Mathematical Modeling – Gray Prediction Model with Matlab Code

Directory

1. Interpretation of Gray Prediction

2. Examples of gray prediction

3. Gray prediction model

3.1 Generate cumulative data

3.2 Accumulated data expression

3.3 Solve unknown parameters

4. Partial code of gray prediction Matlab

5. Forecast results

1. Gray forecast interpretation

Gray prediction is a method to predict the system with uncertain factors. Gray prediction is to identify the degree of difference between the development trends of system factors, that is, to conduct correlation analysis, and generate and process the original data to find the law of system changes, generate a data sequence with strong regularity, and then establish a corresponding differential equation Models to predict the future development trend of things. It uses a series of quantitative values that reflect the characteristics of the predicted object observed at equal time intervals to construct a gray prediction model to predict the characteristic quantity at a certain moment in the future, or the time to reach a certain characteristic quantity.

2. Gray prediction example

The relevant statistical data of various indicators from 1997 to 2002 are as follows:

years	primary industry GDP	Consumption price index	Tertiary Industry GDP
1997	72.03	241.2	1592.74
1998	73.84	241.2	1855.36
1999	74.49	244.8	2129.60
2000	76.68	250.9	2486.86
2001	78.00	250.9	2728.94
2002	79.68	252.2	3038.90

The gray prediction method is used to predict the data of various indicators from 2003 to 2009. And the actual forecast data is known as follows: compare the forecast data with the actual data

years	primary industry GDP	Consumer Price Index	GDP of the tertiary industry
2003	81.21	256.5	3458.05
2004	82.84	259.4	3900.27
2005	84.5	262.4	4399.06
2006	86.19	265.3	4961.62
2007	87.92	268.3	5596.13
2008	89.69	271.4	6311.79
2009	91.49	274.5	7118.96

3. Gray forecasting model

3.1 Generate cumulative data

3.2 Accumulated data expression

3.3 Solve for unknown parameters

4. Partial code of gray prediction Matlab

clc;clear;close all
%raw data
data=[72.03,241.2,1592.74;73.84 ,241.2,1855.36;74.49,244.8,2129.60;...
76.68,250.9,2486.86;78.00,250.9,2728.94;79.68,252.2,3038.90];
%To predict the true value of the data
data_T=[81.21,256.5,3458.05;82.84,259.4,3900.27;84.5,262.4,4399.06;...
86.19,265.3,4961.62;87.92,268.3,5596.1;89.69,271.4,6311.79;91.49,274.5,7118.96];
%% accumulated data
data1=cumsum(data,1);
%% solve coefficient
% predict these three columns separately
X=(1997:2002);% known year data
X_p=(2003:2009);% forecast year data
X_sta=X(1)-1;% The initial reference data
for j=1:size(data,2)
    B=zeros(size(data,1)-1,2);
    for i=1:size(data,1)-1
        B(i,1)=-1/2*(data1(i,j) + data1(i + 1,j));
        B(i,2)=1;
    end
    Y=data(2:end,j);
    a_u=inv(B'*B)*B'*Y;
    a=a_u(1); u=a_u(2);
    T=[X,X_p];
    data_p=(data1(1,j)-u/a).*exp(-a.*(T-X_sta)) + u/a;% accumulated data
    data_p1(1)=data_p(1);
    for n=2:length(data_p)
        data_p1(n)=data_p(n)-data_p(n-1);
    end
    title_str={'primary industry GDP forecast','consumer price index forecast','tertiary industry GDP forecast'};
    figure(1)