The dynamic Gaussian copula model shows default times are invariant, contrary to the immersion property.
problem The dynamic Gaussian copula model's default times exhibit unexpected invariance properties.
method Proof of invariance properties of default times in the dynamic Gaussian copula model.
result Default times in the dynamic Gaussian copula model are invariant, contrary to the immersion property.
Dynamic Vine Copulas detect and quantify time-varying higher-order interactions in multivariate systems.
problem Time-varying dependence in multivariate systems, including tail behavior, asymmetry, and conditional structure.
method Dynamic Vine Copulas (DVC) framework for estimating and diagnosing non-Gaussian dependence, using fixed-root-order C-vines and smooth parameter trajectories.
result DVC detects and quantifies time-varying higher-order interactions, distinguishing between pairwise and conditional dependence.
New formula for portfolio risk management using conditional PDEs.
problem Optimal diversification and risk management of portfolios.
method Closed-form formula for conditional probability, Gaussian copulas, conditional risk-neutral PDE.
result Dynamic monitoring of portfolio volatilities and weights from PDEs.
A new method models volatile financial time series using v-transforms and copulas.
problem Modeling volatile financial time series with standard methods.
method v-transforms and copulas to describe and estimate time series with arbitrary marginal distributions and copula dynamics.
result The model replicates stylized facts of financial return series and facilitates risk quantification.
We follow a long path for Credit Derivatives and Collateralized Debt Obligations (CDOs) in particular, from the introduction of the Gaussian copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the s…
Using one of the key property of copulas that they remain invariant under an arbitrary monotonous change of variable, we investigate the null hypothesis that the dependence between financial assets can be modeled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with…
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and automated variational Gaussian copula approach, in which the parametric Gaussian copul…
New method estimates Gaussian copulas with missing data using EM algorithm.
problem Estimating Gaussian copulas with missing data and prior assumptions.
method Rigorous application of the Expectation Maximization (EM) algorithm for marginal distributions and dependence structure.
result Joint distribution learned is closer to the underlying distribution.
GCMM improves clustering and fits un-synchronized data.
problem Improving clustering performance with copulas.
method Mathematical definition, copula concepts, Expectation Maximum algorithms, nonparametric estimation.
result GCMM outperforms GMM in goodness-of-fit and data analysis.
We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for several copula families such as the Gaussian copula, copulas of a class of Gaussian mi…
Paper models ultra-high dimensional data using Gaussian and vine copulas.
problem Modeling ultra-high dimensional non-Gaussian data.
method Divide-and-conquer approach: Gaussian methods for subsets, vine copulas for reconciled model.
result Feasibility and estimation in thousands of dimensions demonstrated.
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of…
A new vine copula mixture model improves clustering accuracy for non-Gaussian data.
problem Finite mixture models struggle with asymmetric tail dependencies and non-elliptical clusters.
method Proposes a vine copula mixture model for clustering non-Gaussian data, addressing model selection and parameter estimation.
result Significant improvement in clustering accuracy for data with asymmetric tail dependencies or non-Gaussian margins.
The paper examines how heavy-tailed risks behave under Gaussian copula models.
problem Understanding tail risk probabilities with heavy-tailed marginal risks and Gaussian dependence.
method Modeling heavy-tailed risks using regular variation and analyzing tail probabilities under Gaussian copula.
result The rate of decay of tail set probabilities varies with the type of tail sets and Gaussian correlation matrix.
A new copula model for multi-attribute data using optimal transport.
problem Relaxing the Gaussian assumption for multi-attribute graphical models.
method Introducing a new copula (Cyclically Monotone Copula) and using optimal transport theory.
result The model allows arbitrary continuous distributions and is more flexible than classical methods.
We improve Gaussian copula models for imputing mixed data types with precise approximations.
problem Imputing missing values with mixed data types in surveys and medical applications.
method We use randomized quasi-Monte Carlo procedures for direct and arbitrarily precise approximations of model estimation and imputation.
result Our method yields lower errors for model parameters and imputed values compared to existing methods.
Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, i…
A new method aggregates predictions from decentralized learners using Gaussian copulas.
problem Learning from different data sets without sharing data.
method DELCO (Decentralized Ensemble Learning with COpulas) method using Gaussian copulas to aggregate predictions.
result Increased robustness and competitive accuracy in case of dependent classifiers.
New multivariate dependency measure using Gaussian kernel and copula.
problem Measuring dependency between multivariate distributions.
method Gaussian kernel distance to uniform copula, normalization, nonparametric estimate.
result Proposed measure satisfies desirable properties and is compared with existing measures.
We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption…
A2-SBNN models spatial data with copulas for non-Gaussian dependencies.
problem Capturing complex spatial relationships and extreme dependencies in non-Gaussian data.
method Embedding A2 copula into a Bayesian neural network, trained with Wasserstein loss and moment matching.
result A2-SBNN consistently delivers high accuracy across various dependency strengths.
Paper proposes copula-based models for analyzing multivariate zero-inflated continuous data.
problem Challenges in analyzing multivariate zero-inflated continuous data with mixed discreteness and continuity.
method Proposes two copula-based density estimation models and rectified Gaussian copula.
result Demonstrates superior performance compared to conventional methods.
