# Questions tagged [copula]

A copula is a multivariate distribution with uniform marginal distributions. Copulas are mostly used to represent or to model the structure of dependence between random variables, separately from the marginal distributions.

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### Fitting Vine Copula tree by tree

I am using the R programming language. I want to manually fit the D-vine copula for tree level 2 using BiCopHfunc(). Still, I ...
834 views

### How can I sample from a copula with a given correlation in python?

How can I sample from a normal copula with a given correlation in python? I know how to sample from a multivariate normal distribution with a given covariance matrix using numpy and scipy, but I don't ...
1 vote
19 views

### Gap between the given correlation parameter and the empirical correlation in (Gaussian) copula simulation

Now I am trying to simulate normal copula with initial parameters being a correlation matrix of my wish. I found that the empirical correlations are generally lower than what is entered as the initial ...
257 views

### Geometric construction of copula - question regarding C-volume

I am learning about copula's, using Nelsen's book, and more specifically about the geometric method of constructing copula's. The problem is replicated in the following link: http://www.stat.ubc.ca/...
60k views

### Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?

Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Gaussian with their means and variance ...
16 views

### Degrees of freedom in a likelihood ratio test - multivariate normal vs univariate normal and Archimedean copula

Hopefully the title is self explanatory! To be more specific, I have three datasets. First, I fit them to a multivariate normal distribution, and calculate the log-likelihood. Then, I fit normal ...
123 views

### Is conditional expectation evaluated by the copula strictly increasing when the correlation coefficient is positive and vice versa?

I used the copula to evaluate the $\mathbb{E}[Y|X]$ and from my experiments on some copulas, I observed that when the random variables have positive correlation coefficient, $\mathbb{E}[Y|X]$ is ...
409 views

### Fitting a Copula from Scratch

I am trying to learn about how to work with Copulas. I find that I am often getting lost in the notations and distributions, and wanted to try and solidify my understanding. As it stands, here is my ...
221 views

### Why does the multivariate data generated by a copula in R not exhibit the prespecified correlation?

I am using the package copula in R to generate a bivariate sample. The marginal distributions are binomial with p=0.5 and ...
423 views

### How to prove that a function is 2-increasing (copula)

There are three conditions to prove that a function is a copula: $C(u,0)=0=C(0,v)$ grounded. $C(u,1)= u, C(1,v)= v$. $C(u,v)$ 2-increasing function. Here I am concerning in the last condition how to ...
23 views

### How to predict using a copula approach?

I have a dataset with both continuous and discrete variables the target variable is 0-1 and I was wandering on how to predict the target var with the copula regression. I'm using python to do so and I ...
20 views

### How many degrees of freedom in a T-copula is commonly used to model financial data?

I'm looking to fit some T-copulas to my financial return data. Unfortunately, the software I'm using can only fit a T-copula with a fixed degree of freedom parameter. So what parameter should I use? ...
28 views

### How to prove this relation for Kendall's distribution function (or Kendall's measure)

Kendall Distribution Function (Nelsen, 2006, p. 163) Or Kendall Measure (Salvadori et al., 2007, p. 148) Or Kendall Function (Joe, 2014, pp. 419–422) is the cumulative distribution function (CDF) of ...
48 views

### Steps for Forecasting with known copula's parameters

I want to calculate the Mean absolute percentage error (MAPE) for my copula model. I am stuck at the forecasting step. I am not specifying the copula here for different data pairs. I have two time ...
58 views

### Suppose $(X,Y)$ have copula $C(u,v)$, does $(aX,aY)$ have the same copula for $a>0$?

Suppose $(X,Y)$ have copula $c(u,v)$ in the sense of $Pr(X\leq x,Y\leq y)=Pr(F_X(X)\leq F_X(x),F_Y(Y)\leq F_Y(y))=Pr(U\leq u, V\leq v)=c(u,v)$, where $u\equiv F_X(x)$ and $v\equiv F_Y(y)$ and $c(u,v)$ ...
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### Should simulation from a student-t copula distribution yield the input correlation matrix

I am using mathematica to simulate random variates from a student-t copula distribution. Assuming that I input in the correlation matrix R, after generating a certain number of random variates, should ...
1 vote
40 views

### Should I not use copula if there is no significant dependence?

I have two variables, and I would like to get the joint distribution of those. I want to use copulas for that. However, when I checked for the dependence between those, I found no significant ...
85 views

### What is the formula for the conditional inverse function for the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copulas?

I am trying to do a Monte Carlo simulation and want to define a function for the conditional inverse function for the the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copula. Here is an example ...
295 views

### Forecasting using Copula GARCH methods

I need to replicate what Huang and al (2009)* did without using built-in functions in R. What I'm struggling with is how to forecast returns for my two data samples. I've found the GARCH specs and ...
1 vote
54 views