阻滞增长模型

阻滞增长模型 Y=[84779 86727 88761 90409 92420 93267 94774 96259 97542 98705 100072 101654 103008 104357 105851 107507 109300 111026 112704 114333 115823 117171 118517 119850 121121 122389 123626 124761 125786 126743]; T=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30]; for t=1:30 x(t)=exp(-t); y(t)=1/Y(t); end c=zeros(30,1)+1; X=[c,x']; B=inv(X'*X)*X'*y' for i=1:30, z(i)=B(1,1)+B(2,1)*x(i); s(i)=y(i)-sum(y)/30; w(i)=z(i)-y(i); end S=s*s'; Q=w*w'; U=S-Q; F=28*U/Q for j=1:30, Y(j)=1/(B(1,1)+B(2,1)*exp(-j)); end plot(T,Y) B = 1.0e-005 * 0.9315 0.8670 F = 10.7066 4x 1011 10.5 10 9.5 9 8.5 8 7.5051015202530 x=[1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000]; y=[84779 86727 88761 90409 92420 93267 94774 96259 97542 98705 100072 101654 103008 104357 105851 107507 109300 111026 112704 114333 115823 117171 118517 119850 121121 122389 123626 124761 125786 126743]; plot(x,y,'r.') xlabel('年份') ylabel('人口') 5x 101.3 1.25 1.2 1.15 1.1 1.05人口 1 0.95 0.9 0.85 0.81970197519801985199019952000 年份 clear syms a b; c=[a,b]'; A=[125786 126743 127627 128453 129227 129988 130756 131448 132129 132802]; B=cumsum(A); n=length(A); for i=1:(n-1) C(i)=(B(i)+B(i+1))/2; end D=A;D(1)=[]; D=D'; E=[-C;ones(1,n-1)]; c=inv(E*E')*E*D; c=c'; a=c(1);b=c(2); F=[];F(1)=A(1); for i=2:(n+10) F(i)=(A(1)-b/a)/exp(a*(i-1))+b/a; end G=[];G(1)=A(1); for i=2:(n+10) G(i)=F(i)-F(i-1); end t1=1999:2008; t2=1999:2018; G plot(t1,A,'*',t2,G) 5x 101.42 1.4 1.38 1.36 1.34 1.32 1.3 1.28 1.26 1.2419982000200220042006200820102012201420162018 G = 1.0e+005 * Columns 1 through 6 1.2579 1.2691 1.2765 1.2839 1.2914 1.2989 Columns 7 through 12 1.3065 1.3141 1.3217 1.3294 1.3372 1.3450 Columns 13 through 18 1.3528 1.3607 1.3686 1.3765 1.3846 1.3926 Columns 19 through 20 1.4007 1.4089