研究过去和未来数据之间关系的方法。由于能耗数据产生的随机性和噪声波动性，能耗数据存在多尺度特征。小波多尺度分析可以很好地表现数据的本质特征并获得更多的细节信息，所以对能耗数据进行小波多尺度分解。在得到不同尺度下的小波系数后，将属于噪声的小波系数去掉，保留有用信号的小波系数，达到对能耗数据去噪的目的。对去噪后的各尺度下的小波系数建立能反应其本质规律ARMA模型，用所建模型对各尺度小波系数分别进行预测，将预测结果运用小波重构的思想得到最终的预测结果。通过对能耗数据各尺度下的小波系数去噪和预测处理，从而提高能耗数据预测的准确性。 Time series analysis is to analyze the change trend of data series from a time perspective, and it is a method to study the relationship between past and future data. Due to the randomness and noise fluctuation of energy consumption data, energy consumption data has multi-scale characteristics. Wavelet multi-scale analysis can well represent the essential characteristics of data and obtain more detailed information, so wavelet multi-scale decomposition is performed on energy consumption data. After obtaining the wavelet coefficients at different scales, the wavelet coefficients belonging to noise are removed, and the wavelet coefficients of useful signals are retained to achieve the purpose of denoising energy consumption data. For the denoised wavelet coefficients at each scale, an ARMA model that can reflect its essential law is established, and the built model is used to predict the wavelet coefficients of each scale respectively, and the prediction results are obtained using the idea of wavelet reconstruction to obtain the final prediction results. The accuracy of energy consumption data prediction is improved by denoising and predicting processing of wavelet coefficients at each scale of energy consumption data. the

发明内容 Contents of the invention

因为能耗数据的噪声波动性，所以对能耗数据小波分解后产生的高低频系数采用小波去噪处理。小波去噪的基本思路是将带噪信号经过小波变换后，把信号分解到各个尺度，在每个尺度下将属于噪声的小波系数去除，保留有用的小波系数，达到信号去噪的目的。小波阈值去噪是目前应用最广范的方法，当小波系数大于某个临界阈值时系数保留，相反则舍弃。所以在本专利中对小波分解后高频小波系数采用默认阈值去噪处理，然后对去噪处理后的各尺度下的小波系数分别建立ARMA模型进行预测。与传统的直接预测方法相比，对不同尺度下的小波系数分别建立较能反映其本质规律的ARMA模型，这样进一步增加预测的精确性。 Because of the noise fluctuation of energy consumption data, the high and low frequency coefficients generated after wavelet decomposition of energy consumption data are processed by wavelet denoising. The basic idea of wavelet denoising is to decompose the noisy signal into various scales after wavelet transform, remove the wavelet coefficients belonging to the noise at each scale, and retain the useful wavelet coefficients to achieve the purpose of signal denoising. Wavelet threshold denoising is currently the most widely used method. When the wavelet coefficient is greater than a certain critical threshold, the coefficient is retained, otherwise it is discarded. Therefore, in this patent, the high-frequency wavelet coefficients after wavelet decomposition are denoised by default threshold, and then the ARMA models are respectively established for prediction of the wavelet coefficients at each scale after denoising. Compared with the traditional direct prediction method, ARMA models are established for the wavelet coefficients at different scales, which can better reflect their essential laws, so as to further increase the accuracy of prediction. the

ARMA模型根据时间序列本身的数字特征，来寻找变量当前值与其若干滞后值及误差项之间的关系，并在此基础上对后期数据进行预测。但运用ARMA模型的一个前提条件预测的时间序列是平稳的，而经过小波分解后的高低频数据不一定是平稳序列，先对序列的平稳性进行检验。样本中观测值之间的相关程度称为自相关系数，平稳序列之间距离越大相关性越差，所以平稳序列自相关系数会很快地衰减向零，反之非平稳序列的自相关系数衰减向零的速度缓慢。所以计算序列的自相关系数，可以检验序列是否为平稳序列。由于足够多次的差分运算可以充分地提取非平稳序列中的确定信息，所以对于非平稳时间序列，经过d阶差分的方法可以转变为平稳序列。 The ARMA model is based on the digital characteristics of the time series itself to find the relationship between the current value of the variable and its several lag values and error items, and on this basis to predict the later data. However, a precondition of the ARMA model is to predict that the time series is stationary, but the high and low frequency data after wavelet decomposition is not necessarily a stationary sequence. The stationarity of the sequence is first tested. The degree of correlation between the observations in the sample is called the autocorrelation coefficient. The greater the distance between the stationary series, the worse the correlation, so the autocorrelation coefficient of the stationary series will quickly decay to zero, otherwise the autocorrelation coefficient of the non-stationary series decays The speed towards zero is slow. Therefore, calculating the autocorrelation coefficient of the sequence can test whether the sequence is a stationary sequence. Since enough differential operations can fully extract the definite information in the non-stationary sequence, for non-stationary time series, the method of d-order difference can be transformed into a stationary sequence. the

