How to analyze the grey prediction model?

One 、 application

  The grey prediction model can be used for very few （ For example, only 4 individual ）, Effective prediction of data sequences with low data integrity and reliability , It uses differential equations to fully mine the essence of data , Modeling requires less information , High precision , Simple operation , Easy to test , There is no need to consider the distribution law or change trend . However, the grey prediction model is generally only suitable for short-term prediction , Only suitable for the prediction of exponential growth , For example, the number of people , The number of flights , Water consumption prediction , Prediction of industrial output value, etc .

  There are many grey prediction models ,GM(1,1) The model is the most widely used , The first 1 A number represents first-order differentiation , The first 2 A digital 1 Indicates that only 1 A data sequence .

Two 、 operation

SPSSAU operation

（1） Click on SPSSAU Comprehensive evaluation ‘ Grey prediction model ’ Button . Here's the picture

（2） Drag and drop the data and click start analysis

3、 ... and 、 Analysis steps

Four 、 Case background

At present, a city 1986~1992 common 7 Average sound level data of road traffic noise in , Now we hope to predict the average sound level data of instruments in the next phase . The data are as follows ：

5、 ... and 、 The results of the analysis

SPSSAU The resulting analysis results are as follows

1. GM(1,1) Model level ratio table

Grade ratio λ

Data of last period / Current data

example ：71.1/72.4=0.982; And so on .

analysis 1

It can be seen from the above table that , For urban traffic noise /dB(A) Conduct GM(1,1) model building , First, carry out the level ratio test , It is used to judge the applicability of data sequence for model construction . The grade ratio is the data of the previous period / Current data . Results show ： The grade ratio test values are within the standard range [0.779, 1.284] Inside , This means that this data is suitable for GM(1,1) model building .

2. Model building results

analysis 2

It can be seen from the above table that , The development coefficient is obtained after the model is constructed a, Grey action quantity b, The coefficient of development a And grey action b Value is the value used to build the model , It has less practical significance . Posterior ratio C value ; A posteriori error ratio C value 0.231 <=0.35, It means that the accuracy level of the model is very good . If you want to use mathematical formulas to describe the model , As shown below ：

3. Model predictive value table

analysis 3

The table above shows the fitting value of the model , And back 12 Fitting data of the period , Of course, you can also visually view the following figure through graphics , The following figure clearly shows , It will keep falling in the future , This is a GM(1,1) Characteristics of the model , It is only applicable to medium and short-term forecasts , So back 1 Period and backward 2 The data of this period is valuable , More forecasts need to be treated with special caution .

4. GM(1,1) Model check table

analysis 4

  Finally, the residual value is tested , The smaller the relative error value, the better , The value is less than 0.2 Explain that the requirements are met , Less than 0.1 It indicates that high requirements are met ; The smaller the grade ratio deviation, the better , The value is less than 0.2 Explain that the requirements are met , Less than 0.1 It indicates that high requirements are met .

  It can be seen from the above table that , After the model is built, the relative error and order ratio deviation can be analyzed , Verify the effect of the model ; The maximum relative error of the model 0.007 <0.1, It means that the fitting effect of the model meets high requirements . For the order ratio deviation value , The value is less than 0.2 Explain that the requirements are met , If less than 0.1 It means that higher requirements are met ; The maximum relative error of the model 0.020<0.1, It means that the fitting effect of the model meets high requirements .