arXiv subjects

Chen Tong

Publications and source records attributed to Chen Tong.

At least 19 recordsLinked to original sources

arXiv2026

Convolution Skew-$t$ Distributions

We introduce the convolution skew-$t$ (CST) distribution, which combines independent standardized skew-$t$ subvectors through a general loading matrix to accommodate heterogeneous tails, directional asymmetry, and non-elliptical dependence. We establish identification and develop likelihood inference using analytical scores and a one-dimensional reduction of Fisher information. For the finite-variance model, we prove consistency and asymptotic normality of maximum likelihood and characterize the consequences of imposing false symmetry. A raw representation extends the family to all positive tail indices. Simulations assess finite-sample performance, and a realized-volatility application illustrates the empirical value of allowing tail thickness and asymmetry to vary across latent subvectors.

econ.EM↗

arXiv2026

A Balanced Parametrization of Correlation Matrices

We introduce the balanced correlation parametrization (BCP), which maps positive-definite correlation matrices one-to-one onto the set of symmetric hollow (zero-diagonal) matrices with unrestricted off-diagonal entries. A key feature of the parametrization is that both the transformation and its inverse are available in closed form. It can be viewed as a generalization of the transformation underlying the classical correlation $t$-statistic to higher dimensions. It has a direct interpretation as a scaled sum of marginal and partial correlations, is inverse-consistent and equivariant under variable permutations and sign changes, and preserves block structure. A novel property of BCP is that it preserves correlation sparsity as the dimension tends to infinity under suitable factor conditions, providing a basis for sparse high-dimensional correlation modeling. An empirical illustration using standardized idiosyncratic daily stock returns for 1,765 equities over 15 years shows that BCP retains the approximate sparsity pattern and magnitudes of shock correlations, and that it yields accurate positive-definite reconstructions under sparse coordinate restrictions.

econ.EM↗

arXiv2026

Tweedie's Formula and Score-Driven Updating

Tweedie's formula expresses a conditional mean in terms of a score function, and this connects score-driven models with Bayesian updating. We show that the score-driven update is identical to a Bayesian update in some special cases. More generally, we show that score-driven updating is a local approximation to Bayesian updating, with an error of second order in the predictive variance. The second-order approximation error has two components, one from the curvature of the log likelihood and one from the asymmetry of the posterior distribution. Implicit score-driven (ISD) updating, which evaluates the score at the updated parameter, corrects for the former but not the latter. A simple correction for the second component leads to an improved third-order approximation, which we denote ISD*. Numerical experiments show substantial gains from ISD and ISD*.

econ.EM↗

arXiv2026

Nonrelativistic expansions of Dirac-Coulomb energy and first order relativistic Breit potential corrections for light Atomic and molecular systems

The nonrelativistic expansion method is applied to the Dirac-Coulomb energy and first order relativistic Breit potential corrections for light atomic and molecular systems to derive high-order effective energy correction operators for few-body systems. It is found that effective operators at the $mα^8$ order contain incompletely separable divergences. These divergences must be canceled jointly with divergences arising from second- and third-order perturbations of lower-order energy correction operators, and such cancellation can be accomplished automatically by the nonrelativistic numerical expansion approach. Using Gaussian basis sets, we numerically compute contributions to the Dirac-Coulomb energy and relativistic Breit potential corrections up to order $mα^8$ for the ground states of the hydrogen atom, hydrogen molecular ion, helium atom, and hydrogen molecule. These results confirm the reliability of the present method and enable its extension to more complex systems.

physics.atom-ph↗

arXiv2026

Local Optimality and Rigidity of Frobenius Tests for Dense High-Dimensional Covariance Alternatives

