Grey prediction of model GM model in Mathematical modeling model (I.)

The grey model can be used to predict effectively, especially when the data is blurred, such as predicting when to rain, first to explain a simple and most commonly used GM model GM (a)

Generate columns

Set the original time series to X1 (t) T for time t=0,1,2,3 ...., generating the column x0 (t) is the difference that the original sequence of the t>=1 is:

x0(t)=x1(t)-x1(t-1)

Immediate Value column

As the name implies, the average value is taken.

 z1=0.5*x10.5*x1(t-1)

GM (model)

In fact, the generated column is the derivative of the original sequence:

x1(t)‘=x0(t)      =x1(t)-x1(t-1)

We can build relationships as follows:
A, B is constant
Order B=[-Z1, 1]
U=[a, b]. T

a*z1=b    a*z1=bx0=B*uu=(B.T*B).I*B.T*x0x1(k+1)=(x0(1)-b/a)*exp(-a*k)+a/b

So we can make predictions.

Copyright NOTICE: This article for Bo Master original article, without Bo Master permission not reproduced.

Grey prediction of model GM model in Mathematical modeling model (I.)