CN103258069B - A kind of Forecasting Methodology of steel industry electricity needs - Google Patents

Abstract

The invention discloses a method for forecasting electric power demand in the iron and steel industry and load forecasting of the electric power system. This method classifies the influencing factors of electricity consumption in the iron and steel industry, uses a combination of qualitative and quantitative methods to analyze the key influencing factors of electricity consumption in the iron and steel industry, proposes an index system for electricity consumption in the iron and steel industry, and gives a demand forecasting model, for It provides a scientific and practical technical solution for power companies to accurately predict the power demand of related industries and then predict the power demand of the whole society. The invention has the advantages that: it enriches and perfects the existing power demand forecasting method, is of great significance to improving the power demand forecasting level of electric power enterprises, and can produce remarkable economic and social benefits.

Description

A Forecasting Method of Power Demand in Iron and Steel Industry

technical field

The invention relates to the load forecasting of the power system, in particular to the forecasting of the power demand in the iron and steel industry.

Background technique

Power demand forecasting is the basic work of planning, planning, power consumption, dispatching and other departments in the power system. In the process of market-oriented operation of the power industry, power demand forecasting has become one of the core businesses of market transactions, marketing and other departments.

The electricity consumption of the four major energy-consuming industries of iron and steel, non-ferrous metals, chemicals, and non-metallic mineral products accounts for about 1/3 of the electricity consumption of the whole society, and the electricity consumption of high-energy-consuming industries has the characteristics of ups and downs. The reduction has an important impact on the total demand for electricity. The electricity consumption of high energy-consuming industries has the following characteristics:

(1) It accounts for a large proportion of the electricity consumption of the whole society and has a great impact on the growth of electricity consumption. Taking 2010 as an example, the four major energy-intensive industries of iron and steel, non-ferrous metals, chemicals and non-metallic mineral products in the State Grid Corporation’s operating area accounted for 32.1% of the electricity consumption of the whole society. The contribution rate of electricity consumption growth in the whole society is 34%. This fully demonstrates that high-energy-consuming electricity consumption has an important impact on the electricity consumption situation in the company's operating area, and the prediction of high-energy-consuming industries' electricity consumption is of great significance to the electricity consumption forecast of the whole society.

(2) It is greatly affected by the macro-economy, with large fluctuations and difficult forecasting. The growth of electricity consumption is greatly affected by the macro economy, and changes in electricity consumption are highly correlated with the economic situation. Before May 2008, the monthly growth rate of electricity consumption in high energy-consuming industries was generally higher than that of the whole society. After May 2008, affected by the financial crisis, electricity consumption in the whole society and high-energy-consuming electricity consumption both declined, but the electricity consumption in high-energy-consuming industries was more affected and the decline was even greater. After the economy bottomed out in 2009, the power consumption of high-energy-consuming industries picked up faster than that of the whole society. It is easy to be affected by the economic situation and have ups and downs, which makes it more difficult to predict the electricity consumption of high-energy-consuming industries. Especially, it is difficult to obtain ideal prediction results by using the prediction method of historical data extrapolation. It can be said that as long as the power consumption of high energy-consuming industries can be predicted more accurately, the power demand forecast is half successful.

(3) The changing trend of electricity consumption in high-energy-consuming industries is slightly ahead of that of the whole society. Taking the electricity consumption data of the company's operating areas in 2008 as an example, the electricity consumption of high-energy-consuming industries reached its peak in May, and began to decline month by month after June. The electricity consumption of the whole society and industry peaked only in July, and then began to decline. The change of electricity consumption in high energy-consuming industries is 2 months ahead of the electricity consumption of the whole society.

The traditional power demand forecasting technology can be divided into two categories: one is the forecasting technology based on the historical data of power demand itself, such as extrapolation method and time series method. The other type is the forecasting technology that considers the correlation with the influencing factors, such as the elastic coefficient method, the output value unit consumption method, and the regression analysis method. However, none of these forecasting techniques take into account the characteristics of electricity consumption in high-energy-consuming industries, and cannot reflect the inherent laws of changes in electricity consumption in high-energy-consuming industries, and the analysis and prediction results are not satisfactory.

Domestic and foreign literatures have some qualitative analysis on the power consumption characteristics of high energy-consuming industries, but there are very few quantitative analysis, and there are no available analysis and prediction models.

At present, power companies are increasingly aware of the importance of analyzing and predicting electricity consumption in high-energy-consuming industries to predict the electricity consumption of the whole society. There are still deficiencies.

(1) The understanding of factors affecting electricity consumption in high-energy-consuming industries needs to be deepened, and a unified and scientific analysis index system has not been formed. Factors affecting electricity consumption in high energy-consuming industries are complex, some are direct and some are indirect. Due to the in-depth understanding of the influencing factors, there are great differences in the analysis angles of various units on the electricity consumption of high energy-consuming industries. For example, some analyze industry factors, some analyze macroeconomic factors, some analyze output, and some analyze Analyze prices. Without a set of unified analysis indicators, it is difficult to analyze the power consumption of high energy-consuming industries in depth.

(2) The quantitative relationship between electricity consumption and influencing factors in high energy-consuming industries has not been grasped. For example: as we all know, the electricity consumption of the steel industry mainly depends on the steel output, and the steel output depends on the steel demand of downstream industries such as real estate and automobiles. However, there are no available research results on the quantitative relationship between steel output and downstream industry demand. Therefore, most of the current analysis or prediction of high energy-consuming industries is qualitative, and it is difficult to carry out quantitative analysis or prediction.

(3) Lack of targeted forecasting methods. Accurately predicting electricity consumption in high-energy-consuming industries is of great significance to improving the accuracy of electricity consumption forecasting for the whole society. Although there are a lot of achievements in domestic and foreign literature on power demand forecasting methods, these forecasting methods basically do not consider the characteristics of electricity consumption in high-energy-consuming industries, and their pertinence and effectiveness are not strong. There is a lack of effective methods and models for electricity. Sometimes some methods are reluctantly used to get the prediction results, but it is also "knowing what is happening, not knowing why", and it is not clear why the electricity consumption of high-energy-consuming industries changes.

Contents of the invention

The purpose of the present invention is to provide a method for forecasting electricity demand in the iron and steel industry. The method classifies the influencing factors of electricity consumption in the iron and steel industry, uses a combination of qualitative and quantitative methods to analyze the key influencing factors of electricity consumption in the iron and steel industry, and proposes an analysis The index system of electricity consumption in the iron and steel industry and a demand forecasting model are given, which provides a scientific and practical technical solution for power companies to accurately predict the power demand of related industries and then predict the power demand of the whole society.

