灰色模型预测GM(1,1)MATLAB程序代码

function gmcal=gm1(x)

%% 二次拟合预测GM(1,1)模型

%x = [5999,5903,5848,5700,7884];

sizexd2 = size(x,2);

%求数组长度

k=0;

for y1=x

k=k+1;

if k>1

x1(k)=x1(k-1)+x(k);

%累加生成

z1(k-1)=-0.5*(x1(k)+x1(k-1));

%z1维数减1，用于计算B

yn1(k-1)=x(k);

else

x1(k)=x(k);

end

end

%x1,z1,k,yn1

sizez1=size(z1,2);

%size(yn1);

z2 = z1';

z3 = ones(1,sizez1)';

YN = yn1'; %转置

B=[z2 z3];

au0=inv(B'*B)*B'*YN;

au = au0';

afor = au(1);

ufor = au(2);

ua = au(2)./au(1);

constant1 = x(1)-ua;

afor1 = -afor;

x1t1 = 'x1(t+1)';

estr = 'exp';

tstr = 't';

leftbra = '(';

rightbra = ')';

strcat(x1t1,'=',num2str(constant1),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(ua),rightbra) %输出时间响应方程

k2 = 0;

for y2 = x1

k2 = k2 + 1;

if k2 > k

else

ze1(k2) = exp(-(k2-1)*afor);

end

end

sizeze1 = size(ze1,2);

z4 = ones(1,sizeze1)';

G=[ze1' z4];

X1 = x1';

au20=inv(G'*G)*G'*X1;

au2 = au20';

Aval = au2(1);

Bval = au2(2);

strcat(x1t1,'=',num2str(Aval),estr,leftbra,num2str(afor1),tstr,rightbra,'+',leftbra,num2str(Bval),rightbra) %输出时间响应方程

nfinal = sizexd2-1 + 1; %决定预测的步骤数5 这个步骤可以通过函数传入

%nfinal = sizexd2 - 1 + 1;%预测的步骤数 1

for k3=1:nfinal

x3fcast(k3) = constant1*exp(afor1*k3)+ua;

end

%一次拟合累加值

for k31=nfinal:-1:0

if k31>1

x31fcast(k31+1) = x3fcast(k31)-x3fcast(k31-1);

else

if k31>0

x31fcast(k31+1) = x3fcast(k31)-x(1);

else

x31fcast(k31+1) = x(1);

end

end

end

x31fcast

%一次拟合预测值

for k4=1:nfinal

x4fcast(k4) = Aval*exp(afor1*k4)+Bval;

end

%x4fcast

for k41=nfinal:-1:0

if k41>1

x41fcast(k41+1) = x4fcast(k41)-x4fcast(k41-1);

else

if k41>0

x41fcast(k41+1) = x4fcast(k41)-x(1);

else

x41fcast(k41+1) = x(1);

end

end

end

x41fcast,x

%二次拟合预测值

%***精度检验p C************//////////////////////////////////

k5 = 0;

for y5 = x

k5 = k5 + 1;

if k5 > sizexd2

else

err1(k5) = x(k5) - x41fcast(k5);

end

end

%err1

%绝对误差

xavg = mean(x);

%xavg

%x平均值

err1avg = mean(err1);

%err1avg

%err1平均值

k5 = 0;

s1total = 0 ;

for y5 = x

k5 = k5 + 1;

if k5 > sizexd2

else

s1total = s1total + (x(k5) - xavg)^2;

end

end

s1suqare = s1total ./ sizexd2;

s1sqrt = sqrt(s1suqare);

%s1suqare,s1sqrt

%s1suqare 残差数列x的方差 s1sqrt 为x方差的平方根S1

k5 = 0;

s2total = 0 ;

for y5 = x

k5 = k5 + 1;

if k5 > sizexd2

else

s2total = s2total + (err1(k5) - err1avg)^2;

end

end

s2suqare = s2total ./ sizexd2;

%s2suqare 残差数列

err1的方差S2

Cval = sqrt(s2suqare ./ s1suqare);

Cval

%nnn = 0.6745 * s1sqrt

%Cval C检验值

k5 = 0;

pnum = 0 ;

for y5 = x

k5 = k5 + 1;

if abs( err1(k5) - err1avg ) < 0.6745 * s1sqrt

pnum = pnum + 1;

%ppp = abs( err1(k5) - err1avg )

else

end

end

pval = pnum ./ sizexd2;

pval

%p检验值

%arr1 = x41fcast(1:6)

%预测结果为区间范围 预测步长和数据长度可调整程序参数进行改进