All too often measuring statistical dependencies between financial time series is reduced to a linear correlation coefficient. However this may not capture all facets of reality. We study empirical dependencies of daily stock returns by their pairwise copulas. Here we investigate particularly to which extent the non-st…
Novel model captures high-dimensional copulas with spectral dynamics and regularization.
problem Modeling time-varying, asymmetric, tail-dependent copulas in high dimensions.
method Score-driven dynamics for eigenvalues, non-linear shrinkage for biases, parsimonious and scalable.
result Model outperforms recent alternatives in capturing co-movements and diversification potential.
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Stude…
Time series models generalize ARMA and ARFIMA with non-Gaussian dependence.
problem Modeling non-Gaussian serial dependence in time series data.
method Infinite-order partial copula dependence in s-vine processes.
result Rich class of models that generalize linear processes.
The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first elaborate Gaussian VAE, approximating the local covariance matrix of the decoder as an o…
New variational family approximates non-Gaussian posteriors efficiently.
problem Approximating non-Gaussian posteriors in Bayesian models.
method Copula-like variational distributions with efficient sampling and normalizing flows.
result The proposed method performs comparably to state-of-the-art approximations.
A novel stepwise VI method using vine copulas for complex latent dependence.
problem Modeling complex latent dependence structures in probabilistic models.
method Stepwise estimation of vine copula parameters using Rényi divergence and a stopping criterion.
result Our method outperforms mean-field VI and is more parsimonious in complex applications.
We analyze the statistical dependency structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange's TAQ database. With a copula-based approach, we find that the statistical dependencies are very strong in the tails of the marginal distributions. This…
Adaptive Bernstein copulas improve risk management by preventing overfitting and reducing simulation effort.
problem Overfitting and high simulation effort in estimating dependence models.
method Constructive approach to Bernstein copulas with an admissible discrete skeleton.
result Comparison of different copula approaches in risk management shows improved accuracy and efficiency.
New online imputation method for mixed data improves accuracy and speed.
problem Missing value imputation in online settings for mixed data types.
method Online Gaussian copula model for imputation and change point detection.
result The model improves accuracy and speed, especially on large datasets.
Paper compares econometric models with machine learning for energy forecasting.
problem Tackles the trade-off between predictive accuracy and interpretability in energy markets.
method Integrates TVP-SVAR with copulas for forecasting energy--macro dynamics.
result Copula-enhanced econometric models provide interpretable insights while matching machine learning accuracy.
SynC generates synthetic population from aggregated data using Gaussian copula.
problem Generating individual-level data from aggregated datasets is challenging.
method SynC removes outliers, fits with Gaussian copula, merges datasets, and scales them.
result SynC efficiently combines multiple datasets into synthetic individual-level data.
We use copulas to improve SLAM in uncertain environments.
problem Uncertain data association and nonlinear transition models in SLAM.
method Integrate copulas into a Sequential Monte Carlo estimator for SLAM.
result Our method effectively handles SLAM in uncertain environments.
The paper assesses portfolio risk using copula models.
problem Assessing portfolio risk in financial time series.
method Proposes an algorithm for risk measure computation using copula models.
result Risk curves from copula models are lower than historical values.
The article models financial asset returns using Gaussian mixtures and EVT-based copulas to price equity options.
problem Modeling financial asset returns and pricing equity options considering extreme values.
method Modeling marginal distributions with Gaussian mixtures and joint dependence structure with EVT-based copulas.
result The approach accurately prices various equity options on Atos and Dassault Systems actions.
A new autoencoder method uses empirical beta copulas for generating data.
problem Creating a generative model from an autoencoder's latent space.
method Empirical Beta Copula Autoencoder method.
result The Empirical Beta Copula Autoencoder outperforms other methods in simplicity and effectiveness.
The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be inaccurate when there are covariates that cou…
Proposes a new VAE model to avoid posterior collapse by modeling latent variable dependencies.
problem Posterior collapse in variational autoencoders due to assumption of factorized variational posterior.
method Introduces Gaussian Copula Variational Autoencoder (GCVAE) to model latent variable dependencies explicitly.
result Empirical results show GCVAE can avoid posterior collapse while maintaining competitive performance.
Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the `right' copula is not an easy task, and the temptation to prefer a tractable rather than a meaningful candidate from the encompassing…
In this paper we present a new multi-asset pricing model, which is built upon newly developed families of solvable multi-parameter single-asset diffusions with a nonlinear smile-shaped volatility and an affine drift. Our multi-asset pricing model arises by employing copula methods. In particular, all discounted single-…
Copula models for sovereign ratings improved by incorporating climate risk.
problem Modeling nonlinear dependence and clustering in sovereign rating migrations.
method Mixed-difference transformation, MAGMAR(1,1) copula process, consistent and asymptotically normal estimators.
result Gumbel MAGMAR(1,1) specification outperforms other models in empirical performance.
In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estima…
Proposes a copula-driven framework for multimodal learning.
problem Aligning and fusing representations from multiple modalities with complex interactions.
method Copula model for joint distribution of modalities, Gaussian mixture for marginal distributions.
result Superior performance on public MIMIC datasets.
This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory. We explore the relationship between dependence and the possibility to sample final multivariate survival in a long time-interval as a sequ…
The paper estimates CoVaR with various models for financial risk analysis.
problem Estimating conditional value-at-risk with financial time series data.
method Fitting multivariate parametric models and copula functions to capture stylized facts of equity returns.
result Backtesting shows that certain models provide better risk estimates than others.
Deep learning model estimates mutual information with low bias and variance.
problem Estimating mutual information between continuous variables.
method Supervised deep learning approach using Linfoot informational correlation as labels.
result Lower bias and variance compared to other methods.