用差分后的平稳序列的每个序列值x_t，x_t-1，…，x_t-k建立ARMA模型如下： The ARMA model is established by using each sequence value x _t , x _t-1 , ..., x _tk of the stationary sequence after difference as follows:

${x x}_{t t} = = {Σ Σ}_{k k = = 11}^{p p} {a a}_{k k} {x x}_{t t - - k k} + + {ϵ ϵ}_{t t} + + {Σ Σ}_{k k = = 11}^{q q} {b b}_{k k} {ϵ ϵ}_{t t - - k k} - - - - - - ((11))$

式中随机干扰ε_t为均值为零，方差为σ²的白噪声。a₁，a₂，…，a_p；b₁，b₂…，b_q不全为零，分别称为AR系数和MA系数。p,q分别称为AR阶数和MA阶数。 In the formula, random disturbance ε _t is white noise with zero mean and variance σ ² . a ₁ , a ₂ , ..., a _p ; b ₁ , b ₂ ..., b _q are not all zero, which are called AR coefficients and MA coefficients respectively. p and q are called AR order and MA order respectively.

样本的自相关系数r_k表示样本中相隔k期的观测值之间的相关程度，其值可以根据公式如下公式来估计： The autocorrelation coefficient r _k of the sample indicates the degree of correlation between the observed values separated by k periods in the sample, and its value can be estimated according to the following formula:

${\overset{^^}{r r}}_{k k} = = \frac{{Σ Σ}_{t t = = 11}^{n no - - k k} (({x x}_{t t} - - \overset{&OverBar; &OverBar;}{x x})) (({x x}_{t t + + k k} - - \overset{&OverBar; &OverBar;}{x x}))}{{Σ Σ}_{t t = = 11}^{n no} {(({x x}_{t t} - - \overset{&OverBar; &OverBar;}{x x}))}^{22}} - - - - - - ((22))$

其中，n为样本量，k为滞后期，代表样本均值。 Among them, n is the sample size, k is the lag period, stands for the sample mean.

假设ARMA模型p,q已知，则该模型需要估计的未知参数：a₁，a₂，…，a_p；b₁，b₂…，b_q；σ²。首先估计AR参数ARMA序列的自相关函数满足延伸的尤利-沃克(Yule-Walker)方程，代入该方程就可以得到参数a_i的估计值 Assuming that the ARMA model p and q are known, the model needs to estimate the unknown parameters: a ₁ , a ₂ , ..., a _p ; b ₁ , b ₂ ..., b _q ; σ ² . First estimate the AR parameters The autocorrelation function of the ARMA sequence satisfies the extended Yule-Walker equation, Substituting into this equation, the estimated value of the parameter a _i can be obtained

然后估计MA参数。将估计出AR的参数代入式(1)得 Then estimate the MA parameters. will estimate the parameters of AR Substitute into formula (1) to get

${y the y}_{t t} = = {x x}_{t t} - - {Σ Σ}_{j j = = 11}^{p p} {\overset{^^}{{a a}_{j j}} x x}_{t t - - j j} = = {ϵ ϵ}_{t t} + + {Σ Σ}_{j j = = 11}^{q q} {b b}_{j j} {ϵ ϵ}_{t t - - j j} - - - - - - ((33))$

可以看出y_t是MA(q)过程的近似观测数据，序列y_t的自相关系数 It can be seen that y _t is the approximate observation data of the MA(q) process, and the autocorrelation coefficient of the sequence y _t