In order to achieve the above object, the present invention adopts following technical scheme:

Classify the influencing factors of electricity consumption in the iron and steel industry, analyze the key influencing factors of electricity consumption in the iron and steel industry by combining qualitative and quantitative methods, evaluate the correlation between the influencing factors and electricity consumption, and put forward the analysis of electricity consumption in the iron and steel industry The index system is helpful for electric power companies to grasp the internal laws of the growth of electricity consumption in the iron and steel industry.

Using the prediction method in line with the characteristics of high energy-consuming industries, a power demand prediction model for the iron and steel industry was established, the validity of the model was tested, and the prediction accuracy of the model was evaluated. The prediction model has strong pertinence and practicability, and the prediction effect is good.

The present invention has the advantages of enriching and perfecting the existing power demand forecasting method, which is of great significance for improving the power demand forecasting level of electric power enterprises, and can produce significant economic and social benefits:

(1) Applied to power planning, improving the accuracy of load forecasting in planning, which is conducive to optimizing the investment scale of power projects and reducing investment waste.

(2) Applied to the planning, scheduling and market analysis of power grid enterprises, it can improve the accuracy of market analysis, avoid the situation of insufficient supply and serious oversupply, and reduce the losses caused by insufficient power supply and excess investment in power.

(3) Applied to the power generation plan and coal procurement plan of power generation companies, it can help power generation companies optimize thermal coal inventory, reduce thermal coal capital occupation, and avoid insufficient power generation capacity caused by thermal coal shortages.

(4) Power companies can develop power demand forecasting software products according to the present invention.

detailed description

Technical route of the present invention is as follows:

1. Basic steps of electricity demand forecasting

Electricity demand forecasting is divided into the following steps:

(1) Determination of forecast target and forecast content;

(2) Collection of relevant historical data;

(3) Analysis of basic data;

(4) Prediction or acquisition of data related to power system factors;

(5) Selection and trade-off of forecasting models and methods;

(6) modeling;

(7) Data preprocessing;

(8) Model parameter identification;

(9) Model evaluation, to test the significance of the model;

(10) Apply the model for forecasting;

(11) Comprehensive analysis and evaluation of prediction results.

2. Regression prediction method

Power demand is determined by the degree of economic development. The regression forecasting model captures the development law of power demand by establishing the correlation between power demand and economic variables and using regression forecasting technology. The regression prediction method explores the internal relationship and development and change law of economic and social factors and power demand through the analysis and research of historical data, and calculates the future power according to the forecast of the economic and social development of the region during the planning period Requirements, whose task is to determine the relationship between predictors and impact factors. The regression prediction method is the development of the principle of the least square method, which can be divided into one-variable linear regression, multiple linear regression and nonlinear regression models at present.

1. Univariate linear regression model

The expression of the unary linear regression model is as follows:

y=f(S,X)=a+bx+ε

In the formula, S——the parameter vector of the model, S=[a,b] ^T ;

x——independent variable;

y - a random variable that depends on x;

ε——Random error that obeys normal distribution N(0,σ ² ), also known as random interference.

The residual sum of squares is:

$\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; bx</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>$

In the formula, x _i , y _i —— samples.

Use the least squares method to estimate the model parameters a and b, so that Q can reach a minimum value, and the estimated value of the model parameters is:

$\left\{\begin{array}{c}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ \stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}\end{array}\right.$

in $\stackrel{\&OverBar;}{x}=\frac{1}{\mathrm{no}}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{x}_i;$ $\stackrel{\&OverBar;}{\mathrm{the\; y}}=\frac{1}{\mathrm{no}}\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{\mathrm{the\; y}}_i,$ The prediction equation is:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}\mathrm{<span\; class="notranslate">\; x</span>}$

2. Multiple linear regression model

Let y be the explained variable, y _i is the ith observed value of y y=(y ₁ ,y ₂ ...y _n ) ^T , k explanatory variables x=(x ₁ ,x ₂ ...x _k ), β=(β ₀ ,β ₁ ..β _k ) ^T is the regression coefficient, ε=(ε ₁ ,ε ₂ ..ε _n ) ^T represents the random error.

Note that the observation matrix of explanatory variables is $x=\left[\begin{array}{cccc}1& x_{11}& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& x_{1k}\\ 1& x_{\mathrm{twenty\; one}}& \&Center\; Dot;\&Center\; Dot;\&Center\; Dot;& x_{2k}\\ \&Center\; Dot;& \&Center\; Dot;& \mathrm{}& \&Center\; Dot;\\ \&Center\; Dot;& \&Center\; Dot;& \mathrm{}& \&Center\; Dot;\\ \&Center\; Dot;& \&Center\; Dot;& \mathrm{}& \&Center\; Dot;\\ 1& x_{\mathrm{nl}}& \&CenterDot;\&CenterDot;\&CenterDot;& x_{3k}\end{array}\right],$ Then the multiple linear regression model can be written in the form of a matrix:

y=Xβ+ε

(1) OLS estimation

① Estimated value of regression coefficient β

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; Y</span>}$

Meet the nature: $\mathrm{E.}\left(\widehat{\mathrm{\&beta;}}\right)=\mathrm{\&beta;},\mathrm{cov}\left(\widehat{\mathrm{\&beta;}}\right)={\mathrm{\&sigma;}}^2{\left(x^{T}x\right)}^{-1}$

② Random error ε

Each element in the random error ε obeys the normal distribution of N(0,σ ² ). The estimated value of σ is :

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; e</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

(2) Linear correlation significance test

①Correlation coefficient (coefficient of determination)

According to variance analysis, $S_T^2=S_R^2+S_{\mathrm{E.}}^2,$

Correlation coefficient: The correlation coefficient can be used to describe the degree of linear correlation between y and x, and the closer the correlation coefficient is to 1, the better the fitting effect is.

②F test

The F-test indicates whether the linear correlation between y and x is significant.

Assume H ₀ : β ₁ =β ₂ =...β _k =0

If the null hypothesis holds, define the statistic: $f=\frac{\frac{S_R^2}{k}}{\frac{S_{\mathrm{E.}}^2}{\mathrm{no}-k-1}}~f(k,\mathrm{no}-k-1)$ Obey the F distribution with degrees of freedom (k, nk-1), under a certain confidence level a, if F>F _a reject the null hypothesis, otherwise accept the null hypothesis.

