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Prediction - Grey Prediction
2022-07-07 16:28:00 【Lu 727】
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 .
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