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

Abstract

The invention belongs to a method in the field of energy consumption data macro-forecast. The essential characteristics of data can be well presented and more detail information can be obtained by virtue of wavelet multi-scale analysis, and due to randomness and noise volatility, energy consumption data have multi-scale characteristics. Multi-scale decomposition and wavelet denoising processing are performed on the energy consumption data by virtue of wavelet analysis, and macro-forecast is performed on the energy consumption data in combination with an ARMA model. The method comprises the steps of firstly, performing wavelet multi-scale analysis on the energy consumption data, and after obtaining the wavelet coefficients at different scales, removing the wavelet coefficients belonging to noise and remaining the wavelet coefficients of usable signals, thereby achieving the purpose of denoising the energy consumption data, secondly, establishing the ARMA model capable of reflecting the essential rules of the denoised wavelet coefficients at various scales for the denoised wavelet coefficients, and forecasting the wavelet coefficient at each scale by use of the established model, and finally, obtaining the final forecast result from the prediction results by virtue of wavelet reconstruction. As a result, the accuracy of energy consumption data forecast can be improved by performing denoising and forecast processing on the wavelet coefficients at various scales of the energy consumption data.

Description

A kind of energy consumption data macro-forecast method based on wavelet coefficient arma modeling

Technical field

The invention belongs to a kind of method in energy consumption data macro-forecast field.Use wavelet analysis to carry out multi-resolution decomposition and Wavelet Denoising Method to energy consumption data, and in conjunction with arma modeling, energy consumption data is predicted.First Wavelet Denoising Method process is carried out to data, then arma modeling is set up to the wavelet coefficient after process and predict, finally use wavelet reconstruction to obtain final predicting the outcome.Denoising after wavelet decomposition can be carried out to energy consumption data by the method for wavelet analysis, reach the object to energy consumption data denoising.The present invention utilizes the multiple dimensioned theory of small echo from details prediction of energy consumption data more accurately, improves the accuracy of predicted data.

Background technology

The energy is the power of economic growth, and the energy mainly comprises raw coal, crude oil, rock gas, water power, nuclear power etc.Energy consumption data just refers to the data to concrete energy resource consumption.Energy consumption prediction is the situation of the history and current situation by energy resource consumption, the energy resource consumption that prediction is following.

The theoretical research of energy consumption prediction starts from 20 middle of century, and the Forecasting Methodology in this period is mainly predicted as master with classics.Method has: rule of three, unit consumption method, elasticity coefficient method, scale-up factor growth method etc., predict that the result obtained is not accurate enough by these straightforward procedures, precision is poor, so prediction effect is bad.Along with the abundant of energy consumption prediction theory research and development, for energy consumption prediction method more and more, many as homing method, econometric model method, gray forecast approach, time series method, wavelet analysis predicted method, artificial neural network method etc.

Time series analysis method is with time angle to analyze the variation tendency of data sequence, is a kind ofly to study over and the method for relation between Future Data.The randomness produced due to energy consumption data and noise fluctuations, there is Analysis On Multi-scale Features in energy consumption data.Wavelet multi-scale analysis can well representation of data essential characteristic and obtain more detailed information, so carry out Multiscale Wavelet Decomposition to energy consumption data.After obtaining the wavelet coefficient under different scale, the wavelet coefficient belonging to noise is removed, retain the wavelet coefficient of useful signal, reach the object to energy consumption data denoising.Wavelet coefficient under each yardstick after denoising being set up and can react its essential laws arma modeling, with institute's established model, each multi-scale wavelet coefficient is predicted respectively, using the thought of wavelet reconstruction to obtain final predicting the outcome by predicting the outcome.By to the Wavelet coefficient denoising under each yardstick of energy consumption data and prediction processing, thus improve the accuracy of energy consumption data prediction.