③t test

The t test is to test whether the influence degree of each explanatory variable on the explained variable is significant,

Suppose H ₀ :β _i =0,

If the null hypothesis holds, define the statistic: $t=\frac{{\widehat{\mathrm{\&beta;}}}_i}{\sqrt{{\widehat{\mathrm{\&sigma;}}}^2{\left(x^{T}x\right)}_i^{-1}}}~t(\mathrm{no}-k-1),$ Under a certain confidence level a, if t>t _a rejects the null hypothesis, otherwise accepts the null hypothesis.

(3) Forecast

The value of the n+1 period of the given explanatory variable is: C=(1,x _n+l,1 ,..,x _n+l,k ) ^T , so the confidence level of y _n+l is 1-a The prediction interval is $(C^T\widehat{\mathrm{\&beta;}}\&PlusMinus;t_{\frac{a}{2}}\widehat{\mathrm{\&sigma;}}\sqrt{1+\frac{1}{\mathrm{no}}+\frac{{(x_0-\stackrel{\&OverBar;}{x})}^2}{\mathrm{\&Sigma;}{(x_i-\stackrel{\&OverBar;}{x})}^2}}).$

(4) Related issues in regression analysis

①Multicollinearity problem

In the multiple linear regression model, an important assumption is that the explanatory variables of the multiple linear regression are not linearly correlated, but when the multiple linear regression model is actually established, two or more explanatory variables will inevitably be introduced , there are more or less correlations between these variables.

i Consequences of multicollinearity

Under perfect collinearity, (X ^T X) ^-1 does not exist, If it cannot be obtained, the model is a failure.

Under approximately collinearity, |(X ^T X) ^-1 |≈0, so (X ^T X) ^-1 has a large diagonal value, because Therefore, the variance of the estimator of the regression coefficient will also increase, which will invalidate the significance test of the variable and weaken the predictive function of the model.

ⅱMulticollinearity test

Regression model testing method: Regress each _xi on the remaining variables and calculate the corresponding coefficient of determination , to build the statistic: Obey the F distribution with degrees of freedom k-2 and nk-1, if F _i is greater than the critical value, then _xi and other variables are collinear.

ⅲ Multicollinearity Remedy

There are three main methods: stepwise regression, principal component analysis, and reducing the variance of the estimator (increasing the sample size, merging variables).

Stepwise regression method: take y as the explained variable, gradually introduce explanatory variables to form a regression model, and perform model estimation. If the goodness of fit changes significantly, the introduced variable has an impact; if the goodness of fit does not change significantly, the variable is introduced There is collinearity with the variable introduced first.

② Heteroscedasticity problem

In the multiple linear regression model, the variance of the error term ε _i has nothing to do with i, that is is constant. However, due to the setting of the model (the actual nonlinearity is set to be linear), the neglect of important explanatory variables, and the measurement error of the data, etc., is different due to If it is not allowed, the OLS estimated variance is no longer the smallest, and the t test is no longer meaningful. Heteroskedasticity occurs more frequently in cross-sectional data.

The commonly used methods for testing heteroscedasticity mainly include G-Q test (variance monotonic type, large sample, all conditions are met except for homoscedasticity conditions), White test, Glejser test, and ARCH process (time series, large sample).

White test is to construct heteroscedasticity test through an auxiliary regression formula to construct χ ² statistic. Take the binary linear regression model as an example: Y _t =β ₀ +β ₁ X _t1 +β ₂ X _t2 +u _t .

The null hypothesis H ₀ of the White test: there is no heteroscedasticity in u _t in the above formula, and the alternative hypothesis H ₁ : there is heteroscedasticity in u _t .

Step1 first performs OLS regression on the regression model, and finds the residual e _t

Step2 do the following regression model

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}$

Step3 Find the coefficient of determination and statistics The degree of freedom k is the number of terms of the explanatory variables in the auxiliary regression.

The discriminant rule of Step4White test is: if , accept H ₀ , if ${\mathrm{TR}}^2>{\mathrm{\&chi;}}_{a\left(k\right)}^2,$ Reject H ₀ .

③ Autocorrelation problem

In the multiple linear regression model, E(εε ^T /X) = σ ² I, but due to the hysteresis of economic variables or the setting error of the model, E(ε _i ε _j )≠0, i≠j , that is, the correlation of the occurrence sequence, including spatial correlation (section data) and time series correlation. Then the covariance matrix D(ε) of ε=σ ² ΩΩ≠I. Autocorrelation, like heteroscedasticity, will make the OLS estimate no longer BLUE.

ⅰ autocorrelation test

Autocorrelation test includes D-W method and Lagrangian multiplier test (LM test).

The Durbin-Watson statistic measures the first-order serial correlation of the residuals, calculated as:

$\mathrm{<span\; class="notranslate">\; DW</span>}<span\; class="notranslate">\; =</span>\stackrel{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\stackrel{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}}_{\mathrm{<span\; class="notranslate">\; t</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

The range of DW value is (0~4). If it is around 2, there is no correlation in the sequence. According to the number of observed values, look up the table to judge whether there is correlation in the sequence.

The DW statistic is only suitable for the first-order autocorrelation test, but not for the higher-order autocorrelation test. Using LM statistics, a more applicable autocorrelation test method can be established, which can test both first-order autocorrelation and higher-order autocorrelation. The LM test is done through an auxiliary regression formula, and the specific steps are:

Step1 considers that the error term is in the form of n-order autoregressive

u _t =ρ ₁ u _t-1 +...+ρ _n u _tn +v _t ν _t is a random item, which meets various assumptions.

Step2 Null hypothesis is H ₀ :ρ ₁ =ρ ₂ =...=ρ _n =0

Step3 Establish residual auxiliary regression formula:

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; p</span>}}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; kt</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}$

Step4 Calculate the coefficient of determination R ² and construct the LM statistic:

LM=TR ²

The LM statistic asymptotically obeys distribution, the discriminant rule is: if Accept H ₀ ;

like $\mathrm{LM}={\mathrm{TR}}^2>{\mathrm{\&chi;}}_{\left(\mathrm{no}\right)}^2,$ Reject H ₀ .

ⅱ Correction for heteroscedasticity and autocorrelation - generalized least squares GLS.

For problems with heteroscedasticity and autocorrelation, a generalized linear model can be used to represent:

y＝Xβ+εD(ε)＝σ ² Ω

Among them, Ω is a positive definite matrix, so Ω ^-1 is also positive definite, so there is an invertible matrix G, so that Ω ^-1 =G ^T G, so transform the original linear model:

Gy＝GXβ+Gε

So D(Gε)=σ ² GΩG ^T , and because GΩG ^T =I, D(Gε)=σ ² I is obtained.

