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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What does evalue the density of a fitted model at specific points mean?

I have read a description of R package and find the following: "Evaluate the density of the fitted model at (2.747, 0.1467, 0.13, 0.05334)". I do not understand what the author mean by ...
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integral related to a general bivariate copula C(u,v) of |u-v|

I'm trying to compute the following integral over the unit square $I^2=[0,1]^2$: $$ \int_0^1\int_0^1 |u-v|dC(u,v), $$ where $C(u,v)$ is a generic bivariate copula, which should be equal to $$ 1-2\...
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Are multivariate and cumulative exchangable in copula?

In copula model, some researchers, identify it as a multivariate distribution function, while other present it as a cumulative distribution function. I believe multivariate differs of cumulative. But ...
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How can I generate random observations from a concrete copula?

Let us assume that we have two continuous random variables $X$, $Y$, with known distributions (not necessarily normal), connected/related via a concrete copula. What is a procedure to generate random ...
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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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Copula Application

Among other things, I am working on dependency structures for the reliability analysis of river embankments and use Copulas for this purpose. I have 3 questions about this: Strucure I am not yet ...
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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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t-Copula Simulations of Bivariate Random Variables: Assigned Correlation != Calculated Linear Correlation

I have an n x n correlation matrix of random variables. Consider the following example: What I would like to do is study the behavior of the joint distributions using a t-Copula with, say, 5 degrees ...
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Why is a 3-copula better than a 2-copula?

Suppose that I have known that $X$ and $Y$ have high dependency, $Y$ and $Z$ have high dependency, and $Z$ and $X$ also have high dependency through three different 2-copulas. Suppose I fit one 3-...
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Joint Exceedance Probability for Multivariate Distribution

I was reading this paper: https://nhess.copernicus.org/preprints/nhess-2020-28/nhess-2020-28.pdf Where the notion of "joint exceedance probability" is discussed for the bivariate case. That ...
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Location-scale parameter with non-informative (improper) prior : at what condition is the posterior proper?

Consider the setup: Let $(X_i | \mu = m, \sigma = s)$ be a continuous random variable with pdf$$f_{X_i | \mu, \sigma}(x | m, s) = f_{X_i | \mu , \sigma}\big( \frac{x-m}{s} | 0,1 \big) \ s^{-1}, x \in \...
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Normalizing daily data to simulate, and then de-normalize, N-day data

I am attempting to model an N-day joint density for a portfolio of assets. To keep things simple, I have assumed a Gaussian copula but have gotten pretty unrealistic results assuming lognormal returns....
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Copula for 3 variables

I want to make Copula analysis for 3 variables to understand the dependency. I applied following code to obtain $c_{1,2}$ and $c_{1,3}$ ...
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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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From marginal distribution to joint distribution with independence

Consider a random vector $(X,Y,Z)$, Let $f_X, f_Y, f_Z$ be the probability distributions of each component. Question: Does there always exist a distribution $f$ for the whole vector $(X,Y,Z)$ such ...
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Does empirical cumulative distribution function (ECDF) has its Akaike information criterion (AIC)?

Working on multivariate distribution fitting, and right now I have marginal univariate transform models and a copula model. Was thinking if I pick ECDF for marginals, do I still have meaningful AIC? ...
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Integrating out variables in a Gaussian copula density

Consider a multivariate continuous distribution with a Gaussian copula, i.e. we can write its PDF as $$ p(x)= \biggl(\prod_{j=1}^D p_j(x_j)\biggr) c\bigl(F_1 (x_1), \dots , F_D(x_D)\bigr) \enspace, $...
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How to compute the combined probability of loss for 2 time series (consisting of historical stock prices)?

May I please ask the community's support with the following problem? I have 2 time series, with approximately 1000 observations each (same number of observations for both). They represent the daily ...
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Is a bivariate copula relevant in this physics setting manifesting uniform univariate marginals--and, if so, how can it be constructed?

To quickly place our probabilistic (copula) question in its subject matter setting, we note that a fundamental concept in quantum theory is that of entanglement QuantumEntanglement. The states of ...
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What are examples of symmetric copulas $f(x,y)=f(y,x)$ having relative minima for $f(x,x)$?

In a previous posting on this site RepulsiveBehavior I attempted to detail a quantum-information-theoretic separability/entanglement problem I am pursuing. Detailed issues of sampling sizes for a data ...
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Setting negative dependence for N random variables with copulas

I would like to use normal copulas to set the dependence of N random variables. That is, I want the correlation $\rho$ to be equal between all variables. I am doing this with the copula package in R. ...
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Do any standard copulas fit well these sampled bivariate data--exhibiting repulsive behavior--having uniform marginals

I'm currently developing a data set that consists of two $50 \times 50$ matrices, which I designate as q1 and Q1. I strongly believe (bordering on formal proof [cf. Corollary 1 in marginalinvariance]) ...
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How are copulas used in the real world?

I have been reading about copula models. Essentially, copula models seem to be a creative method for creating a joint probability distribution from several variables, in which each individual variable ...
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Confidence region in copula

I have started to use statistical copulas in R with the package copula. I want to use the copula essentially as a kernel density estimator. To be precise, my plan ...
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Can every multivariate distribution be expressed as a function of univariate distributions of the same random variables?

