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 ...
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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 ...
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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 ...
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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/...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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? ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Correlation of a Gaussian copula
Suppose I have a 2D Gaussian copula with correlation matrix
$$
R = \begin{bmatrix}
1 & \rho \\
\rho & 1
\end{bmatrix}
$$
for $\rho\in[-1,1]$. The Copula is
$$
C_R(u)=\Phi_R\big(\Phi^{-1}(u_1),\...
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How to calibrate and simulate a copula-garch model in R using rmgarch package
So I have been trying to calibrate and simulate cryptocurrencies for VaR and ES analysis using the rmgarch package in R. I have been using the t-copula, my reason being that cryptocurrencies' ...
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How to write a function for the normal copula in R?
How can I write the following function for the normal copula in R?
$$
C_\theta(u, v)=\Phi_\theta\left(\Phi^{-1}(u), \Phi^{-1}(v)\right),
$$
where $\Phi$ is the $N(0,1)$ cdf, $\Phi^{-1}$ is the ...
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How do we select the best copula family?
Suppose that I have bivariate data, and I need to model the bivariate dependence structure using a copula. Suppose further, I do not know what the best-fit copula family to my data is. Hence, I can ...
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Return period of vine copula
In the formula for "OR" joint return period of 3-dimensional copula modeling, we need to find C(u,v,w) but when we model using vine, we are only able to obtain the copula C(uv|w). So, how to ...
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What are the convincing examples of copulas uncovering not obvious statistical dependences (or the lack of them)?
What may be a good, strong and convincing example demonstrating the power of copulas by uncovering some not obvious statistical dependencies?
I am especially interested in the example contrasting ...
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Expression of estimated standart deviation in GAMLSS model
I'm trying to replicate the results of the North Carolina Birth Data Analysis in the paper A Bivariate Copula Additive Model for Location, Scale and Shape by Giamperro Marra and Rosalba Radice (https:/...
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Gaussian copula, t-student copula and Frank copula, seem are the same?
I read about Gaussian, t-student and Frank copula. Gaussian copula is similar to Frank copula where both of them cannot model tail dependencies. Also, I read that, t-student copula is symmetric tails ...
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Grid search for estimation of degrees of freedom parameters in likelihood function
In the script below I attempt to estimate parameters for Apple and Amazon using a Gaussian Copula with t-Student marginals for the purpose of this exercice.
When executing the script, I notice at each ...
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Why use a copula to generate synthetic data?
For class, I am tasked to generate synthetic stock data using the copula R package. The step-by-step process is picking 2 stocks (i.e., Amazon & Apple), fit their marginal distributions (I am ...
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Endogeneity Analysis without the access of raw data?
I currently have the correlation/covariance matrix for a set of variables, as well as the output from a regression analysis, but lack access to the underlying raw dataset. Given these constraints, ...
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How to construct a multivariate Beta distribution?
What is a multidimensional generalization of the Beta distribution, in compliance with the following specification?
I am not looking for the Dirichlet distribution.
I am looking for a generalization ...
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Derivation of Sklar's theorem for copula
The joint probability distribution, or bivariate CDF, of two random variables $X$ and $Y$ is
$$F(x,y) = P(X\leq x, Y\leq y)$$
where $F(x) = P(X\leq x)$ would be the marginal distribution of $X$.
Sklar'...
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How are the joint distribution and dependency related? [closed]
Here are some notes about copula functions,
Copula is a probability model that represents a multivariate uniform distribution, which examines the association or dependence between many variables. Put ...
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How to draw samples from two correlated Negative Binomial variables?
Data and problem description: my data is the number of corner kicks of home team, away team, total corner kicks and corner kicks difference. Below is code for data and the plots (assuming the number ...
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Obtain minimum-variance hedge ratio from a copula-GARCH model
Let $r_{s, t}$ and $r_{f, t}$ be the return rates of the spot and futures of a commodity at time $t$. The hedging ratio based on variance minimization is calculated by finding the minimum of the ...
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More than one possibility for the generator function of a Clayton's copula?
This question is about the bivariate family of Clayton's copulas, defined as:
$$
C(u,v)=\left(u^{-\theta} + v^{-\theta}\right)^{-1/\theta} \; \text{,} \quad \quad \text{(1)}
$$
with $\theta \in [-1, +\...
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Advantages of using Vine Copulas over Regular Copulas?
I am new to Copulas and am trying to conceptually understand that differences between the two main types of Copulas: Regular Copulas and Vine Copulas. Both are used to simulate data from correlated ...
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Using copulas to fit hourly observations to daily data
I've been trying to automatically find low periods in some data that I have. The data is structured as hourly observations across a period of two years. Thus far I've experimented with a number of ...
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Parametric copulas with marginals that are regressions
In Dependence Modeling with Copulas (Harry Joe) I'm struggling to interpret the meaning of a statement. In Chaper 5.1, it is stated:
Parametric inference for copulas
For dependence modeling with ...
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best strategy to test bivariate data
Here's a revised version of your text:
I have two sets of data: Intensity and Duration. For each set, I possess both observation data and model data, denoted as (I_obs, I_mod) and (D_obs, D_mod) ...
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Generate samples from multivariate correlated data which have non-parametric cumulative distribution functions
I have 40 samples that contain information about 6 variables (hence a 40x6 data matrix). Each variable (column) has a cumulative distribution function (marginal distribution) based on the 40 values, ...
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Tail dependence index for Gaussian copula is 0 [closed]
Why is Gaussian Copula's Tail Dependence Zero?
I am confused about the second equation. Why does the derivative of C(q,q) can be written in two parts? And why each part has a conditional ...
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Why don't we see Copula Models as much as Regression Models?
Is there any reason that don't see Copula Models as much as we see Regression Models (e.g. https://en.wikipedia.org/wiki/Vine_copula, https://en.wikipedia.org/wiki/Copula_(probability_theory)) ?
I ...
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What is this copula?
I have a bivariate sample in the [0,1] square for which I am trying to find the copula that best describes it. (I am new to copulas.)
So far, I have tried all classes in the "copula" R ...
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Difficulties reproducing an R-blogger's example of modelling dependency with copulas
This is the R-bloggers article in which a t-distribution copula (?) is fitted to explain the dependency between fluctuations in two stocks tickers. I don't understand what they are trying to achieve, ...
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Copula to ensure one team wins and the other loses (Bernoulli margins)
Team $1$ has a historical win percentage of $p_1$.
Team $2$ has a historical win percentage of $p_2$.
The upcoming game features team $1$ against team $2$ and cannot end in a tie (one team wins, and ...
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Are precipitation and soil moisture time-independent variables?
I was studying about Copula functions from here. It says:
Basically, copula is a set of mathematical tools that have the ability to connect two or more time-independent variables (Nelsen, $2003$)
As ...
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Are there margins such that, while the "correlation" parameters of a Gaussian copula are positive, the correlations between the margins are negative?
Let there be a multivariate distribution $F$ with margins $F_1,\dots,F_n$ and a Gaussian copula with "correlation" matrix $\Sigma$. Let the off-diagonal elements of $\sigma$ be positive.
Let ...
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Why is Gaussian Copula's Tail Dependence Zero?
I know that the Gaussian copula has a zero tail dependence (tail independence) due to the exponential behaviour at the tail. I am just wondering if there is a rigorous proof for this?
For simplicity ...
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Is it possible to sample a copula in the original units?
I have a fairly high dimensional dataset that is not mvnormal. I used a copula to model the data and it fits well. How can I go about generating random samples from that copula that are in the ...
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