Summary of the invention

Because the noise fluctuations of energy consumption data, so adopt Wavelet Denoising Method process to the low-and high-frequency coefficient produced after energy consumption data wavelet decomposition.The basic ideas of Wavelet Denoising Method are by signals with noise after wavelet transformation, and signal decomposition to each yardstick, removed by the wavelet coefficient belonging to noise under each yardstick, the wavelet coefficient remained with, reaches the object of signal denoising.Wavelet threshold denoising is the method for current most widely used model, and when wavelet coefficient is greater than certain threshold limit value, coefficient retains, and then gives up on the contrary.So adopt default threshold denoising to high-frequency wavelet coefficient after wavelet decomposition in this patent, then arma modeling is set up respectively to the wavelet coefficient under each yardstick after denoising and predict.Compared with traditional DIRECT FORECASTING METHOD, the arma modeling compared with reflecting its essential laws is set up respectively to the wavelet coefficient under different scale, so further accuracy increasing prediction.

Arma modeling, according to the numerical characteristic of time series itself, is found the relation between variable currency and its some lagged value and error term, and is predicted late time data on this basis.But the time series using a precondition prediction of arma modeling is stable, and the low-and high-frequency data not necessarily stationary sequence after wavelet decomposition, first the stationarity of sequence is tested.Degree of correlation in sample between observed reading is called coefficient of autocorrelation, and the larger correlativity of spacing of stationary sequence is poorer, so stationary sequence coefficient of autocorrelation can be decayed to zero soon, otherwise the decay of the coefficient of autocorrelation of non-stationary series is slow to the speed of zero.So the coefficient of autocorrelation of the sequence of calculation, can checking sequence whether be stationary sequence.Can extract the comformed information in non-stationary series fully due to enough calculus of differencess repeatedly, so for nonstationary time series, the method for dividing through d jump can change stationary sequence into.

With each sequential value x of differentiated stationary sequence _t, x _t-1..., x _t-kset up arma modeling as follows:

$x_t=\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{a}_k{x}_{t-k}+{\mathrm{\ϵ}}_t+\underset{k=1}{\overset{q}{\mathrm{\Σ}}}{b}_k{\mathrm{\ϵ}}_{t-k}---\left(1\right)$

Random disturbance ε in formula _tfor average is zero, variance is σ ²white noise.A ₁, a ₂..., a _p; b ₁, b ₂, b _qbe not zero entirely, be called AR coefficient and MA coefficient.P, q are called AR exponent number and MA exponent number.

The coefficient of autocorrelation r of sample _kdegree of correlation between the observed reading representing in sample the k phase of being separated by, its value can be estimated according to the following formula of formula:

${\hat{r}}_k=\frac{\underset{t=1}{\overset{n-k}{\mathrm{\Σ}}}(x_t-\stackrel{\‾}{x})(x_{t+k}-\stackrel{\‾}{x})}{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}{(x_t-\stackrel{\‾}{x})}^2}---\left(2\right)$

Wherein, n is sample size, and k is the lag period, representative sample average.

Suppose arma modeling p, q is known, then this model needs the unknown parameter of estimation: a ₁, a ₂..., a _p; b ₁, b ₂, b _q; σ ².First AR parameter is estimated the autocorrelation function of ARMA sequence meets You Li-Wo Ke (Yule-Walker) equation of extension, substitute into this equation and just can obtain parameter a _iestimated value

Then MA parameter is estimated.The parameter of AR will be estimated substitution formula (1)

$y_t=x_t-\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{\widehat{a_j}x}_{t-j}={\mathrm{\ϵ}}_t+\underset{j=1}{\overset{q}{\mathrm{\Σ}}}{b}_j{\mathrm{\ϵ}}_{t-j}---\left(3\right)$

Y can be found out _tthe approximate observation data of MA (q) process, sequences y _tcoefficient of autocorrelation

$\widehat{r_{\mathrm{ym}}}=\widehat{r_{\mathrm{xm}}}-\underset{k=1}{\overset{p}{\mathrm{\Σ}}}\widehat{a_k}{\hat{r}}_{x(m-k)},0\≤m\≤q---\left(4\right)$

The canonical equation of known MA (q) model: $r_{\mathrm{ym}}={\mathrm{\σ}}^2\underset{i=0}{\overset{q}{\mathrm{\Σ}}}{b}_i{b}_{i+m},0\≤m\≤q---\left(5\right)$

Will substitute into above formula, just can obtain the parameter of MA part adopt Akaike information criterion (AIC:An Information Criterion) as the criterion of determining rank estimated parameter.AIC function is defined as:

$\mathrm{AIC}\left(l\right)=\log {\widehat{\mathrm{\σ}}}^2\left(l\right)+\frac{2l}{n},l=p+q---\left(6\right)$

In practical application, the exponent number of model is all lower, so to the different value of p, q Modling model respectively from low order to high-order, after carrying out moments estimation to parameter, the value of more each model AIC, making it reach minimum model is exactly selected optimum prediction model.With the optimum prediction model selected, wavelet coefficient is predicted, obtain the predicted value of wavelet coefficient.