$\overset{^^}{{r r}_{ym ym}} = = \overset{^^}{{r r}_{xm xm}} - - {Σ Σ}_{k k = = 11}^{p p} \overset{^^}{{a a}_{k k}} {\overset{^^}{r r}}_{x x ((m m - - k k))},, 00 \leq \leq m m \leq \leq q q - - - - - - ((44))$

已知MA(q)模型的正则方程： $r_{ym} = σ^{2} Σ_{i = 0}^{q} b_{i} b_{i + m}, 0 \leq m \leq q - - - (5)$ The regular equation of the MA(q) model is known: $r_{ym} = σ^{2} Σ_{i = 0}^{q} b_{i} b_{i + m}, 0 \leq m \leq q - - - (5)$

将代入上式，就可以求出MA部分的参数将所估计的参数采用最小信息量准则(AIC:An Information Criterion,)作为定阶的准则。AIC函数定义为： Will Substituting into the above formula, the parameters of the MA part can be obtained The estimated parameters adopt the minimum information criterion (AIC: An Information Criterion,) as the order-setting criterion. The AIC function is defined as:

$AIC AIC ((l l)) = = log log {\overset{^^}{σ σ}}^{22} ((l l)) + + \frac{22 l l}{n no},, l l = = p p + + q q - - - - - - ((66))$

实际应用中模型的阶数都比较低，所以从低阶到高阶对p,q不同取值分别建立模型，对参数进行矩估计后，比较各模型AIC的值，使其达到最小的模型就是所选的最佳预测模型。用选择的最佳预测模型对小波系数进行预测，得到小波系数的预测值。 In practical applications, the order of the model is relatively low, so the models are established for different values of p and q from the low order to the high order, and after the moment estimation of the parameters, the AIC value of each model is compared to make it the smallest model. The best predictive model selected. Predict the wavelet coefficients with the selected best prediction model, and obtain the predicted value of the wavelet coefficients. the

最后对高低频系数进行小波重构，得到最后的预测结果。重构时运用Mallat算法，先将第三层的低频系数和第三层的高频系数预测结果经过滤波器系数加权和得到第二层的低频系数的预测值；结合第二层高频系数预测值得到第一层的低频系数预测值；最后结合第一层高频系数预测值，得到最终预测结果。 Finally, wavelet reconstruction is performed on the high and low frequency coefficients to obtain the final prediction result. When reconstructing, the Mallat algorithm is used. First, the low-frequency coefficients of the third layer and the prediction results of the high-frequency coefficients of the third layer are weighted by filter coefficients to obtain the predicted value of the low-frequency coefficients of the second layer; combined with the prediction of the high-frequency coefficients of the second layer The predicted value of the low-frequency coefficient of the first layer is obtained; finally, the final prediction result is obtained by combining the predicted value of the high-frequency coefficient of the first layer. the

附图说明 Description of drawings

图1本发明的总体思路 The general train of thought of the present invention of Fig. 1

具体实施方式 Detailed ways

步骤1：能耗数据生成。 Step 1: Energy consumption data generation. the

在国家统计年鉴上获得所需要的从1978-2012年的能源消费总量的数据，将获得的数据作为时间序列进行分析处理。 Obtain the required data of total energy consumption from 1978 to 2012 in the National Statistical Yearbook, and analyze and process the obtained data as a time series. the

步骤2：用小波对能耗数据进行去噪处理。 Step 2: Use wavelet to denoise the energy consumption data. the

(1)对进行小波分解的小波函数进行选择。将经过小波变换得到的图形与实际的能耗序列进行对比，观察小波变换得到的图形是否具有原图形的外貌特征，从而选取合适的小波函数。 (1) Select the wavelet function for wavelet decomposition. Compare the graph obtained by wavelet transform with the actual energy consumption sequence, and observe whether the graph obtained by wavelet transform has the appearance characteristics of the original graph, so as to select the appropriate wavelet function. the

(2)将能耗数据通过所选小波函数进行三层分解，得到第三层的低频系数ca3和第一、二、三层的高频系数cd1、cd2、cd3。 (2) Decompose the energy consumption data into three layers through the selected wavelet function, and obtain the low-frequency coefficient ca3 of the third layer and the high-frequency coefficients cd1, cd2, and cd3 of the first, second, and third layers. the

(3)对分解后的高低频系数ca3、cd1、cd2、cd3采用默认阈值去噪。 (3) Denoise the decomposed high and low frequency coefficients ca3, cd1, cd2, and cd3 with default thresholds. the

