?a2?1.0086。 ?这样就得到了Wt的随机线性模型。Wt?0.3720Wt?1?0.1314Wt?2?at。在进行
??W???的预报值,然后在预报时，可以先对Wt进行预报，然后加上均值得到Ytt??Y??X。 反差分得到原始序列的预报值Xttt?12
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附录1
1、 某市1985-1993年各月工业生产总值(单位:万元) 1985.01 10.93 9.34 11.00 10.98 1985.07 10.62 10.90 12.77 12.15 1986.01 9.91 10.24 10.41 10.47 1986.07 11.32 11.73 12.61 13.04 1987.01 10.85 10.30 12.74 12.73 1987.07 13.18 13.75 14.42 13.95 1988.01 12.94 11.43 14.36 14.57 1988.07 15.18 15.94 16.54 16.90 1989.01 13.70 10.88 15.79 16.36 1989.07 16.62 16.96 17.69 16.40 1990.01 13.73 12.85 15.68 16.79 1990.07 16.80 17.27 20.83 19.18 1991.01 15.73 13.14 17.24 17.93 1991.07 17.70 19.87 21.17 21.44 1992.01 17.88 16.00 20.29 21.03 1992.07 21.55 22.01 22.68 23.02 1993.01 19.61 17.15 22.46 24.19 1993.07 22.91 24.03 23.94 24.12 11.29 12.24 11.51 13.14 13.08 14.53 14.25 16.88 17.22 17.51 17.59 21.40 18.82 22.14 21.78 24.55 23.40 25.87 11.84 12.30 12.45 14.15 14.27 14.91 15.86 18.10 17.75 19.73 18.51 23.76 19.12 22.45 22.51 24.67 26.26 28.25
?k的值 2、样本自相关函数?1 0.4282 7 0.0023 13 -0.00698 19 0.0654 2 0.2907 8 0.0458 14 -0.0568 20 0.0852 3 0.1878 9 0.0849 15 -0.0063 21 -0.0595 4 0.0421 10 0.0035 16 0.1523 22 -0.0880 5 0.0870 11 -0.0483 17 0.1411 23 -0.0112 6 0.0478 12 -0.1972 18 0.1165 24 -0.063 ?的值 3、样本偏相关函数?kk1 0.4282 7 -0.0383 13 2 0.1314 8 0.0447 14 3 0.0291 9 0.0852 15 4 -0.0930 10 -0.0834 16 6
5 0.0855 11 -0.0865 17 6 -8.1917e-04 12 -0.1878 18
0.1346 19 -0.0662 -0.0017 20 0.1134 0.0483 21 -0.1357 0.1705 22 -0.1198 0.0707 23 0.0966 -0.0456 24 -0.0721 附录2
Matlab源代码
X=[10.93,9.34,11.00,10.98,11.29,11.84, 10.62,10.90,12.77,12.15,12.24,12.30, 9.91,10.24,10.41,10.47,11.51,12.45, 11.32,11.73,12.61,13.04,13.14,14.15, 10.85,10.30,12.74,12.73,13.08,14.27, 13.18,13.75,14.42,13.95,14.53,14.91, 12.94,11.43,14.36,14.57,14.25,15.86, 15.18,15.94,16.54,16.90,16.88,18.10, 13.70,10.88,15.79,16.36,17.22,17.75, 16.62,16.96,17.69,16.40,17.51,19.73, 13.73,12.85,15.68,16.79,17.59,18.51, 16.80,17.27,20.83,19.18,21.40,23.76, 15.73,13.14,17.24,17.93,18.82,19.12, 17.70,19.87,21.17,21.44,22.14,22.45, 17.88,16.00,20.29,21.03,21.78,22.51, 21.55,22.01,22.68,23.02,24.55,24.67, 19.61,17.15,22.46,23.19,23.40,26.26,
22.91,24.03,23.94,24.12,25.87,28.25]; %M=linspace(1985,1994,108); X2=zeros(1,108); for i=1:18
X2((1+6*(i-1)):6*i)=X(i,:); end
plot(M,X2) %X2为原始序列 M2=linspace(1986,1994,96); Y=zeros(1,96); for i=1:96
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输入原始数据
Y(i)=X2(i+12)-X2(i); end figure
plot(M2,Y) %Y为季节差分后的序列 save X2 save Y load Y s=sum(Y);
m=s/length(Y); %求序列均值 Y2=zeros(1,length(Y)); for i=1:length(Y) Y2(i)=Y(i)-m; end
plot(M2,Y2); %Y2为零均值化后的序列 K=24; %取K=24
r0=(1/length(Y2))*sum(Y2.^2); %求r0 r=zeros(1,24); %求rk k=1:24; su=0; for i=1:24
for j=1:length(Y2)-i su=su+Y2(j)*Y2(j+i); end
r(i)=(1/length(Y2))*su; su=0; end
p=r/r0; % p为自相关函数
%求偏相关函数 fai=zeros(1,24); fai(1)=p(1); for i=2:24; p2=zeros(1,i); p2(1)=1;
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p2(2:i)=p(1:(i-1)); t=toeplitz(p2); t2=inv(t); an=t2*p(1:i)'; fai(i)=an(i); end
fai2=zeros(1,25); fai2(1)=1;
fai2(2:25)=fai; úi2为加上fai00后的偏相关函数 p3=zeros(1,25); p3(1)=1;
p3(2:25)=p; %p3为加上p0后的自相关函数 n=[0:24]; figure plot(n,p3); grid figure plot(n,fai2); grid
%模型参数估计
rou=zeros(1,2); %取φ2j=φj，j=0，1 rou(1)=p(1); rou(2)=p(2); p4=zeros(1,2); p4(1)=1; p4(2)=p(1); T=toeplitz(p4);
F=inv(T)*rou'; %F为φ1和φ2组成的向量
tao=r0*(1-F(1)*p(1)-F(2)*p(2)); %tao为噪声方差 save F
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