Finally wavelet reconstruction is carried out to low-and high-frequency coefficient, obtain last predicting the outcome.Use Mallat algorithm during reconstruct, the device coefficient weighted sum after filtering that first low frequency coefficient of third layer and the high frequency coefficient of third layer predicted the outcome obtains the predicted value of the low frequency coefficient of the second layer; The low frequency coefficient predicted value of ground floor is obtained in conjunction with second layer high frequency coefficient predicted value; Finally in conjunction with ground floor high frequency coefficient predicted value, finally predicted the outcome.

Accompanying drawing explanation

Fig. 1 general thought of the present invention

Embodiment

Step 1: energy consumption data generates.

Obtaining the data of the required total energy consumption from 1978-2012 national statistics year in view of this, the data of acquisition are carried out analyzing and processing as time series.

Step 2: denoising is carried out to energy consumption data with small echo.

(1) wavelet function carrying out wavelet decomposition is selected.The figure obtained through wavelet transformation and actual energy consumption sequence are contrasted, whether the figure that observation wavelet transformation obtains has the macroscopic features of former figure, thus chooses suitable wavelet function.

(2) energy consumption data is carried out three layers of decomposition by selected wavelet function, obtain the low frequency coefficient ca3 of third layer and high frequency coefficient cd1, cd2, cd3 of first, second and third layer.

(3) default threshold denoising is adopted to low-and high-frequency coefficient ca3, cd1, cd2, the cd3 after decomposition.

Step 3: low-frequency data and three floor height audio data are set up suitable arma modeling respectively and predicts.

(1) stationarity inspection being carried out to coefficient: by calculating their coefficient of autocorrelation, observing and whether going to zero to judge to be stationary sequence very soon.If data are just carried out first order difference computing by non-stationary series, then judge stationarity, if not steadily just continue calculus of differences until sequence is stationary sequence.

(2) coefficient of autocorrelation of sequence of calculation sample use You Li-Wo Ke (Yule-Walker) equation, substitute into this equation and just can obtain parameter a ₁, a ₂..., a _pestimated value

(3) by formula (3) known y _tbe the approximate observation data of MA (q) process, and calculate sequences y _tcoefficient of autocorrelation will substitute into the canonical equation of MA (q) model, just can obtain the parameter of MA part

(4) the optimum prediction model selected: to the different value of p, q Modling model respectively from low order to high-order, after estimating parameter, the value of more each model AIC, making it reach minimum model is exactly selected optimum prediction model.

(5) use recurrence equation to carry out 2 step predictions with selected best arma modeling to low-and high-frequency coefficient, obtain the predicted value of the low-and high-frequency coefficient of required each layer.

Step 4: obtain final predicting the outcome after wavelet reconstruction.

Use Mallat algorithm during reconstruct, after the device coefficient weighting after filtering that first high frequency coefficient 2 step of the low frequency coefficient of third layer and third layer predicted the outcome, obtain 2 step predicted values of the low frequency coefficient of the second layer; The low frequency coefficient 2 step predicted value of ground floor is obtained in conjunction with second layer high frequency coefficient 2 step predicted value; The predicted value of the energy resource consumption total amount in time to be predicted is finally obtained in conjunction with ground floor high frequency coefficient 2 step predicted value.

Claims (5)

1., based on an energy consumption data macro-forecast method for wavelet coefficient arma modeling, it is characterized in that:

Multi-scale wavelet decomposition is carried out to energy consumption data, under each yardstick, adopts wavelet threshold denoising method, when wavelet coefficient is greater than certain threshold limit value, coefficient retains, and then gives up on the contrary, is removed by the wavelet coefficient belonging to noise, the wavelet coefficient remained with, reaches the object of signal denoising.Then set up arma modeling respectively to the wavelet coefficient under each yardstick after denoising to predict, increase the accuracy of prediction.