步骤3：将低频数据和三层高频数据分别建立合适的ARMA模型进行预测。 Step 3: Establish appropriate ARMA models for low-frequency data and three-layer high-frequency data for prediction. the

(1)对系数进行平稳性检查：通过计算它们的自相关系数，观察是否很快趋于零来判断是不是平稳序列。如果是非平稳序列就将数据进行一阶差分运算，再判断平稳性，若非平稳就继续差分运算直到序列是平稳序列。 (1) Check the stationarity of the coefficients: by calculating their autocorrelation coefficients and observing whether they tend to zero quickly to judge whether it is a stationary sequence. If it is a non-stationary sequence, the first-order difference operation is performed on the data, and then the stationarity is judged. If it is not stable, the difference operation is continued until the sequence is a stationary sequence. the

(2)计算序列样本的自相关系数运用尤利-沃克(Yule-Walker)方程，代入该方程就可以得到参数a₁，a₂，…，a_p的估计值 (2) Calculate the autocorrelation coefficient of the sequence sample Using the Yule-Walker equation, By substituting this equation, the estimated values of parameters a ₁ , a ₂ ,..., a _p can be obtained

(3)由公式(3)可知y_t是MA(q)过程的近似观测数据，并且计算出序列y_t的自相关系数将代入MA(q)模型的正则方程，就可以求出MA部分的参数 (3) From the formula (3), it can be known that y _t is the approximate observation data of the MA(q) process, and the autocorrelation coefficient of the sequence y _t is calculated Will By substituting the regular equation of the MA(q) model, the parameters of the MA part can be obtained

(4)选择的最佳预测模型：从低阶到高阶对p,q不同取值分别建立模型，对参数进行估计后，比较各模型AIC的值，使其达到最小的模型就是所选的最佳预测模型。 (4) Select the best prediction model: build models for different values of p and q from low-order to high-order, and after estimating the parameters, compare the AIC values of each model to make it the smallest model is the selected one best predictive model. the

(5)用所选的最佳ARMA模型对高低频系数运用递推方程进行2步预测，得到所需各层的高低频系数的预测值。 (5) Use the selected optimal ARMA model to predict the high and low frequency coefficients using the recursive equation in two steps to obtain the predicted values of the high and low frequency coefficients of each layer required. the

步骤4：小波重构后得到最终的预测结果。 Step 4: Get the final prediction result after wavelet reconstruction. the

重构时运用Mallat算法，先将第三层的低频系数和第三层的高频系数2步预测结果经过滤波器系数加权后得到第二层的低频系数的2步预测值；结合第二层高频系数2步预测值得到第一层的低频系数2步预测值；最后结合第一层高频系数2步预测值得到待预测年份的能源消耗总量的预测值。 When reconstructing, the Mallat algorithm is used. First, the low-frequency coefficients of the third layer and the high-frequency coefficients of the third layer are weighted by the filter coefficients to obtain the two-step prediction values of the low-frequency coefficients of the second layer; combined with the second layer The 2-step forecast value of the high-frequency coefficient is used to obtain the 2-step forecast value of the low-frequency coefficient of the first layer; finally, the forecast value of the total energy consumption in the year to be predicted is obtained by combining the 2-step forecast value of the high-frequency coefficient of the first layer. the

Claims

1. A macro-prediction method for energy consumption data based on wavelet coefficient ARMA model, characterized in that:

Multi-scale wavelet decomposition is performed on the energy consumption data. At each scale, the wavelet threshold denoising method is adopted. When the wavelet coefficient is greater than a certain critical threshold, the coefficient is retained, otherwise it is discarded, and the wavelet coefficient belonging to the noise is removed to retain the useful Wavelet coefficients to achieve the purpose of signal denoising. Then the ARMA model is established for the wavelet coefficients of each scale after denoising processing to predict, so as to increase the accuracy of prediction.