In this way, there is no problem of autocorrelation and heteroscedasticity in the generalized linear model (1-19), and we get:

$\widehat{\mathrm{\&beta;}}={\left(x^T{\mathrm{\&Omega;}}^{-1}x\right)}^{-1}{x}^T{\mathrm{\&Omega;}}^{-1}\mathrm{the\; y},$ GLS estimation of β It is BLUE of β.

And σ ² is estimated by OLS is an unbiased, consistent estimator of ^σ2 .

Only multiple linear regression models that pass hypothesis testing can be applied in practice.

3. Nonlinear regression model

The form of the correlation between the independent variable and the dependent variable of the nonlinear regression model is nonlinear, which is more common in the actual system. However, nonlinear regression models are complex and difficult to operate. Common nonlinear models mainly refer to those that can be processed by converting nonlinear relationships into linear relationships through appropriate variable substitution.

(1) Hyperbolic model:

(2) Power function curve model: y=ax ^b (x>0, a>0)

(3) Exponential curve model: y=ae ^bx (a>0)

(4) Inverted exponential curve model:

(5) S-curve model:

3. Correlation Analysis of Electricity Consumption in Iron and Steel Industry

3.1 Correlation analysis method

Correlation analysis is the process of describing the strength of the correlation between variables and expressing it with appropriate statistical indicators. Its purpose is to find out the factors that have a significant impact on the electricity consumption of the iron and steel industry as the basis for building a model.

3.1.1 Correlation coefficient

Correlation coefficient, also called product-difference correlation coefficient, is a common indicator used to quantitatively describe the degree of linear correlation.

According to the above assumptions, let (X ₁ ,X ₂ ) obey the two-dimensional normal distribution in is the mean and variance of X ₁ , is the mean and variance of X ₂ , and ρ is the correlation coefficient between X ₁ and X ₂ . The formula for the correlation coefficient ρ is:

ρ＝Cov(X ₁ ,X ₂ )/(Var(X ₁ )Var(X ₂ )) ^1/2 (5.1)

Using the moment estimation method, the moment estimation value of ρ is obtained as:

$\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{{<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5.2</span>}<span\; class="notranslate">\; )</span>$

3.1.2 Stepwise regression analysis

In practical problems, people always hope to select some variables as independent variables from many variables that have an impact on the dependent variable y, and use the method of multiple regression analysis to establish an "optimal" regression equation in order to predict or control the dependent variable. The so-called "optimal" regression equation mainly refers to the desire to include all independent variables that have a significant impact on the dependent variable y in the regression equation and not include independent variables that have no significant impact on y. Stepwise regression analysis is a regression analysis method proposed according to this principle. Its main idea is to introduce all independent variables into the regression equation one by one according to their significance or contribution to y from large to small, and those variables that have no significant effect on y may never be introduced. regression equation. In addition, the variables that have been introduced into the regression equation may also lose their importance after introducing new variables, and need to be removed from the regression equation. Introducing a variable or removing a variable from the regression equation is called a stepwise regression step, and F test is performed at each step to ensure that the regression equation only contains variables that have a significant impact on y before introducing new variables, and the insignificant ones Variables have been eliminated.

The implementation process of stepwise regression analysis is to calculate the partial regression sum of squares (that is, contribution) for the variables that have been introduced into the regression equation at each step, and then select a variable with the smallest partial regression square sum, and perform a significant analysis at a predetermined F level. If it is significant, the variable does not need to be removed from the regression equation, and at this time, the other variables in the equation do not need to be removed either. On the contrary, if it is not significant, the variable should be eliminated, and then the F test is performed on other variables in the equation according to the partial regression square sum from small to large. All variables that have no significant impact on y are eliminated, and all remaining variables are significant. Then calculate the partial regression sum of squares for the variables that have not been introduced into the regression equation, and select the variable with the largest partial regression square sum, and also perform a significance test at a given F level, and if it is significant, introduce the variable into the regression Equation, this process continues until the variables in the regression equation can not be eliminated and no new variables can be introduced, then the stepwise regression process ends.

3.1.3 Granger causality test

The Granger causality test was proposed and established by Professor Clive Granger, the winner of the 2003 Nobel Prize in Economics. Compared with correlation coefficient and regression analysis, Granger causality test illustrates the causal relationship of variables in terms of the sequence of changes, and separates causality from correlation from a statistical perspective. If it is combined with the correct economic theory, it can more accurately reflect the economic dynamics of the active subjects in reality.

Granger uses the concept of an information set for the definition of causality and emphasizes the timing of events. Let I _n be all the information in the universe up to period n, Y _n be all Y _t (t=1,2,…n) up to period n, and X _n+1 be the value of X in period n+1 , I _n -Y _n is all the information except Y. If the addition of Y changes the probability distribution of X: F(X _n+1 /I _n )≠F(X _n+1 /(I _n -Y _n )), the variable Y is considered to have Granger causality to X .

In practice, it is very difficult to test the distribution function of variables, and a simpler method is to deal with it from the perspective of expectation, and test E(X _n+1 /I _n )≠E(X _n+1 /(I _n -Y _n )). If δ _n+1 =E(X _n+1 /I _n )−E(X _n+1 /(I _n −Y _n )) is significantly different from 0, then Y is the Granger cause of X. Later, it was developed to test the causal relationship by prediction accuracy. If σ ² (X _n+1 /I _n )<σ ² (X _n+1 /(I _n -Y _n )), then Y is the Granger of X reason. The information set I _n not only includes all the relevant variables but also includes the infinite lag values of X and Y, but in reality, we cannot get all the data information I _n , only under the condition of the available information set J _n , The relationship of the variables is tested, this Granger causality is derived based on the available information set _Jn .

3.1.4 Seasonal adjustment

The X-12 method was established and developed by the National Census Bureau of the U.S. Department of Commerce on the basis of the moving average ratio method. It is characterized in that it can adapt to the nature of various economic indicators and choose the calculation method according to the purpose of various seasonal adjustments. In addition, in the case of no selection, the calculation method can also be automatically selected according to the characteristics of the data according to the statistical benchmarks programmed in advance. During the calculation process, moving averages of different lengths can be used according to the size of the random factors in the data. The larger the factor, the larger the moving average length. After several adjustments and improvements, this method has become a fairly fine and typical seasonal adjustment method. It has been adopted by the official and non-governmental organizations (IMF) in Europe, America, Japan and other countries, and has become a commonly used seasonal adjustment method. Adjustment method.