We study identity testing for high-dimensional covariance matrices against dense alternatives of unknown direction, with $p/n \to γ$. Along a globally positive quadratic precision path, mixing Gaussian alternatives over a Gaussian Orthogonal Ensemble direction yields a contiguous experiment whose log likelihood reduces to the corrected Frobenius statistic; its upper-tail test attains the limiting weighted-power envelope at every fixed strength. Fixing the prior's Frobenius radius perturbs the mixture by only $O(p^{-1/2})$ in total variation, and exact whitening carries the experiment, the statistic, and its null law to any known null covariance. Separately, under a product-coordinate null, feasibility needs only $4+η$ moments, plus identical distributions over time when means are estimated; studentization and an exact degrees-of-freedom correction preserve the local power. A stability inequality turns near-envelope attainment into null agreement with the Frobenius rule, so uniform noninferiority on the typical dense bulk precludes gains at any contiguous alternative. For trace-matched rank-one alternatives, the corrected statistic is the first likelihood direction when $\vartheta_n \to 0$ and $n\vartheta_n \to \infty$; at fixed strength, the log likelihood ratio in the Onatski-Moreira-Hallin fixed-spike benchmark is governed by a richer linear spectral statistic below the Baik-Ben Arous-Peche threshold, while eigenvalue separation permits cost-free largest-eigenvalue enhancement above it. Simulations illustrate the theory.

math.ST↗

arXiv2026

voigtinference: Exact likelihood calculus and conditional attribution for the Voigt profile

Fast, accurate algorithms for the Faddeeva function w(z), and hence the Voigt profile K(x,a), have existed for four decades, and analytic first derivatives are available in some implementations. What the established libraries reviewed here have not provided is the full likelihood calculus of the normalized Voigt distribution: applications still commonly resort to pseudo-Voigt approximations, finite-difference derivatives, or numerical convolution for parameter inference. Because w'(z) = -2z w(z) + 2i/sqrt(pi), every derivative of the Voigt log-likelihood is an algebraic function of K and the dispersion part L(x,a) = Im w(z), from the single complex evaluation that delivers the profile. This yields the score and Hessian in closed form, and the expected Fisher information by one-dimensional quadrature of an analytic integrand; for fixed interior widths sigma, gamma > 0, the MLE of the center and both widths is consistent and asymptotically normal at rate sqrt(n), despite the distribution having no finite mean or variance, so conventional likelihood-based standard errors apply. The conditional mean of the Gaussian component given an observation is (y - mu) - gamma L/K: a redescending function that attributes moderate deviations to the Gaussian (Doppler/resolution) component and extreme ones to the Lorentzian tail. The package voigtinference (Python, NumPy/SciPy, with a cross-validated Julia companion) supplies the toolkit: score, full parameter Hessian, expected information, Newton-based unbinned maximum likelihood with boundary diagnostics, conditional component moments, and evaluation validated against high-precision references at extreme width ratios. It applies directly to unbinned non-relativistic, constant-width Breit-Wigner x Gaussian resonance fits and supplies analytic Jacobians for line-shape refinement. Companion paper: arXiv:2605.01665.

stat.CO↗

arXiv2026

Split-Session Cluster GARCH for Overnight and Intraday Returns: The Role of Tail Heterogeneity

We propose the Split-Session Cluster GARCH model for heavy-tailed multivariate dependence among asset returns decomposed into overnight and intraday components. The model uses convolution-$t$ distributions to allow tail behavior to differ across clusters defined by trading sessions and, within each session, by economic sectors. It also accommodates block-structured conditional correlation matrices, preserving parsimony and scalability in high-dimensional settings. The resulting likelihood remains tractable and yields a score-driven specification for dynamic correlations. We apply the model to U.S. equity returns in six-asset and 100-asset applications. The results reveal pronounced tail heterogeneity between overnight and intraday returns. Model comparisons show that session-specific tail parameters substantially improve fit relative to a common multivariate-$t$ specification, while sector-level tail partitioning delivers additional gains concentrated mainly in the overnight component. In the 100-asset application, asset-level tail heterogeneity delivers the strongest out-of-sample likelihood and global minimum-variance (GMV) portfolio performance.

econ.EM↗

arXiv2026

Moments by Integrating the Moment-Generating Function

We introduce a general integral framework for computing fractional, complex, absolute, and logarithmic moments from the moment-generating function (MGF) under explicit regularity conditions. By evaluating a complex extension of the MGF along a vertical contour, we obtain exact integral expressions that bypass the need for explicit probability densities and high-order derivatives. We establish conditions for negative fractional moments using the symmetric Cauchy principal value, including the requirement that the distribution have no point mass at the centering point. We demonstrate the theoretical scope and computational practicality of the framework through applications to the normal-inverse Gaussian distribution and a semicontinuous compound Poisson-Gamma distribution. In the latter case, the framework handles point masses at the boundary by evaluating conditional fractional moments.

