灰色预测模型matlab程序精确版

灰色预测模型matlab程序精确版%x=[1019,1088,1324,1408,1601];gm1(x);测试数据%二次拟合预测GM(1,1)模型functiongmcal=gm1(x)ifnargin==0x=[1019,1088,1324,1408,1601]endformatlonggsizex=length(x);%求数组长度k=0;fory1=xk=k+1;ifk>1x1(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Byn1(k-1)=x(k);elsex1(k)=x(k);endend%x1,z1,k,yn1sizez1=length(z1);%size(yn1);z2=z1';z3=ones(1,sizez1)';YN=yn1';%转置%YNB=[z2z3];au0=inv(B'*B)*B'*YN;au=au0';%B,au0,auafor=au(1);ufor=au(2);ua=au(2)./au(1);%afor,ufor,ua%输出预测的au和u/a的值constant1=x(1)-ua;afor1=-afor;x1t1='x1(t+1)';estr='exp';tstr='t';end%x4fcastfork41=nfinal:-1:0ifk41>1x41fcast(k41+1)=x4fcast(k41)-x4fcast(k41-1);elseifk41>0x41fcast(k41+1)=x4fcast(k41)-x(1);elsex41fcast(k41+1)=x(1);endendendx41fcast,x%二次拟合预测值%***精度检验pC************//////////////////////////////////k5=0;fory5=xk5=k5+1;ifk5>sizexelseerr1(k5)=x(k5)-x41fcast(k5);endend%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;fory5=xk5=k5+1;ifk5>sizexelses1total=s1total+(x(k5)-xavg)^2;endends1suqare=s1total./sizex;s1sqrt=sqrt(s1suqare);%s1suqare,s1sqrt%s1suqare残差数列x的方差s1sqrt为x方差的平方根S1k5=0;s2total=0;fory5=xk5=k5+1;ifk5>sizexelses2total=s2total+(err1(k5)-err1avg)^2;endends2suqare=s2total./sizex;%s2suqare残差数列err1的方差S2Cval=sqrt(s2suqare./s1suqare);Cval%nnn=0.6745*s1sqrt%CvalC检验值k5=0;pnum=0;fory5=xk5=k5+1;ifabs(err1(k5)-err1avg)<0.6745*s1sqrtpnum=pnum+1;%ppp=abs(err1(k5)-err1avg)elseendendpval=pnum./sizex;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运行结果x=10191088132414081601ans=x1(t+1)=8908.4929exp(0.11871t)+(-7889.4929)ans=x1(t+1)=8945.2933exp(0.11871t)+(-7935.7685)x31fcast=Columns1through310191122.893478570971264.43142178303Columns4through61423.809872354881603.277582074421805.36675232556x41fcast=Columns1through310191118.056854351291269.65470492098Columns4through61429.691537401951609.90061644041