3.1.5 Trend adjustment

Trend means that the time series X _t has a tendency to change with time. After X-12 seasonal adjustment, we can get the trend item and fluctuation item TC _t (TC _t =T _t +C _t ) in the time series. In order to obtain the long-term change trend of the components, it is necessary to separate the trend item and the fluctuation item. Simpler methods such as regression analysis, exponential smoothing, and difference methods are used to deal with the trending part of the time series. The focus is on HP ( Hodrick-Prescott) filtering method.

3.1.6 Correlation Analysis Ideas

Correlation analysis has three purposes: first, to quantify the influencing factors obtained in qualitative analysis, and to establish indicators that can quantitatively describe the influencing factors; second, to verify the correctness of qualitative analysis through quantitative analysis of indicators; third, to The three-level influencing factors are screened to obtain important influencing factors for analysis and modeling.

Based on the above purpose, correlation analysis is carried out by using the method of correlation coefficient, Granger causality test and regression analysis. The three analysis methods have their own advantages and disadvantages. Using three quantitative analysis methods for correlation analysis can achieve the purpose of complementing each other and verifying each other, and improve the reliability of influencing factors and correlation analysis.

The steps of correlation analysis are:

(1) Quantify the influencing factors and determine the index set of influencing factors. According to the qualitative research, the three-level influencing factors of high energy-consuming industries are analyzed, such as subdividing domestic demand from the perspective of downstream industries, and expressing international demand from the perspective of import and export volume and policies. Use real estate investment to describe the demand of the real estate industry, automobile production to describe the demand of the automobile industry, and so on.

(2) Use the trend comparison chart of influencing factors and electricity consumption to preliminarily analyze the correlation characteristics of influencing factors and electricity consumption.

(3) Calculate the correlation coefficient between electricity consumption, product output and influencing factors, and analyze their correlation.

(4) Use Granger causality test to analyze whether there is a causal relationship between electricity consumption and influencing factors from a statistical point of view.

(5) Use the stepwise regression method to analyze the influencing factors selected by the first two methods, and eliminate unimportant influencing factors.

(6) On the basis of synthesizing the results of the three analysis methods, the main influencing factors of electricity consumption in the industry are obtained.

3.2 Correlation Analysis of Electricity Consumption in Iron and Steel Industry

3.2.1 Index Set of Influencing Factors

1. Analysis and establishment of index set

The influencing factors and related indicators of electricity consumption in the iron and steel industry are summarized in the table below.

Table 5.1 Summary of Factors and Indicators Affecting Electricity Consumption in Iron and Steel Industry

2. Data collection and processing

The data involved in the research mainly include electricity consumption data, industry data, and product data. Among them, the electricity consumption data includes the electricity consumption of ferrous metal smelting and rolling processing industry from January 2004 to December 2009; the product data includes the output of crude steel, steel products, and pig iron; the downstream industry data mainly includes the product output of various downstream industries , investment, and domestic steel comprehensive price index, raw material price index and other data related to product gross profit.

The data sources mainly include: the website of the National Bureau of Statistics, the statistical database of China Economic Network, the website of China Iron and Steel Industry Association, China Iron and Steel Network, Steel Home Network, Soushu.com, etc. Data processing mainly includes two aspects: investment data processing and price data processing. The investment data is adjusted by the fixed asset investment price index (current quarter), and the nominal investment data is converted into actual investment data. The processing of price data is mainly to adjust the relevant price data into a fixed-base data series based on January 2004.

3.2.2 Correlation analysis results

1. Screening results of primary influencing factors

Through the comprehensive analysis of various methods, the three indicators of product output: crude steel output, steel output, and pig iron output are highly correlated with electricity consumption, and the correlation between steel output and electricity consumption is stronger. When establishing a prediction model Steel production can be considered as an independent variable.

2. Screening results of the second and third level influencing factors

Through correlation coefficient analysis, Granger causality test, and stepwise regression analysis, the three-level indicators are screened layer by layer, and the correlation results can be summarized. After comprehensive screening by various methods, the following indicators have the most significant impact on electricity consumption in the iron and steel industry: investment in real estate development, investment in fixed assets in the transportation industry, automobile production, comprehensive domestic steel price index, and raw material price index.

Table 3 Summary of Correlation Analysis Results of Influencing Factors

4. Prediction model of electricity consumption in steel industry

4.1 Regression Model of Electricity Consumption and Steel Production in Iron and Steel Industry

4.1.1 Regression Analysis of Absolute Number of Electricity Consumption and Absolute Number of Steel Production

Let yt be the observed value of electricity consumption _{, and xt be} the observed value of steel production. First, the ordinary least squares (OLS) method is used to solve the model:

y _t =c+βx _t +u _t (7.1)

In order to get the basic information of the model and the corresponding coefficient test and model fitting.

1. Establishment and testing of the initial model

A linear regression model was established for electricity consumption and steel production in the iron and steel industry. The explanatory variable of the model is steel production, and the explained variable is electricity consumption. The data used are all absolute numbers, and the sample interval of the data is from January 2004 to In December 2009, a total of 72 sets of monthly data, the main parameters and statistics of the model calculated by Eviews software are shown in Table 7.1.

Table 7.1 Regression Results and Related Information of Electricity Consumption and Production

Table 7.1 shows the explanatory variable—steel production and the regression coefficient of the constant item, the standard error of the coefficient, the t statistic corresponding to the coefficient and its accompanying probability to test the validity of the coefficient. If the accompanying probability is less than 0.05, it means that the regression coefficient is valid, otherwise accept the null hypothesis that the regression coefficient is zero, indicating that the explanatory variable (or constant item) is not related to the dependent variable. Through the preliminary regression analysis, it is found that the steel output has a significant impact on the electricity consumption of the steel industry. The significance test of the coefficient has passed, and the coefficient of determination value is 0.95. The coefficient of determination reflects the fitting effect of the model. The higher the value is The closer to 1, the better the model fit.

The trend of the actual value of electricity consumption is very similar to the estimated value, which shows the validity of the model estimation; the average absolute error of the model is 868 million kWh, and the average relative error is 3.77%. After testing, the model has autocorrelation and heteroscedasticity. Therefore, adjustments to the initial model are also required.

