Prediction - Grey Prediction

1、 effect

Grey prediction is a method to predict the system with uncertain factors . Grey prediction identifies the difference of development trend between system factors , That is, correlation analysis , And generate and process the original data to find the law of system change , Generate data sequences with strong regularity , Then the corresponding differential equation model is established , So as to predict the future development trend of things .

2、 Input / output description

Input ：１ Quantitative variables of time series data
Output ： Fitting prediction results of grey prediction ​

3、 Case example

be based on 2000-2021 Annual sales volume of a product in , Use the grey prediction model to predict the future annual sales .

4、 Modeling steps

1. Before establishing the grey prediction model, we must ensure the feasibility of the modeling method , That is, it is necessary to carry out level comparison test on the known original data Let the initial nonnegative data sequence be ：

Only when all σ(k) Only when all of them fall within the scope of calculation can the model be established . The calculation and judgment formulas of the stage ratio are :

Through the accumulation operation, we get The first-order cumulative sequence of can weaken The disturbance of ：

yes   The sequence generated by the immediate mean of :

So we can get GM(1,1) The corresponding differential equation of the model is :

among by GM(1,1) Background value of the model .​

2. Build data matrix B And data vector Y , Respectively :

Then the least square estimation parameter sequence of the grey differential equation satisfies :

among ,a Development trend of main control system , It is called the development coefficient ; b The size of reflects the relationship between data changes , It is called grey action .​

3. Establish a model and solve the generated value and the restored value . Solve according to the formula , The prediction model can be obtained :

After repeated reduction , Get the restore prediction .