数学建模论文-中国GDP增长的数学模型及其分析与预测(3)

回归预测

V=[3624.1,4038.2 ,4517.8 ,4862.4,5294.7,5934.5,7171.0,8964.4,10202.2 ,11962.5 ,14928.3 ,16909.2 ,18547.9 ,21617.8 ,26638.1 ,35334.

0 ,48198.0 ,60794.0 ,71176.6 ,78973.0 ,84402.3 ,89677.1 ,99214.6 ,109655.2 ,120332.7 ,135822.8 ,159878.3 ,183217.4 ,211923.5 ,257305.6 ,314045.0 ]'; c =1:31; R=c';

x = [ones( size( R ) ), R, R.^2,R.^3,R.^4,R.^5,R.^6,R.^7]; alpha = 0.05;

[b, bint, r, rint, stat] = regress(V, x, alpha); n = 1000;

t = linspace( min(R), max(R), n); y = polyval( fliplr( b' ), t );

% y = b(1) + b(2) * t + b(3) * t.^2; figure;

plot(t, y,'-',R,V,'+');

title('图3 GDP随时间变化曲线'); xlabel('时间'); ylabel('GDP总量');

legend('拟合值','实际值'); AMIRM模型源代码

a=[3624.1,4038.2 ,4517.8 ,4862.4,5294.7,5934.5,7171.0,8964.4,10202.2 ,11962.5 ,14928.3 ,16909.2 ,18547.9 ,21617.8 ,26638.1 ,35334.0 ,48198.0 ,60794.0 ,71176.6 ,78973.0 ,84402.3 ,89677.1 ,99214.6 ,109655.2 ,120332.7 ,135822.8 ,159878.3 ,183217.4 ,211923.5 ,257305.6 ,314045.0 ]; r11=autocorr(a); r12=parcorr(a); da=diff(a);

r21=autocorr(da); r22=parcorr(da); n=length(da); for i=0:3 for j=0:3

spec=garchset('R',i,'M',j,'Display','off'); [coeffX,errorsX,LLFX]=garchfit(spec,da); num=garchcount(coeffX);

[aic,bic]=aicbic(LLFX,num,n);

fprintf('R=%d,M=%d,AIC=%f,BIC=%f\n',i,j,aic,bic); end end

r=input('R='); m=input('M=');

spec2=garchset('R',r,'M',m,'Display','off'); [coeffX,errorsX,LLFX]=garchfit(spec2,da);

[sigmaForecast,w_Forecast]=garchpred(coeffX,da,10);

x_pred=a(end)+cumsum(w_Forecast); 图4

x=2010:2018; y=[0.164750791 0.144006536 0.128116248 0.115549596 0.105358526 0.096924374 0.08982624 0.083767808 0.078534426]'; plot(x, y,'-+');

title('图1 GDP年增长率随时间变化曲线'); xlabel('时间/年'); ylabel('%');