2. Adjustments to the initial model

The autocorrelation of the model is adjusted by adding the lag period of the relevant factors. The corresponding regression results and related information are shown in the table below.

Table 7.2 Regression results and related information with lagged variables added

The results described in the above table show that each indicator has passed the significance test, and the goodness of fit value of the model is 0.97, which shows that the fitting effect is very good.

In the further inspection and analysis of the above model, it is found that the autocorrelation of the model is eliminated, but heteroscedasticity still exists, and the heteroscedasticity will affect the validity of the OLS estimation of the model. Therefore, on the basis of the impact indicators of the model, the weighted least squares method is used for analysis, and the regression results obtained are shown in the table below.

Table 7.3 Regression results and related information of weighted least squares method

The results described in the table above show that the model has passed the overall significance and coefficient significance tests, and the goodness-of-fit value is 0.99, which shows that the fitting effect is very good. The average absolute error of the model is 811 million kWh, and the average relative error is 3.53%.

3. Statistical testing of the model

(1) Heteroscedasticity test

In the heteroscedasticity test, the value of the accompanying probability corresponding to the F statistic is 0.92, which is greater than 0.05, indicating that there is no heteroscedasticity in the model.

Table 7.4 ARCH(1) test results

(2) Autocorrelation test

We use the Ljun-BoxQ statistic to test the serial correlation, and the probability value corresponding to any first-order Q statistic is greater than 0.05, indicating that there is no serial correlation in the disturbance term of the model.

(3) Normality test of residuals

The accompanying probability corresponding to the Jarque-Bera statistic is 0.72, which is greater than 0.05, indicating that the residual item of the model obeys a normal distribution, that is, the t statistic test is valid.

Based on the above inspection and analysis, it shows that the obtained model satisfies the relevant prerequisites of the least squares method, and the obtained regression model is valid, so that the relationship between electricity consumption and the absolute number of steel production can be expressed in the following form:

y _t =0.03x _t +0.42y _t-1 +17.57 (7.2)

Among them, y _t is the electricity consumption of the iron and steel industry (100 million kWh), x _t is the steel output (10,000 tons), and y _t-1 is the electricity consumption of the steel industry in the previous period. The meaning of formula (7.2) is: the electricity consumption of the iron and steel industry is affected by the steel production in the current period and the electricity consumption in the previous period. When the electricity consumption in the previous period is known, for every 10,000 tons of steel output, The electricity consumption of the iron and steel industry will increase by 0.03 billion kwh. Combined with the previous analysis, the average absolute error of the model is 811 million kWh, and the average relative error is 3.53%.

4.1.2 Regression Analysis of Electricity Consumption Growth Rate and Steel Production Growth Rate

1. Establishment and testing of the initial model

Here, the initial regression model is established using the year-on-year growth rate of electricity consumption and steel production. The data sample range is from January 2005 to December 2009, with a total of 60 sets of monthly data. The regression model is established through Eviews software. The regression results are shown in the table shown in 7.5.

Table 7.5 Regression Results and Related Information of Electricity Consumption and Production

Through preliminary regression analysis, it is found that the growth rate of steel production has a certain impact on the growth rate of electricity consumption in the steel industry, and the coefficient significance test of the growth rate of steel production has passed. The goodness of fit value of the model is 0.67, indicating that the fitting effect is general. Moreover, the average relative error of the model is 6.7%, which is relatively large. At the same time, combined with related tests, the model still has autocorrelation, so the model needs to be adjusted.

2. Adjustments to the initial model

The model is adjusted by adding the lag period of relevant factors, and then the model is statistically tested. The regression results and related information after adding lagged variables are shown in the table below.

Table 7.6 Regression results and related information with lagged variables added

By adjusting the autocorrelation of the model, the goodness of fit has been significantly improved, indicating that the fitting effect of the model has become better. At the same time, the overall significance of the model and the significance of each coefficient have passed the test. The fitting effect of the obtained model has been greatly improved, the trend graph between the estimated value and the actual value of electricity consumption is very similar, and the average relative error of the model is 4.82%.

3. Statistical testing of the model

(1) Heteroscedasticity test

In the heteroscedasticity test, the value of the accompanying probability corresponding to the F statistic is 0.15, which is greater than 0.05, indicating that there is no heteroscedasticity in the model.

Table 7.7 ARCH(1) test results

(2) Autocorrelation test

We use the Ljun-BoxQ statistic to test the serial correlation. The sample interval is from February 2005 to December 2009. The probability value corresponding to any first-order Q statistic is greater than 0.05, indicating that there is no sequence in the disturbance item of the model. Correlation.

(3) Normality test of residuals

The accompanying probability corresponding to the Jarque-Bera statistic is 0.38, which is greater than 0.05, indicating that the residual item of the model obeys a normal distribution, that is, the previous t statistic test is valid.

Based on the above inspection and analysis, it shows that the model we obtained meets the relevant prerequisites of the least squares method, that is, the regression model is effective, so that the relationship between electricity consumption and the growth rate of steel production can be expressed in the following form:

y _t =0.55x _t +0.60y _t-1 -0.13 (7.3)

Among them, y _t is the monthly growth rate of electricity consumption in the iron and steel industry, x _t is the monthly growth rate of steel production, and y _t-1 is the monthly growth rate of electricity consumption in the previous period.

The meaning of formula (7.3) is: the growth rate of electricity consumption in the iron and steel industry is affected by the growth rate of steel production in the current period and the growth rate of electricity consumption in the previous period. An increase of 1%, the electricity consumption of the steel industry will increase by 0.55%. Combined with the previous analysis, the average relative error of the model is 4.82%.

4.1.3 Model comparative analysis

Comparing the relationship models between electricity consumption and steel production as shown in Table 7.8, the two models have passed various tests, indicating that the models are reasonable and effective. The fitting errors of the two models are relatively small, and the form is relatively simple. In terms of prediction, the model fitting error of predicting the absolute number of electricity consumption is smaller and the fitting effect is better.

Table 7.8 Summary of relationship models between electricity consumption and output

4.2 Regression Model of Electricity Consumption and Three-Level Influencing Factors in Iron and Steel Industry

In the correlation analysis between the electricity consumption of the iron and steel industry and the influencing factors of related downstream industries, we obtained six three-level factors that significantly affect the electricity consumption of the iron and steel industry: the completed investment in real estate development, fixed asset investment in the transportation industry, Automobile industry output, steel export volume, domestic steel comprehensive price index, raw material price index. In order to more effectively predict the electricity consumption of the iron and steel industry, the following regression analysis is performed on the relationship between electricity consumption and impact indicators.