econ.EM↗

arXiv2026

The Parabolic Mellin Transform: Gamma and Zeta Integral Representations

We introduce the Parabolic Mellin Transform (PMT), defined by ${P}_σ[f](z)=\int_{-\infty}^{\infty}w^{2z}f(w^2)dt$, where $w=σ+it$ and $σ>0$. Under the substitution $u=w^2$, the vertical line $\operatorname{Re}(w)=σ$ is mapped to the parabolic contour $C_σ$ in the $u$-plane. For the Gaussian kernel, the PMT yields $\int_{-\infty}^{\infty}w^{2z}e^{w^2}dt=π/Γ(\tfrac{1}{2}-z)=\cos(πz)Γ(z+\tfrac{1}{2})$, a parabolic-contour form of the classical Hankel representation for the reciprocal Gamma function. The advantage of this parametrization is that the contour integral becomes a Gaussian-damped vertical-line integral. We develop scaling, differentiation, and Dirichlet-composition identities for the PMT and use them to derive integral representations of the Hurwitz zeta, Riemann zeta, and Dirichlet eta functions. The framework provides a unified transform dictionary for Gamma-type and zeta-type special functions and yields equivalent reformulations of the Riemann hypothesis and the Lindelöf hypothesis in terms of zeros and growth of parabolic-contour integrals.

math.NT↗

arXiv2026

Exact Likelihood Inference and Robust Filtering for Gauss-Cauchy Convolution Models

The convolution of a Gaussian and a Cauchy distribution, known as the Voigt distribution, is widely used in spectroscopy and provides a natural framework for modeling heavy-tailed measurement noise. We derive analytical expressions for its density, score, Hessian, Fisher information, and conditional moments using the scaled complementary error function, enabling stable maximum likelihood estimation without numerical convolution, finite-difference derivatives, or pseudo-Voigt approximations. The conditional expectation of the latent Gaussian component is governed by a redescending location score, so extreme observations are automatically discounted rather than propagated. This structure leads to the Gauss-Cauchy Convolution (GCC) filter for state-space models with Gaussian latent dynamics and Voigt measurement errors, where the Masreliez Gaussian prediction approximation preserves a Voigt prediction-error density. In an application to log realized volatility for the Technology Select Sector SPDR Fund, the GCC filter separates persistent latent variation from transient measurement noise and attains the highest implemented prediction-error criterion among the Gaussian, Student-$t$, Huber, and related filtering specifications considered.

econ.EM↗

arXiv2026

Principled Identification of Structural Dynamic Models

We take a new perspective on identification in structural dynamic models: rather than imposing restrictions alone, we optimize an objective. While definitive structural identification ultimately requires exogenous economic insight, a weighted correlation-maximizing objective yields an Order- and Scale-Invariant Scheme (OASIS) that selects the orthogonal rotation most aligned with designated target variables. In traditional SVARs, these targets are the reduced-form innovations, making OASIS a natural reference rotation. We show that recursive Cholesky identification is a constrained version of the same objective and that OASIS is systematically closer to perfect correlation, closing roughly twice as much of the gap as recursive orderings, both theoretically and empirically. The same framework also provides a principled estimation strategy for Proxy VARs (IV-SVARs), where the weighted criterion is essential for resolving overdetermination in multi-proxy systems while symmetrically accommodating proxy leakage. Revisiting 22 published SVARs, we find that reduced-form innovations are typically only weakly correlated, helping explain the historical robustness of recursive schemes. Applying OASIS to seminal proxy applications, however, reveals economically important leakage across shocks and shows that accounting for such leakage can materially alter substantive conclusions.