2. a kind of energy consumption data macro-forecast method based on wavelet coefficient arma modeling as claimed in claim 1, is characterized in that the described each sequential value x with differentiated stationary time series _t, x _t-1..., x _t-kset up arma modeling as follows:

$x_t=\underset{k=1}{\overset{p}{\mathrm{\Σ}}}{a}_k{x}_{t-k}+{\mathrm{\ϵ}}_t+\underset{k=1}{\overset{q}{\mathrm{\Σ}}}{b}_k{\mathrm{\ϵ}}_{t-k}---\left(1\right)$

Random disturbance ε in formula _tfor average is zero, variance is σ ²white noise.A ₁, a ₂..., a _p; b ₁, b ₂, b _qbe not zero entirely.

The coefficient of autocorrelation r of sample _kdegree of correlation between the observed reading representing in sample the k phase of being separated by, can estimate according to following formula:

${\hat{r}}_k=\frac{\underset{t=1}{\overset{n-k}{\mathrm{\Σ}}}(x_t-\stackrel{\‾}{x})(x_{t+k}-\stackrel{\‾}{x})}{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}{(x_t-\stackrel{\‾}{x})}^2}---\left(2\right)$

Wherein, n is sample size, and k is the lag period, representative sample average.

3. a kind of energy consumption data macro-forecast method based on wavelet coefficient arma modeling as claimed in claim 1, is characterized in that the unknown parameter of described estimation arma modeling: a ₁, a ₂..., a _p; b ₁, b ₂, b _q; σ ².

First estimate AR parameter the autocorrelation function of ARMA sequence meets You Li-Wo Ke (Yule-Walker) equation of extension, substitute into this equation and just can obtain parameter a _iestimated value then estimate MA parameter, will the parameter of AR be estimated substitution formula (1)

$y_t=x_t-\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{\widehat{a_j}x}_{t-j}={\mathrm{\ϵ}}_t+\underset{j=1}{\overset{q}{\mathrm{\Σ}}}{b}_j{\mathrm{\ϵ}}_{t-j}---\left(3\right)$

Y can be found out _tthe approximate observation data of MA (q) process, sequences y _tcoefficient of autocorrelation

$\widehat{r_{\mathrm{ym}}}=\widehat{r_{\mathrm{xm}}}-\underset{k=1}{\overset{p}{\mathrm{\Σ}}}\widehat{a_k}{\hat{r}}_{x(m-k)},0\≤m\≤q---\left(4\right)$

The canonical equation of known MA (q) model: $r_{\mathrm{ym}}={\mathrm{\σ}}^2\underset{i=0}{\overset{q}{\mathrm{\Σ}}}{b}_i{b}_{i+m},0\≤m\≤q---\left(5\right)$

Will substitute into above formula, just can obtain the parameter of MA part

4. a kind of energy consumption data macro-forecast method based on wavelet coefficient arma modeling as claimed in claim 1, it is characterized in that described adopting Akaike information criterion (AIC:An Information Criterion) as the criterion of determining rank estimated parameter.AIC function is defined as:

$\mathrm{AIC}\left(l\right)=\log {\widehat{\mathrm{\σ}}}^2\left(l\right)+\frac{2l}{n},l=p+q---\left(6\right)$

In practical application, the exponent number of model is all lower, so to the different value of p, q Modling model respectively from low order to high-order, after carrying out moments estimation to parameter, the value of more each model AIC, making it reach minimum model is exactly selected optimum prediction model.With the optimum prediction model selected, wavelet coefficient is predicted, obtain the predicted value of wavelet coefficient.

5. a kind of energy consumption data macro-forecast method based on wavelet coefficient arma modeling as claimed in claim 1, is characterized in that described carrying out wavelet reconstruction to low-and high-frequency coefficient, obtains last predicting the outcome.

Use Mallat algorithm during reconstruct, the device coefficient weighted sum after filtering that first low frequency coefficient of third layer and the high frequency coefficient of third layer predicted the outcome obtains the predicted value of the low frequency coefficient of the second layer; The low frequency coefficient predicted value of ground floor is obtained in conjunction with second layer high frequency coefficient predicted value; Finally in conjunction with ground floor high frequency coefficient predicted value, finally predicted the outcome.