图片：
程序代码：
- % Code to generate iso-probability contour plots of bivariate
- % distributions, all with N(0,1) marginal distributions and connected via various copulas
- %
- %Andrew Patton
- %
- %21 august 2006
- % Written for the following paper:
- %
- % Patton, A.J., 2006, Copula-Based Models for Financial Time Series.
- % To be published in T.G. Andersen, R.A. Davis, J.-P. Kreiss and T. Mikosch (eds.),
- % "Handbook of Financial Time Series", Springer Verlag.
- %
- % http://fmg.lse.ac.uk/~patton
- T = 100;% takes only around 15 seconds when T=100 on a single-processor 2.6GHz machine
- % i cannot see a difference in the printed graph based on T=100 vs T=500,
- % though it is a lot smaller and faster to load. so just use T=100;
- tic;
- xx = (-2:4/(T-1):2)';
- uu = normcdf(xx);
- v = (0.02:0.03:0.2);
- % 1. Normal copula
- rho = 0.5;
- zz = nines(T,T);% this the the part of the pdf from the X variable
- tic;
- for ii=1:T;
- zz(:,ii) = bivnormpdf(xx,xx(ii),[0,0],theta2rho(rho));
- end
- toc
- figure(101);subplot(3,2,1),contour(xx,xx,zz,v,'r-'),...
- title('Normal copula, \rho = 0.5');
- figure(102);subplot(3,2,1),contour(xx,xx,zz,v,'k-'),...
- title('Normal copula, \rho = 0.5');
- hold on;subplot(3,2,1),plot([-2,2],[0,0],'k--',[0,0],[-2,2],'k--');hold off;
- % 2. Student's t copula
- rho = 0.5;
- nu = 3;
- zz = normpdf(xx)*ones(1,T);% this the the part of the pdf from the X variable
- tic;
- for ii=1:T;
- zz(:,ii) = zz(:,ii).*normpdf(xx(ii)).*tcopula_pdf(uu,uu(ii),rho,nu);
- end
- toc
- figure(101);subplot(3,2,2),contour(xx,xx,zz,v,'m-'),...
- title('Student''s t copula, \rho = 0.5, \nu = 3'),...
- figure(102);subplot(3,2,2),contour(xx,xx,zz,v,'k-'),...
- title('Student''s t copula, \rho = 0.5, \nu = 3'),...
- hold on;subplot(3,2,2),plot([-2,2],[0,0],'k--',[0,0],[-2,2],'k--');hold off;
- % 3. Clayton copula
- kappa = 1;
- zz = normpdf(xx)*ones(1,T);% this the the part of the pdf from the X variable
- tic;
- for ii=1:T;
- zz(:,ii) = zz(:,ii).*normpdf(xx(ii)).*clayton_pdf(uu,uu(ii),kappa);
- end
- toc
- figure(101);subplot(3,2,3),contour(xx,xx,zz,v,'Color',[0 0.7 0]),...
- title('Clayton copula, \kappa = 1');
- figure(102);subplot(3,2,3),contour(xx,xx,zz,v,'k-'),...
- title('Clayton copula, \kappa = 1');
- hold on;subplot(3,2,3),plot([-2,2],[0,0],'k--',[0,0],[-2,2],'k--');hold off;
- % 4. Gumbel copula
- kappa = 1.5;
- zz = normpdf(xx)*ones(1,T);% this the the part of the pdf from the X variable
- tic;
- for ii=1:T;
- zz(:,ii) = zz(:,ii).*normpdf(xx(ii)).*gumbel_pdf(uu,uu(ii),kappa);
- end
- toc
- figure(101);subplot(3,2,4),contour(xx,xx,zz,v,'Color',[1 0.4 0]),...
- title('Gumbel copula, \kappa = 1.5');
- figure(102);subplot(3,2,4),contour(xx,xx,zz,v,'k-'),...
- title('Gumbel copula, \kappa = 1.5');
- hold on;subplot(3,2,4),plot([-2,2],[0,0],'k--',[0,0],[-2,2],'k--');hold off;
- % 5. SJC copula
- tauU = 0.45;
- tauL = 0.2;
- zz = normpdf(xx)*ones(1,T);% this the the part of the pdf from the X variable
- tic;
- for ii=1:T;
- zz(:,ii) = zz(:,ii).*normpdf(xx(ii)).*sym_jc_pdf(uu,uu(ii),tauU,tauL);
- end
- toc
- figure(101);subplot(3,2,5),contour(xx,xx,zz,v,'Color',[0.5 0.5 0.5 ]),...
- title('SJC copula, \tau^U = 0.45, \tau^L = 0.2');
- figure(102);subplot(3,2,5),contour(xx,xx,zz,v,'k-'),...
- title('SJC copula, \tau^U = 0.45, \tau^L = 0.2');
- hold on;subplot(3,2,5),plot([-2,2],[0,0],'k--',[0,0],[-2,2],'k--');hold off;
- % 6. Mixture of normals copula
- rho1 = 0.95;
- rho2 = 0.05;
- zz = nines(T,T);% this the the part of the pdf from the X variable
- tic;
- for ii=1:T;
- zz(:,ii) = 0.5*bivnormpdf(xx,xx(ii),[0,0],theta2rho(rho1)) + 0.5*bivnormpdf(xx,xx(ii),[0,0],theta2rho(rho2));
- end
- toc
- figure(101);subplot(3,2,6),contour(xx,xx,zz,v,'Color',[0 0 1 ]),...
- title('Mixed normal copula, \rho_1 = 0.95, \rho_2 = 0.05');
- figure(102);subplot(3,2,6),contour(xx,xx,zz,v,'k-'),...
- title('Mixed normal copula, \rho_1 = 0.95, \rho_2 = 0.05');
- hold on;subplot(3,2,6),plot([-2,2],[0,0],'k--',[0,0],[-2,2],'k--');hold off;
工具箱压缩包下载：
|
熟悉论坛请点击新手指南
京公网安备 11010802022788号
论坛法律顾问：王进律师
知识产权保护声明
免责及隐私声明