econ.EM↗

arXiv2026

A Unifying Integral Representation of the Gamma Function and Its Reciprocal

We derive an integral expression $G(z)$ for the reciprocal gamma function, $1/Γ(z)=G(z)/π$, that is valid for all $z\in\mathbb{C}$, without the need for analytic continuation. The same integral avoids the singularities of the gamma function and satisfies $G(1-z)=Γ(z)\sin(πz)$ for all $z\in\mathbb{C}$.

math.CV↗

arXiv2025

Dual-Path Knowledge-Augmented Contrastive Alignment Network for Spatially Resolved Transcriptomics

Spatial Transcriptomics (ST) is a technology that measures gene expression profiles within tissue sections while retaining spatial context. It reveals localized gene expression patterns and tissue heterogeneity, both of which are essential for understanding disease etiology. However, its high cost has driven efforts to predict spatial gene expression from whole slide images. Despite recent advancements, current methods still face significant limitations, such as under-exploitation of high-level biological context, over-reliance on exemplar retrievals, and inadequate alignment of heterogeneous modalities. To address these challenges, we propose DKAN, a novel Dual-path Knowledge-Augmented contrastive alignment Network that predicts spatially resolved gene expression by integrating histopathological images and gene expression profiles through a biologically informed approach. Specifically, we introduce an effective gene semantic representation module that leverages the external gene database to provide additional biological insights, thereby enhancing gene expression prediction. Further, we adopt a unified, one-stage contrastive learning paradigm, seamlessly combining contrastive learning and supervised learning to eliminate reliance on exemplars, complemented with an adaptive weighting mechanism. Additionally, we propose a dual-path contrastive alignment module that employs gene semantic features as dynamic cross-modal coordinators to enable effective heterogeneous feature integration. Through extensive experiments across three public ST datasets, DKAN demonstrates superior performance over state-of-the-art models, establishing a new benchmark for spatial gene expression prediction and offering a powerful tool for advancing biological and clinical research.

q-bio.QM↗

arXiv2025

Option Pricing with Time-Varying Volatility Risk Aversion

We introduce a pricing kernel with time-varying volatility risk aversion to explain observed time variations in the shape of the pricing kernel. When combined with the Heston-Nandi GARCH model, this framework yields a tractable option pricing model in which the variance risk ratio (VRR) emerges as a key variable. We show that the VRR is closely linked to economic fundamentals, as well as sentiment and uncertainty measures. A novel approximation method provides analytical option pricing formulas, and we demonstrate substantial reductions in pricing errors through an empirical application to the S&P 500 index, the CBOE VIX, and option prices.

q-fin.PR↗

arXiv2025

Dynamic Factor Correlation Model

We introduce a new dynamic factor correlation model with a novel variation-free parametrization of factor loadings. The model is applicable to high dimensions and can accommodate time-varying correlations, heterogeneous heavy-tailed distributions, and dependent idiosyncratic shocks, such as those observed in returns on stocks in the same subindustry. We apply the model to a "small universe" with 12 asset returns and to a "large universe" with 323 asset returns. The former facilitates a comprehensive empirical analysis and comparisons and the latter demonstrates the flexibility and scalability of the model.

econ.EM↗

arXiv2024

Cluster GARCH

We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions for the log-likelihood function and its derivatives are tractable, and the latter facilitate a score-drive model for the dynamic correlation structure. We apply the Cluster GARCH model to daily returns for 100 assets and find it outperforms existing models, both in-sample and out-of-sample. Moreover, the convolution-t distribution provides a better empirical performance than the conventional multivariate t-distribution.

econ.EM↗

arXiv2024

Convolution-t Distributions

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody cluster structures with flexible nonlinear dependencies and heterogeneous marginal distributions. Importantly, convolution-t distributions have simple density functions that facilitate estimation and likelihood-based inference. The characteristic features of convolution-t distributions are found to be important in an empirical analysis of realized volatility measures and help identify their underlying factor structure.

econ.EM↗

arXiv2023

Characterizing Correlation Matrices that Admit a Clustered Factor Representation

The Clustered Factor (CF) model induces a block structure on the correlation matrix and is commonly used to parameterize correlation matrices. Our results reveal that the CF model imposes superfluous restrictions on the correlation matrix. This can be avoided by a different parametrization, involving the logarithmic transformation of the block correlation matrix.

econ.EM↗