2. a kind of energy consumption data macro-prediction method based on wavelet coefficient ARMA model as claimed in claim 1, it is characterized in that each sequence value x _t of the stationary time series after using difference, x _t-1 , ..., x _tk builds the ARMA model as follows:

{x x}_{t t} = = {Σ Σ}_{k k = = 11}^{p p} {a a}_{k k} {x x}_{t t - - k k} + + {ϵ ϵ}_{t t} + + {Σ Σ}_{k k = = 11}^{q q} {b b}_{k k} {ϵ ϵ}_{t t - - k k} - - - - - - ((11))

In the formula, random disturbance ε _t is white noise with zero mean and variance σ ² . a ₁ , a ₂ , ..., a _p ; b ₁ , b ₂ ..., b _q are not all zero.

The autocorrelation coefficient r _k of the sample indicates the degree of correlation between the observed values separated by k periods in the sample, which can be estimated according to the following formula:

{\overset{^^}{r r}}_{k k} = = \frac{{Σ Σ}_{t t = = 11}^{n no - - k k} (({x x}_{t t} - - \overset{&OverBar; &OverBar;}{x x})) (({x x}_{t t + + k k} - - \overset{&OverBar; &OverBar;}{x x}))}{{Σ Σ}_{t t = = 11}^{n no} {(({x x}_{t t} - - \overset{&OverBar; &OverBar;}{x x}))}^{22}} - - - - - - ((22))

Among them, n is the sample size, k is the lag period, stands for the sample mean.

3. A kind of macro-prediction method of energy consumption data based on wavelet coefficient ARMA model as claimed in claim 1, it is characterized in that the unknown parameter of described estimated ARMA model: a ₁ , a ₂ ,..., a _p ; b ₁ , b ₂ ..., b _q ; σ ² .

First estimate the AR parameters The autocorrelation function of the ARMA sequence satisfies the extended Yule-Walker equation, Substituting into this equation, the estimated value of the parameter a _i can be obtained Then estimate the MA parameters, which will estimate the parameters of the AR Substitute into formula (1) to get

{y the y}_{t t} = = {x x}_{t t} - - {Σ Σ}_{j j = = 11}^{p p} {\overset{^^}{{a a}_{j j}} x x}_{t t - - j j} = = {ϵ ϵ}_{t t} + + {Σ Σ}_{j j = = 11}^{q q} {b b}_{j j} {ϵ ϵ}_{t t - - j j} - - - - - - ((33))

It can be seen that y _t is the approximate observation data of the MA(q) process, and the autocorrelation coefficient of the sequence y _t

\overset{^^}{{r r}_{ym ym}} = = \overset{^^}{{r r}_{xm xm}} - - {Σ Σ}_{k k = = 11}^{p p} \overset{^^}{{a a}_{k k}} {\overset{^^}{r r}}_{x x ((m m - - k k))},, 00 \leq \leq m m \leq \leq q q - - - - - - ((44))

The regular equation of the MA(q) model is known:

r_{ym} = σ^{2} Σ_{i = 0}^{q} b_{i} b_{i + m}, 0 \leq m \leq q - - - (5)

Will Substituting into the above formula, the parameters of the MA part can be obtained

4. A kind of energy consumption data macro-prediction method based on wavelet coefficient ARMA model as claimed in claim 1, it is characterized in that described parameter adopts minimum information criterion (AIC: An Information Criterion,) as definite level criteria. The AIC function is defined as:

AIC AIC ((l l)) = = log log {\overset{^^}{σ σ}}^{22} ((l l)) + + \frac{22 l l}{n no},, l l = = p p + + q q - - - - - - ((66))

In practical applications, the order of the model is relatively low, so the models are established for different values of p and q from the low order to the high order, and after the moment estimation of the parameters, the AIC value of each model is compared to make it the smallest model. The best predictive model selected. Predict the wavelet coefficients with the selected best prediction model, and obtain the predicted value of the wavelet coefficients.

5. A method for macroscopic prediction of energy consumption data based on wavelet coefficient ARMA model as claimed in claim 1, characterized in that said high and low frequency coefficients are reconstructed by wavelet to obtain the final prediction result.

When reconstructing, the Mallat algorithm is used. First, the low-frequency coefficients of the third layer and the prediction results of the high-frequency coefficients of the third layer are weighted by the filter coefficients to obtain the predicted value of the low-frequency coefficients of the second layer; combined with the prediction of the high-frequency coefficients of the second layer The predicted value of the low-frequency coefficient of the first layer is obtained; finally, the final prediction result is obtained by combining the predicted value of the high-frequency coefficient of the first layer.