灰色預測模型matlab程序精確版%x=[1019,1088,1324,1408,1601];gm1(x);測試數據%二次擬合預測GM(1,1)模型functiongmcal=gm1(x)ifnargin==0x=[1019,1088,1324,1408,1601]endformatlonggsizex=length(x);%求數組長度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維數減1，用于計算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';%轉置%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%輸出預測的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%二次擬合預測值%***精度檢驗pC************//////////////////////////////////k5=0;fory5=xk5=k5+1;ifk5>sizexelseerr1(k5)=x(k5)-x41fcast(k5);endend%err1%絕對誤差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殘差數列x的方差s1sqrt為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殘差數列err1的方差S2Cval=sqrt(s2suqare./s1suqare);Cval%nnn=0.6745*s1sqrt%CvalC檢驗值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檢驗值%arr1=x41fcast(1:6)%預測結果為區間范圍預測步長和數據長度可調整程序參數進行改進運行結果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