Can every multivariate distribution $p(X)$ of a multivariate random variable $X = [X_1, X_2, \dots, X_d]^{T} \in \mathbb{R}^d$, be defined as some function of univariate distributions on $X_i$? I ...
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Marginal Parameter Estimation vs. Joint Parameter Estimation

I have the following question relating to Marginal Parameter Estimation vs. Joint Parameter Estimation . Suppose you generate random points from a (univariate) normal distribution ~ (0,1). Then, you ...
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Simulating Correlated Continuous Variable Given 2 Existing Binary Variables

I am looking to draw samples from a Beta distribution (let's say α = 3 and β = 2) conditional on two existing binary variables in a correlated manner. Let's call the variable distributed as a Beta as <...
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Synthetic multivariate time series for anomaly detection

I built an anomaly detection classifier which worked perfectly with the anomaly detection task in my dataset (multivariate time series). Now I'm trying to understand what are its weakness and my idea ...
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Formula for multivariate Joe copula

According to p. 150-151 of Cherubini et al. "Copula Methods in Finance" (2004), here are some $n$-variate Archimedean copulas: Clayton copula The generator is $\phi(u) = u^{-\alpha}-1$ and ...
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How to show Clayton copula is continuous and decreasing at $\theta=-1$?

Clayton copula is defined as \begin{align*}C_{\theta}(x,y) =& \text{ } (max(x^{-\theta}+y^{-\theta} - 1),0)^{-\frac{1}{\theta}} \text{ if } (x,y) \in (0,1]^2\\ =& \text{ }0 \text{ otherwise} \...
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Sklar’s Extension Theorem and support restrictions

This question is about an application of the Sklar's Extension Theorem, whose proof can be found in Sklar, A. (1996), "Random variables, distribution functions, and copulas: A personal look ...
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Copula Probability default n >= 2 case

I have been reading about Copula distributions and how they can be used to find probability of default for correlated assets. Let's say I have two assets $J$ that both have a marginal distribution of $...
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Normality of sum of normal random variables

If $(X,Y)$ and $(X+Y,Z)$ both follow nondegenerate bivariate Gaussian distributions, is it possible that $(X,Y,Z)$ follow a nondegenerate trivariate distribution that is not Gaussian? I want to make a ...
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4 votes
2 answers
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Bivariate Distribution with Uniform Marginals is Bound to be Uniform?

If $X\sim U , Y\sim U$ , and $X,Y$ may be non-independent. Can we say the joint distribution of $X,Y$ is uniform?
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Independent copula vs Student-$t$ copula with zero correlation matrix?

Suppose I have the random variables $X_1, \dots, X_n$ with the marginal distributions are not normal (in fact, unknown marginal distribution). Will there be any difference between the assumption $X_1, ...
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How can a copula be seen as a characterization of association?

On the post A formal definition of a “measure of association” @kjetil b halvorsen commented the following: A copula could be seen as a characterization of association, so maybe a "measure of ...
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Mutual information is not zero for independent variables and negative for weakly dependency

To the best of my knowledge, mutual information (MI) is zero if and only if the variables are independent. I have simulated copula data and computed the ...
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4 votes
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Correlation of the sample as the estimation of parameter of Gaussian copula

Given 3 variables $X, Y, Z$ and I assume that the multivariate distribution of them is a Gaussian copula. Now I need to estimate the correlation matrix of the Gaussian copula. As in many textbooks, i ...
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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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How to determine the lag.max length for daily (10 years) data stock prices data set in R

I have 20 years of daily data set for some stock prices. I would like to investigate the autocorrelation for this using acf plot and ...
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2 votes
1 answer
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How to forecast from GARCH-copula model?

I am reading to understand how to forecasting time-series data from the GARCH-copula model. I am looking forward to understanding the steps. From my understanding, we should follow the following steps:...
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2 votes
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How to transfer the residuals to the uniform margin for copula-GARCH model in R?

I am studying the copula model in finance. To the best of my knowledge, I need to fit the GARCH model to my data (to each time series). Then, I need to get the residuals for each. After that, I need ...
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3 votes
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Generating an analytical copula for an example problem

I am currently doing research that requires me to understand dependence modeling. As a first step, I am reading An Introduction to Copulas. I am, stuck on the first example problem which I have re-...
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How to simulate from Nelsen 4.2.12 copula?

I want to simulate a 3 dimensional copula from Nelsen 4.2.12 copula (copula marked as 4.2.12 in Nelsen 2006, page 116). I found an algorithm, which uses partial derivatives, in Nelsen (2006), page 41 ...
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How many pairwise copulas in a $k$-dimensional R-vine?

I am studying R-vine copulas. Let $k$ denote the number of random variables the joint distribution of which we are modeling. R-vine breaks down the $k$-variate copula into $K$ bivariate copulas. I am ...
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4 votes
1 answer
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Introductory reading on vine copulas

I am looking for a gentle introduction into vine copulas and R-vines in particular. (There is a related thread for copulas in general, but the answers there do not seem to contain an introduction into ...
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2 votes
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Should I say "copula" or "copula function"? Is the latter superfluous?

I am writing a paper involving copulas and have been thinking of whether I should say "copula function" or just "copula", as I am not sure whether the term "copula" ...
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Simulate random variables with "inner" and "outer" correlation

Let us say we have data grouped in $m$ different classes, each of size $n_j$ for $j = 1,...,m$. We denote as $X_k^{(j)}$ the $k$-th member of group $j$. We want to simulate unit-variance random ...
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Inferring properties of the sum of R.V.s from the copula

This is not a completely well defined question, so even help making it coherent will be useful. Setting: Suppose I know the marginal distributions of random variables describing the expected losses ...
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How to estimate probability of $\geq$ 1 success from a non-IID vector of probabilities, given many such vectors (now with asteroids)

I've got a deep neural net that returns sequences of probabilities. There are 25 probabilities per sequence. Many of these probabilities are zero, as a result of padding; when the input to the ...
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