Let yt be the electricity consumption of the iron and steel industry, _{x 1t} be the completed investment in real estate development, x _2t be the investment in fixed assets in the transportation industry, x _3t be the output of the automobile industry, x _4t be the export volume of steel products, and x _5t be the comprehensive price index of domestic steel products , x _6t is the raw material price index. First, the model is solved using the ordinary least squares (OLS) method:

y _t = c+β ₁ x _1t +β ₂ x _2t +β ₃ x _3t +β ₄ x _4t +β ₅ x _5t +β ₆ x _6t +u _t (7.4)

By solving the above regression model, the fitting error between the actual value and the estimated value of electricity consumption can be obtained, so as to make a preliminary judgment on the validity of the model. Then, the same as the previous research, in the multivariate OLS estimation, the regression sequence also needs to meet some preconditions, so the final model will be tested for heteroscedasticity, autocorrelation and normality, and the model that passes the test can be used more effectively. Forecast electricity usage.

4.2.1 Regression Model of Absolute Number of Electricity Consumption and Absolute Number of Tertiary Influencing Factors

1. Establishment and testing of the initial model

Establish a multiple linear regression model for the electricity consumption of the steel industry and the third-level influencing factors. The explanatory variables of the model are various third-level influencing indicators, and the explained variable is electricity consumption. The data used are all absolute numbers, and the sample interval of the data From January 2004 to December 2009, there are 72 sets of monthly data in total. The main parameters and statistics of the model calculated by Eviews software are shown in Table 7.9.

Table 7.9 Regression Results and Related Information of Electricity Consumption and Influencing Factors

Through preliminary regression analysis, the correlation between electricity consumption and six third-level influencing factors is obtained. Except for the fixed asset investment in the transportation industry, the coefficients of the other five influencing factors have passed the significance test. In order to ensure the accuracy of the model Effectiveness, after removing the fixed asset investment indicators in the transportation industry, the following regression results are obtained.

Table 7.10 Regression results and related information of electricity consumption and deleted influencing factors

Through further regression analysis, it is found that the remaining five influencing factors have a strong correlation with electricity consumption, and the corresponding coefficients have passed the significance test, and the coefficient of determination of the model is 0.95, indicating that the fitting effect is very good. OK, at the same time the overall significance test of the model passes. The average absolute error of the model fitting is 952 million kWh, and the average relative error is 4.42%. The fitting effect is average. Further combined with the statistical test of the model, the model has autocorrelation and heteroscedasticity. Therefore, it is also necessary to use related methods to adjust the initial model. 2. Adjustments to the initial regression model

Based on the previous analysis, the autocorrelation of the model is eliminated by adding relevant factors to the model in the previous period, and the corresponding regression results are shown in the table below.

Table 7.11 Regression results and related information with lagged variables added

After adjustment, all the coefficients in the model have passed the significance test, and the coefficient of determination of the model is 0.97, which shows that the fitting effect of the model is very good. The average absolute error of the adjusted model is 807 million kWh, and the average relative error is 3.82%, which shows that our adjustment has achieved the purpose of reducing the model error.

3. Statistical testing of the model

(1) Heteroscedasticity test

Table 7.12 ARCH(1) test results

In the heteroscedasticity test, the value of the accompanying probability corresponding to the F statistic is 0.32, which is greater than 0.05, indicating that there is no heteroscedasticity in the model.

(2) Autocorrelation test

We use the Ljun-BoxQ statistic to test the serial correlation. The sample interval is from February 2004 to December 2009. The probability value corresponding to any first-order Q statistic is greater than 0.05, indicating that there is no sequence in the disturbance item of the model. Correlation.

(3) Normality test of residuals

The accompanying probability corresponding to the Jarque-Bera statistic is 0.72, which is greater than 0.05, indicating that the residual item of the model obeys a normal distribution, that is, the previous t statistic test is valid.

Based on the above test and analysis, it shows that the obtained model meets the relevant preconditions of the least squares method, that is, the obtained regression model is effective, so that the relationship between electricity consumption and the absolute number of influencing factors can be expressed in the following form:

y _t = 1.18x _1t +0.48x _3t +5.10x _4t +0.46x _5t -0.90x _6t +0.43y _t-1 +96.18 (7.5)

Among them, y _t is the electricity consumption of the iron and steel industry (100 million kWh), x _1t is the completed investment in real estate development (10 billion yuan), x _3t is the output of automobiles (10,000 units), x _4t is the steel export volume (million tons ), x _5t is the comprehensive price index of domestic steel products, x _6t is the price index of raw materials, and y _t-1 is the previous period of electricity consumption in the steel industry.

The meaning of formula (7.5) is: the electricity consumption of the iron and steel industry is affected by the current investment in real estate development, automobile production, steel export volume, domestic steel comprehensive price index, raw material price index and the electricity consumption of the previous period. Moreover, there is a positive correlation between electricity consumption in the iron and steel industry and the completed investment in real estate development, automobile production, steel export volume, domestic steel comprehensive price index, and electricity consumption in the previous period, and a negative correlation with the raw material price index in the iron and steel industry. relation. The average absolute error of the model is 807 million kWh, and the average relative error is 3.82%.

4.2.2 Regression Analysis of Growth Rate of Electricity Consumption and Growth Rate of Three Influencing Factors

1. Establishment and testing of the initial model

Next, the regression model is established by using the year-on-year growth rate of electricity consumption and the third-level influencing factors. The sample period of the data is from January 2005 to December 2009, with a total of 60 sets of monthly data. The regression model is established through the Eviews software. The regression results are shown in the following table shown.

Table 7.13 Regression Results and Related Information of Growth Rate of Electricity Consumption and Growth Rate of Influencing Factors

The results in the above table show that the coefficients of the growth rate of the six influencing factors have passed the significance test, which means that the coefficient estimates of the influencing indicators are all valid. The value of the coefficient of determination is 0.86, indicating that the fitting effect of the model is good. The average relative error of the model is 4.12%. Furthermore, combined with relevant statistical tests, the model has autocorrelation. Therefore, the autocorrelation of the model is adjusted.

2. Use the generalized least squares method for regression analysis

By using the generalized least squares method, the regression results of the model are obtained as shown in the table below.

Table 7.14 Regression results and related information of generalized least squares method

The above table shows that the coefficient test of raw material prices fails. Although the fitting effect of the model is very good, and combined with the relevant statistics test, the model does not have autocorrelation under the generalized least squares regression, but it is still necessary to remove the increase in the raw material price index. Regression analysis can only be done after the fast speed to ensure the validity of the estimated results of the model.

