Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2406.15582

Graphical copula GARCH modeling with dynamic conditional dependence

Lupe Shun Hin Chan·Amanda Man Ying Chu·Mike Ka Pui So
View original source ↗Read source document ↗Export metadata ↓

Abstract

Modeling returns on large portfolios is a challenging problem as the number of parameters in the covariance matrix grows as the square of the size of the portfolio. Traditional correlation models, for example, the dynamic conditional correlation (DCC)-GARCH model, often ignore the nonlinear dependencies in the tail of the return distribution. In this paper, we aim to develop a framework to model the nonlinear dependencies dynamically, namely the graphical copula GARCH (GC-GARCH) model. Motivated from the capital asset pricing model, to allow modeling of large portfolios, the number of parameters can be greatly reduced by introducing conditional independence among stocks given some risk factors. The joint distribution of the risk factors is factorized using a directed acyclic graph (DAG) with pair-copula construction (PCC) to enhance the modeling of the tails of the return distribution while offering the flexibility of having complex dependent structures. The DAG induces topological orders to the risk factors, which can be regarded as a list of directions of the flow of information. The conditional distributions among stock returns are also modeled using PCC. Dynamic conditional dependence structures are incorporated to allow the parameters in the copulas to be time-varying. Three-stage estimation is used to estimate parameters in the marginal distributions, the risk factor copulas, and the stock copulas. The simulation study shows that the proposed estimation procedure can estimate the parameters and the underlying DAG structure accurately. In the investment experiment of the empirical study, we demonstrate that the GC-GARCH model produces more precise conditional value-at-risk prediction and considerably higher cumulative portfolio returns than the DCC-GARCH model.

Explore related subjects

stat.MEstat.APstat.CO

Keep this discovery

BibTeXRIS

Lupe Shun Hin Chan, Amanda Man Ying Chu, Mike Ka Pui So. 2024-06-21. Graphical copula GARCH modeling with dynamic conditional dependence. https://arxiv.org/abs/2406.15582

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Surprise Reduction and Nullification in Bayesian and Inverse Bayesian Inference under Ambiguous Prediction-Error Attribution

In non-stationary environments, prediction errors may signal environmental change or transient outliers, and adaptive systems must track such changes without overreacting to outliers. We distinguish surprise reduction, which updates beliefs to fit observations, from surprise nullification, which weakens constraints imposed by the predictive structure, and formalize both within Bayesian and inverse Bayesian (BIB) inference. Belief and likelihood updates are derived from variational objectives sharing a nullification strength, determined endogenously by minimizing surprise under the candidate post-update predictive distribution. In the Gaussian case, nullification expands belief and likelihood variances by a common factor relative to standard Bayesian updating, leaving the ratio unchanged. BIB thus defers attribution of the prediction error, committing to neither latent-state change nor observation-process uncertainty. The nullification strength is carried over as a candidate and is maintained or released according to the predictive surprise of the next observation. In a mean estimation task with outliers and changepoints, no scanned parameter setting of a Sage-Husa-type adaptive Kalman filter, fixed-strength BIB variant, or belief-forgetting-only variant outperforms BIB in both changepoint tracking and post-outlier stability. An oracle-informed reduced Bayesian model tracks changepoints better but is less stable after outliers. Although BIB maintains no explicit hypotheses about changepoints or outliers, it generates event-dependent dynamics. The learning rate increases after changepoints, whereas after outliers, nullification is released, and this increase is suppressed. Deferring attribution and letting subsequent observations differentiate the responses may constitute a principle of adaptive inference in non-stationary environments.

stat.ME↗
arXiv2026

Generalized Ridge Refitting for the Lasso and Prediction Improvement Bounds

We study a class of Lasso based estimators obtained by applying a quadratic correction on the Lasso equicorrelation set. The penalty matrix determines both the magnitude and geometry of the correction and contains, among other cases, the isotropic Lasso--Ridge correction, least squares refitting, Gram proportional interpolation between the Lasso and least squares, and coordinate specific penalties. We first derive a closed form representation and isolate the positive gain component of the resulting prediction improvement. We then control the remaining stochastic linear term in expectation by localizing the random signed equicorrelation model around a deterministic reference support. This yields a finite sample expectation bound that explicitly accounts for the randomness induced by Lasso model selection. The resulting decomposition provides a unified framework for understanding when Lasso based quadratic corrections can improve prediction.

stat.ME↗
arXiv2026

Discretization in covariate-adaptive randomization: gains and losses

Covariate-adaptive randomization(CAR) is widely implemented in clinical trials to balance prognostic covariates across treatment arms. Continuous covariates are often discretized into strata in practice, yet their consequences are not clearly understood. This paper provides a comprehensive study of the impact of discretization on both the CAR design process and the inferential results thereafter. We establish the asymptotic properties of both imbalance measures and treatment effect estimators under discretized and non-discretized settings. Practical recommendations are given on when and how discretization should be employed. We show that discretization in design is generally recommended, as it enhances robustness against model misspecification. However, if the true model is known, the most efficient strategy is to balance covariates according to that model in the design. The theoretical results are corroborated by extensive simulation studies and an empirical application to a diabetes trial dataset. Together, the results clarify the gains and losses of discretization in CAR and pave the way for learning impact of discretization to other designs and beyond.

stat.ME↗