arXiv subjects

Donggyu Kim

Publications and source records attributed to Donggyu Kim.

At least 37 records · Page 2Linked to original sources

arXiv2025

Low-Rank Structured Nonparametric Prediction of Instantaneous Volatility

Based on Itô semimartingale models, several studies have proposed methods for forecasting intraday volatility using high-frequency financial data. These approaches typically rely on restrictive parametric assumptions and are often vulnerable to model misspecification. To address this issue, we introduce a novel nonparametric prediction method for the future intraday instantaneous volatility process during trading hours, which leverages both previous days' data and the current day's observed intraday data. Our approach imposes an interday-by-intraday matrix representation of the instantaneous volatility, which is decomposed into a low-rank conditional expectation component and a noise matrix. To predict the future conditional expected volatility vector, we exploit this low-rank structure and propose the Structural Intraday-volatility Prediction (SIP) procedure. We establish the asymptotic properties of the SIP estimator and demonstrate its effectiveness through an out-of-sample prediction study using real high-frequency trading data.

econ.EM↗

arXiv2025

Matrix-based Prediction Approach for Intraday Instantaneous Volatility Vector

In this paper, we introduce a novel method for predicting intraday instantaneous volatility based on Ito semimartingale models using high-frequency financial data. Several studies have highlighted stylized volatility time series features, such as interday auto-regressive dynamics and the intraday U-shaped pattern. To accommodate these volatility features, we propose an interday-by-intraday instantaneous volatility matrix process that can be decomposed into low-rank conditional expected instantaneous volatility and noise matrices. To predict the low-rank conditional expected instantaneous volatility matrix, we propose the Two-sIde Projected-PCA (TIP-PCA) procedure. We establish asymptotic properties of the proposed estimators and conduct a simulation study to assess the finite sample performance of the proposed prediction method. Finally, we apply the TIP-PCA method to an out-of-sample instantaneous volatility vector prediction study using high-frequency data from the S&P 500 index and 11 sector index funds.

econ.EM↗

arXiv2025

Large Volatility Matrix Prediction using Tensor Factor Structure

Several approaches for predicting large volatility matrices have been developed based on high-dimensional factor-based Itô processes. These methods often impose restrictions to reduce the model complexity, such as constant eigenvectors or factor loadings over time. However, several studies indicate that eigenvector processes are also time-varying. To address this feature, this paper generalizes the factor structure by representing the integrated volatility matrix process as a cubic (order-3 tensor) form, which is decomposed into low-rank tensor and idiosyncratic tensor components. To predict conditional expected large volatility matrices, we propose the Projected Tensor Principal Orthogonal componEnt Thresholding (PT-POET) procedure and establish its asymptotic properties. The advantages of PT-POET are validated through a simulation study and demonstrated in an application to minimum variance portfolio allocation using high-frequency trading data.

econ.EM↗

arXiv2025

Reconstructing hypergraph matching polynomials

By utilizing the recently developed hypergraph analogue of Godsil's identity by the second author, we prove that for all $n \geq k \geq 2$, one can reconstruct the matching polynomial of an $n$-vertex $k$-uniform hypergraph from the multiset of all induced sub-hypergraphs on $\lfloor \frac{k-1}{k}n \rfloor + 1$ vertices. This generalizes the well-known result of Godsil on graphs in 1981 to every uniform hypergraph. As a corollary, we show that for every graph $F$, one can reconstruct the number of $F$-factors in a graph under analogous conditions. We also constructed examples that imply the number $\lfloor \frac{k-1}{k}n \rfloor + 1$ is the best possible for all $n\geq k \geq 2$ with $n$ divisible by $k$.

math.CO↗

arXiv2024

Property of Inverse Covariance Matrix-based Financial Adjacency Matrix for Detecting Local Groups

In financial applications, we often observe both global and local factors that are modeled by a multi-level factor model. When detecting unknown local group memberships under such a model, employing a covariance matrix as an adjacency matrix for local group memberships is inadequate due to the predominant effect of global factors. Thus, to detect a local group structure more effectively, this study introduces an inverse covariance matrix-based financial adjacency matrix (IFAM) that utilizes negative values of the inverse covariance matrix. We show that IFAM ensures that the edge density between different groups vanishes, while that within the same group remains non-vanishing. This reduces falsely detected connections and helps identify local group membership accurately. To estimate IFAM under the multi-level factor model, we introduce a factor-adjusted GLASSO estimator to address the prevalent global factor effect in the inverse covariance matrix. An empirical study using returns from international stocks across 20 financial markets demonstrates that incorporating IFAM effectively detects latent local groups, which helps improve the minimum variance portfolio allocation performance.

