Here is a more convenient way to fit trivariate copulas symmetrically.
Load Data
Arrange the data so that it becomes a matrix whose columns are each variable.
load stockreturns
x = stocks(:,1:3);
Fit the Copula
Just like bivariate copula, the fitting step begins by determining the marginal distribution, then transforming the data.
C = symmetricfit(x);
% ===== OUTPUT ======
Marginal Distribution:
No. 1: Dist Name = Logistic
mu = -0.19364, sigma = 0.58158
No. 2: Dist Name = Generalized Extreme Value
k = -0.21362, sigma = 1.1975, mu = -0.66838
No. 3: Dist Name = Generalized Extreme Value
k = -0.36064, sigma = 1.6488, mu = -0.92152
Case = 3-Copula Symmetric
Selected by = Akaike Information Criterion
Fittest copula:
Copula Name = Gaussian
param1 =
1.0000 0.7223 0.3642
0.7223 1.0000 0.3652
0.3642 0.3652 1.0000
Goodness-of-fits:
AIC (Joint PDF) = 906.6
CvM = 0.023
RMSE = 0.015
pVal = 0.725
You can see the step-by-step for more details.
The joint CDF and joint PDF values can be returned in the same way.
jpdf = jointpdf(C,x);
jcdf = jointcdf(C,x);
Download: this example is available on demo4.m. Visit Github
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