Simulating stock returns as normally distributed to run through a copula

Question

pete4466 2022-4-11

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1693745-simulating-stock-returns-as-normally-distributed-to-run-through-a-copula

评论： Kausthub 2024-1-31

I am trying to model stock index returns for 4 different indices as normally distributed, to then run these distributions through a copula to obtain their correlation structure. I keep encountering the error ,

Error using copulafit (line 75)

U must contain values strictly between 0 and 1.

I know this is because the normal cdf of each set of returns varies between [0,1] , but when I model the returns as having a kernel distribution, the code runs fine, so how do I get a normal distribution cdf estimate for each set of returns that is between (0,1), so that the returns are able to be inputted to copulafit.m ?

Here's the code for a normal distribution estimate, that doesn't work.

% returns_N(:,1234) = returns for each of the 4 indices 
u= normcdf(returns_N(:,1),mean(returns_N(:,1)),std(returns_N(:,1)));
v= normcdf(returns_N(:,2),mean(returns_N(:,2)),std(returns_N(:,2)));
w= normcdf(returns_N(:,3),mean(returns_N(:,3)),std(returns_N(:,3)));
x= normcdf(returns_N(:,4),mean(returns_N(:,4)),std(returns_N(:,4)));
correlation_gaussian_normal = copulafit('Gaussian',[u v w x]);
%Error using copulafit (line 75)
%U must contain values strictly between 0 and 1.

Heres the code for a kernel distribution estimate, that works fine

u = ksdensity(returns_N(:,1),returns_N(:,1),'function','cdf');
v = ksdensity(returns_N(:,2),returns_N(:,2),'function','cdf');
w = ksdensity(returns_N(:,3),returns_N(:,3),'function','cdf');
x = ksdensity(returns_N(:,4),returns_N(:,4),'function','cdf');
correlation_gaussian_kernel = copulafit('Gaussian',[u v w x]);

3 个评论
显示 1更早的评论隐藏 1更早的评论

Phillip McCart 2022-6-3

在 MATLAB Online 中打开

Did you ever find the answer to this?

I'm having a the same problem but I'm using ecdf instead of normcdf

[fx,~]=ecdf(x);
[fy,~]=ecdf(y);
u = [x,y];
[rhohat,nuhat,nuci]=copulafit(u)
Error using copulafit (line 75)
U must contain values strictly between 0 and 1.

I've verified that the values of fx and fy lie between 0 and 1 or are 0 and 1. I've tried deleting the zeroes and the beginning of fx, fy and same goes for the 1s and the end.

I'm so confused! U doesn't contain any values greater than 1 or less than zero!!

Kausthub 2024-1-31

Hi Phillip, shouldn't it be u = [fx,fy] instead of u = [x,y] since you have verified the values of fx and fy lie between (0,1)?

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Kausthub 2024-1-31

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1693745-simulating-stock-returns-as-normally-distributed-to-run-through-a-copula#answer_1400691

编辑：Kausthub 2024-1-31

在 MATLAB Online 中打开

Hi Pete and Phillip,

I understand that you are facing issues regarding the "normcdf" function. The range of "normcdf" and "ecdf" is [0,1] which is inclusive of both 0 and 1, whereas "copulafit" requires values strictly between (0,1) i.e., exclusive of both 0 and 1. Since, there is possiblity of "normcdf" and "ecdf" returning 0 or 1, the "copulafit" function errors when it recieves an input containing either of 0 or 1. For example:

x = [-2,-1,0,1,11];
mu = 2;
sigma = 1;
u = normcdf(x,mu,sigma)
u = 1×5
    0.0000    0.0013    0.0228    0.1587    1.0000
correlation_gaussian_kernel = copulafit('Gaussian', [u]);
Error using copulafit
U must contain values strictly between 0 and 1.