econ.EM↗

arXiv2024

Robust Realized Integrated Beta Estimator with Application to Dynamic Analysis of Integrated Beta

In this paper, we develop a robust non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noises, which is robust to the stylized features, such as the time-varying beta and the dependence structure of microstructure noises. With this robust realized integrated beta estimator, we investigate dynamic structures of integrated betas and find an auto-regressive--moving-average (ARMA) structure. To model this dynamic structure, we utilize the ARMA model for daily integrated market betas. We call this the dynamic realized beta (DR Beta). We further introduce a high-frequency data generating process by filling the gap between the high-frequency-based non-parametric estimator and low-frequency dynamic structure. Then, we propose a quasi-likelihood procedure for estimating the model parameters with the robust realized integrated beta estimator as the proxy. We also establish asymptotic theorems for the proposed estimator and conduct a simulation study to check the performance of finite samples of the estimator. The empirical study with the S&P 500 index and the top 50 large trading volume stocks from the S&P 500 illustrates that the proposed DR Beta model with the robust realized beta estimator effectively accounts for dynamics in the market beta of individual stocks and better predicts future market betas.

stat.ME↗

arXiv2024

Note on Hamiltonicity of basis graphs of even delta-matroids

We show that the basis graph of an even delta-matroid is Hamiltonian if it has more than two vertices. More strongly, we prove that for two distinct edges $e$ and $f$ sharing a common end, it has a Hamiltonian cycle using $e$ and avoiding $f$ unless it has at most two vertices or it is a cycle of length at most four. We also prove that if the basis graph is not a hypercube graph, then each vertex belongs to cycles of every length $\ell\ge 3$, and each edge belongs to cycles of every length $\ell \ge 4$. For the last theorem, we provide two proofs, one of which uses the result of Naddef (1984) on polytopes and the result of Chepoi (2007) on basis graphs of even delta-matroids, and the other is a direct proof using various properties of even delta-matroids. Our theorems generalize the analogous results for matroids by Holzmann and Harary (1972) and Bondy and Ingleton (1976).

math.CO↗

arXiv2024

Technologies for Modulation of Visible Light and their Applications

Control over the amplitude, phase, and spatial distribution of visible-spectrum light underlies many technologies, but commercial solutions remain bulky, require high control power, and are often too slow. Active integrated photonics for visible light promises a solution, especially with recent materials and fabrication advances. In this review, we discuss three growing application spaces which rely on control of visible light: control and measurement of atomic quantum technologies, augmented-reality displays, and measurement and control of biological systems. We then review the commercial dynamic surfaces and bulk systems which currently provide visible-light modulation and the current state-of-the-art integrated solutions. Throughout the review we focus on speed, control power, size, optical bandwidth, and technological maturity when comparing technologies.

physics.optics↗

arXiv2024

GECKO: Generative Language Model for English, Code and Korean

We introduce GECKO, a bilingual large language model (LLM) optimized for Korean and English, along with programming languages. GECKO is pretrained on the balanced, high-quality corpus of Korean and English employing LLaMA architecture. In this report, we share the experiences of several efforts to build a better data pipeline for the corpus and to train our model. GECKO shows great efficiency in token generations for both Korean and English, despite its small size of vocabulary. We measure the performance on the representative benchmarks in terms of Korean, English and Code, and it exhibits great performance on KMMLU (Korean MMLU) and modest performance in English and Code, even with its smaller number of trained tokens compared to English-focused LLMs. GECKO is available to the open-source community under a permissive license. We hope our work offers a research baseline and practical insights for Korean LLM research. The model can be found at: https://huggingface.co/kifai/GECKO-7B

cs.CL↗

arXiv2024

Twin-width of random graphs

We investigate the twin-width of the Erdős-Rényi random graph $G(n,p)$. We unveil a surprising behavior of this parameter by showing the existence of a constant $p^*\approx 0.4$ such that with high probability, when $p^*\le p\le 1-p^*$, the twin-width is asymptotically $2p(1-p)n$, whereas, when $0 p>1-p^*$, the twin-width is significantly higher than $2p(1-p)n$. In addition, we show that the twin-width of $G(n,1/2)$ is concentrated around $n/2 - \sqrt{3n \log n}/2$ within an interval of length $o(\sqrt{n\log n})$. For the sparse random graph, we show that with high probability, the twin-width of $G(n,p)$ is $Θ(n\sqrt{p})$ when $(726\ln n)/n\leq p\leq1/2$.