3. Adjustments to the initial model

Based on the analysis of the generalized least squares method, first remove the influencing factor of raw material price growth in the initial regression model, and the regression results are shown in the table below.

Table 7.15 Regression results and relevant information on the growth rate of electricity consumption and the growth rate of influencing factors after deletion

The results stated in the above table show that, except for the growth rate of real estate development investment, the coefficients of other indicators have passed the significance test, so the indicator of real estate development investment growth rate needs to be further removed. Secondly, due to the existence of autocorrelation in the model, the generalized least squares method cannot effectively reduce the fitting error of the model. Therefore, after we eliminated the raw material price index through the generalized least squares method, combined with regression analysis, we eliminated the real estate development investment. The growth rate, and then based on this, the method of adding the previous items of relevant factors to the model in Table 7.15 to eliminate the autocorrelation of the model, and the corresponding regression results are shown in the following table.

Table 7.16 Regression results and related information with lagged variables added

In the above table, each indicator has passed the significance test, further combined with relevant statistical tests, the model still has heteroscedasticity. In order to ensure the validity of the model estimation, a new regression is performed after the heteroscedasticity treatment is performed on the model, and the results in the following table are obtained.

Table 7.17 Regression results and related information of the adjusted model

The data described in the above table shows that the coefficients of each influencing factor have passed the significance test, and the value of the coefficient of determination is 0.92, indicating that the fitting effect of the model is good. And the average relative error of the model is 3.54%, compared with the initial regression model, the error has been reduced.

4. Statistical testing of the model

(1) Heteroscedasticity test

Since the value of the associated probability corresponding to the F statistic is 0.59, which is greater than 0.05, it shows that there is no heteroscedasticity in the model.

Table 7.18 ARCH(1) test results

(2) Autocorrelation test

The Ljun-BoxQ statistic is used to test the serial correlation. The sample interval is from February 2005 to December 2009. The probability value corresponding to any first-order Q statistic is greater than 0.05, indicating that there is no serial correlation in the disturbance term of the model. sex.

(3) Normality test of residuals

The accompanying probability corresponding to the Jarque-Bera statistic is 0.59, which is greater than 0.05, indicating that the residual item of the model obeys a normal distribution, that is, the previous t statistic test is valid.

Based on the above inspection and analysis, it shows that the obtained model meets the relevant preconditions of the least squares method, that is, the obtained regression model is valid, so that the relationship between power consumption and the growth rate of the influencing factors can be expressed in the following form:

y _t ＝0.13x _2t +0.19x _3t +0.03x _4t +0.16x _5t +0.65y _t-1 -0.11x _3t-1 +0.12x _3t-2 (7.6)

Among them, y _t is the growth rate of electricity consumption in the iron and steel industry, x _2t is the growth rate of fixed asset investment in the transportation industry, x _3t is the growth rate of the output of the automobile industry, x _4t is the growth rate of steel export volume, and x _5t is the comprehensive price index of domestic steel products Growth rate, y _t-1 is the previous period of the growth rate of electricity consumption in the iron and steel industry, x _3t-1 is the previous period of the growth rate of the output of the automobile industry, x _3t-2 is the first two periods of the growth rate of the output of the automobile industry, And each indicator is the growth rate of the current month based on the original data.

The meaning of formula (7.6) is: the growth rate of electricity consumption in the iron and steel industry is affected by the growth rate of fixed asset investment in the transportation industry, the growth rate of automobile production, the growth rate of steel export volume, the growth rate of domestic steel comprehensive price index and the power consumption in the previous period. The growth rate of automobile production, the growth rate of automobile production, and the influence of the growth rate of automobile production in the first two periods. And the growth rate of electricity consumption in the iron and steel industry and the growth rate of fixed asset investment in the transportation industry, the growth rate of automobile production, the growth rate of steel export volume, the growth rate of domestic steel comprehensive price index, the growth rate of electricity consumption in the previous period and the growth rate of automobile production in the first two periods There is a positive correlation between the growth rates and a negative correlation with the growth rate of automobile production in the previous period. The average relative error of the model is 3.54%, and the fitting effect is good.

4.2.3 Model comparative analysis

Comparing the previous two models of the relationship between electricity consumption and steel production as shown in Table 7.19, both models have passed various tests, indicating that the models are reasonable and effective. The fitting errors of the two models are relatively small, and the form is relatively Simple, relatively speaking, the model fitting effect of predicting the growth rate of electricity consumption is better.

Table 7.19 Summary of Three-Level Influencing Factor Prediction Models

Claims (1)

1. A method for forecasting electricity demand in the iron and steel industry, characterized in that the method for forecasting comprises the following steps: (1) Collect and organize the historical data of electricity consumption and steel production in the iron and steel industry; (2) Establish a linear regression model for electricity consumption and steel production in the iron and steel industry. The explanatory variable of the model is steel production, and the explained variable is electricity consumption. The data uses absolute numbers to obtain the regression of explanatory variables—steel production and constant items The coefficient, the standard error of the coefficient, the statistics corresponding to the coefficient and its accompanying probability are used to test the validity of the coefficient; if the accompanying probability is less than 0.05, the regression coefficient is used, otherwise the assumption that the regression coefficient is zero is accepted; (3) Adjust the autocorrelation of the model by adding the lag period of the relevant factors, and then test the significance of each index, the whole and the coefficient; (4) Carry out heteroscedasticity test, autocorrelation test and residual normality test on the model, so that the model meets the relevant preconditions of the least squares method; (5) Through the above steps, the relationship between electricity consumption and the absolute number of steel production is obtained as follows: in, It is the electricity consumption of the iron and steel industry, unit: 100 million kWh; is steel output, unit: 10,000 tons, is the electricity consumption of the steel industry in the previous period; (6) Establish a regression model for the year-on-year growth rate of electricity consumption and steel production, and then conduct significance test and autocorrelation test for the coefficient of steel production growth rate; (7) Adjust the model by adding the lag period of the relevant factors, and then carry out the heteroscedasticity test, autocorrelation test and normality test of the residual error on the model, so that the model meets the relevant prerequisites of the least squares method; (8) Through the above steps, the relationship between electricity consumption and the growth rate of steel production is obtained as: in, The monthly growth rate of electricity consumption in the steel industry, is the monthly growth rate of steel production, It is the monthly growth rate of electricity consumption in the previous period.