arma(4,2)模型.docVIP

ARMA(4,2)模型： 其中 1. 随机产生300个观测值 y=zeros(1,500); epsilon=randn(1,500); for i=5:500 y(i)=-0.9*y(i-1)-1.4*y(i-2)-0.7*y(i-3)-0.6*y(i-4)+epsilon(i)+0.5*epsilon(i-1)-0.4*epsilon(i-2); end t=1:300; x(t)=y(t+200); 2．计算自协方差函数估计 meanx=mean(x); stdx=std(x); gamma(1)=var(x); s=0; for k=1:40 for i=1:300-k s=s+(x(i)-meanx)*(x(i+k)-meanx); end gamma(k+1)=s/300; s=0; end 3． a的矩估计 biggamma=[gamma(3) gamma(2) gamma(1) gamma(2); gamma(4) gamma(3) gamma(2) gamma(1); gamma(5) gamma(4) gamma(3) gamma(2); gamma(6) gamma(5) gamma(4) gamma(3)]; bgamma=[ gamma(4); gamma(5); gamma(6); gamma(7)]; a=inv(biggamma)*bgamma; a = -0.8005 -1.3718 -0.6047 -0.5903 4. 计算MA(q)序列:的自协方差函数估计 ay=[-1;a]; gamma1=[gamma(5) gamma(4) gamma(3) gamma(2) gamma]; for k=1:11 biggamma1=[gamma1((k+4):(k+8)); gamma1((k+3):(k+7)); gamma1((k+2):(k+6)); gamma1((k+1):(k+5)); gamma1(k:(k+4))]; gammay(k)=ay*biggamma1*ay; end 5. 取，利用逆相关函数方法计算出系数的估计量 (1) 建立模型，得到样本Yule-Walker系数 for i=1:10 for n=1:10 biggammay2(i,n)=gammay(abs(i-n)+1); end end bgammay2=gammay(2:11); a2=inv(biggammay2)*(bgammay2); sum=0; for k=1:10 sum=sum+a2(k)*gammay(k+1); end sigmapfy=gammay(1)-sum; (2) 计算(或MA(2))样本逆相关函数 nigammay(1)=[-1;a2(:)]*[-1;a2(:)]/sigmapfy; nigammay(2)=[-1;a2(1:9)]*a2(:)/sigmapfy; nigammay(3)=[-1;a2(1:8)]*a2(2:10)/sigmapfy; (3) 计算出系数的估计量 for i=1:2 for n=1:2 biggammay3(i,n)=nigammay(abs(i-n)+1); end end bgammay3=nigammay(2:3); b=-inv(biggammay3)*(bgammay3); sigmapf=1/( nigammay(1)+b(1)*nigammay(2)+b(2)*nigammay(3)); b,sigmapf b = 0.2530 -0.2381 sigmapf = 1.2538 5. 以上述所得为初值， 采用有哪些信誉好的足球投注网站的方法， 计算该ARMA(4,2)模型的参数计算最大似然估计。 (1) 计算, 这时 EYY=zeros(40,40); bb=[1 b zeros(1,40)]; for s=1:40 for t=1:40 if s=4 t=4 EYY(s,t)=gamma(abs(t-s)+1); elseif min(s,t)=4 max(s,t)4 EYY(t,s)=gamma(abs(s-t)+1)-a(1)*gamma(abs(abs(s-t)-1)+1)-a(2)*gamma(abs(abs(s-t)-2)+1)-... a(3)*gamma(abs(abs(s-t)-3)+1)-a(4)*gamma(abs(abs(s-t)-4)+1); else EYY(s,t)=bb(1)*bb(1+abs(t-s))+bb(2)*bb(2+abs(t-s))+bb(3)*bb(3+abs(t-s)); end end end (2) 利用公式（3.6）计算和逐步预测的均方误差 mu(1)