G(1,1):
clc;clear; %建立符号变量a(发展系数)和b(灰作用量) syms a b; c = [a b]'; %原始数列 A A = [174, 179, 183, 189, 207, 234, 220.5, 256, 270, 285]; n = length(A); %对原始数列 A 做累加得到数列 B B = cumsum(A); %对数列 B 做紧邻均值生成 for i = 2:n C(i) = (B(i) + B(i - 1))/2; end C(1) = []; %构造数据矩阵 B = [-C;ones(1,n-1)]; Y = A; Y(1) = []; Y = Y'; %使用最小二乘法计算参数 a(发展系数)和b(灰作用量) c = inv(B*B')*B*Y; c = c'; a = c(1); b = c(2); %预测后续数据 F = []; F(1) = A(1); for i = 2:(n+10) F(i) = (A(1)-b/a)/exp(a*(i-1))+ b/a; end %对数列 F 累减还原,得到预测出的数据 G = []; G(1) = A(1); for i = 2:(n+10) G(i) = F(i) - F(i-1); %得到预测出来的数据 end disp('预测数据为：'); G %模型检验 H = G(1:10); %计算残差序列 epsilon = A - H; %法一：相对残差Q检验 %计算相对误差序列 delta = abs(epsilon./A); %计算相对误差Q disp('相对残差Q检验：') Q = mean(delta) %法二：方差比C检验 disp('方差比C检验：') C = std(epsilon, 1)/std(A, 1) q %法三：小误差概率P检验 S1 = std(A, 1); tmp = find(abs(epsilon - mean(epsilon))< 0.6745 * S1); disp('小误差概率P检验：') P = length(tmp)/n %绘制曲线图 t1 = 1995:2004; t2 = 1995:2014; plot(t1, A,'ro'); hold on; plot(t2, G, 'g-'); xlabel('x'); ylabel('y'); legend('实际','预测'); title('量增长曲线'); grid on;G（1，n）
A=[560823,542386,604834,591248,583031,640636,575688,689637,570790,519574,614677]; x0=[104,101.8,105.8,111.5,115.97,120.03,113.3,116.4,105.1,83.4,73.3; 135.6,140.2,140.1,146.9,144,143,133.3,135.7,125.8,98.5,99.8; 131.6,135.5,142.6,143.2,142.2,138.4,138.4,135,122.5,87.2,96.5; 54.2,54.9,54.8,56.3,54.5,54.6,54.9,54.8,49.3,41.5,48.9]; [n,m]=size(x0); AGO=cumsum(A); T=1; x1=zeros(n,m+T); for k=1:(m-1) Z(k)=(AGO(k)+AGO(k+1))/2; %Z(i)为xi(1)的紧邻均值生成序列 end for i=1:n for j=1:m for k=1:j x1(i,j)=x1(i,j)+x0(i,k);%原始数据一次累加,得到xi(1) end end end x11=x1(:,1:m); X=x1(:,2:m)';%截取矩阵 Yn =A;%Yn为常数项向量 Yn(1)=[]; %从第二个数开始，即x(2),x(3)... Yn=Yn'; %Yn=A(:,2:m)'; B=[-Z',X]; C=((B'*B)\(B'*Yn))';%由公式建立GM(1,n)模型 a=C(1); b=C(:,2:n+1); F=[]; F(1)=A(1); u=zeros(1,m); for i=1:m for j=1:n u(i)=u(i)+(b(j)*x11(j,i)); end end for k=2:m F(k)=(A(1)-u(k-1)/a)/exp(a*(k-1))+u(k-1)/a; end G=[]; G(1)=A(1); for k=2:m G(k)=F(k)-F(k-1);%两者做差还原原序列，得到预测数据 end t1=1:m; t2=1:m; plot(t1,A,'bo--'); hold on; plot(t2,G,'r*-'); title('销售预测结果'); legend('真实值','预测值');https://blog.csdn.net/wuli_dear_wang/article/details/80587650