math.CO↗

arXiv2024

Large Global Volatility Matrix Analysis Based on Observation Structural Information

In this paper, we develop a novel large volatility matrix estimation procedure for analyzing global financial markets. Practitioners often use lower-frequency data, such as weekly or monthly returns, to address the issue of different trading hours in the international financial market. However, this approach can lead to inefficiency due to information loss. To mitigate this problem, our proposed method, called Structured Principal Orthogonal complEment Thresholding (Structured-POET), incorporates observation structural information for both global and national factor models. We establish the asymptotic properties of the Structured-POET estimator, and also demonstrate the drawbacks of conventional covariance matrix estimation procedures when using lower-frequency data. Finally, we apply the Structured-POET estimator to an out-of-sample portfolio allocation study using international stock market data.

econ.EM↗

arXiv2024

Revisiting Early-Learning Regularization When Federated Learning Meets Noisy Labels

In the evolving landscape of federated learning (FL), addressing label noise presents unique challenges due to the decentralized and diverse nature of data collection across clients. Traditional centralized learning approaches to mitigate label noise are constrained in FL by privacy concerns and the heterogeneity of client data. This paper revisits early-learning regularization, introducing an innovative strategy, Federated Label-mixture Regularization (FLR). FLR adeptly adapts to FL's complexities by generating new pseudo labels, blending local and global model predictions. This method not only enhances the accuracy of the global model in both i.i.d. and non-i.i.d. settings but also effectively counters the memorization of noisy labels. Demonstrating compatibility with existing label noise and FL techniques, FLR paves the way for improved generalization in FL environments fraught with label inaccuracies.

cs.LG↗

arXiv2023

Orthogonal matroids over tracts

We generalize Baker-Bowler's theory of matroids over tracts to orthogonal matroids, define orthogonal matroids with coefficients in tracts in terms of Wick functions, orthogonal signatures, circuit sets, and orthogonal vector sets, and establish basic properties on functoriality, duality, and minors. Our cryptomorphic definitions of orthogonal matroids over tracts provide proofs of several representation theorems for orthogonal matroids. In particular, we give a new proof that an orthogonal matroid is regular if and only if it is representable over $\mathbb{F}_2$ and $\mathbb{F}_3$, which was originally shown by Geelen, and we prove that an orthogonal matroid is representable over the sixth-root-of-unity partial field if and only if it is representable over $\mathbb{F}_3$ and $\mathbb{F}_4$.

math.CO↗

arXiv2023

The Effect of Trust and its Antecedents on Robot Acceptance

As social and socially assistive robots are becoming more prevalent in our society, it is beneficial to understand how people form first impressions of them and eventually come to trust and accept them. This paper describes an Amazon Mechanical Turk study (n = 239) that investigated trust and its antecedents trustworthiness and first impressions. Participants evaluated the social robot Pepper's warmth and competence as well as trustworthiness characteristics ability, benevolence and integrity followed by their trust in and intention to use the robot. Mediation analyses assessed to what degree participants' first impressions affected their willingness to trust and use it. Known constructs from user acceptance and trust research were introduced to explain the pathways in which one perception predicted the next. Results showed that trustworthiness and trust, in serial, mediated the relationship between first impressions and behavioral intention.

cs.RO↗

arXiv2023

Dynamic Realized Minimum Variance Portfolio Models

This paper introduces a dynamic minimum variance portfolio (MVP) model using nonlinear volatility dynamic models, based on high-frequency financial data. Specifically, we impose an autoregressive dynamic structure on MVP processes, which helps capture the MVP dynamics directly. To evaluate the dynamic MVP model, we estimate the inverse volatility matrix using the constrained $\ell_1$-minimization for inverse matrix estimation (CLIME) and calculate daily realized non-normalized MVP weights. Based on the realized non-normalized MVP weight estimator, we propose the dynamic MVP model, which we call the dynamic realized minimum variance portfolio (DR-MVP) model. To estimate a large number of parameters, we employ the least absolute shrinkage and selection operator (LASSO) and predict the future MVP and establish its asymptotic properties. Using high-frequency trading data, we apply the proposed method to MVP prediction.

stat.ME↗

arXiv2023

Prime vertex-minors of a prime graph

A graph is prime if it does not admit a partition $(A,B)$ of its vertex set such that $\min\{|A|,|B|\} \geq 2$ and the rank of the $A\times B$ submatrix of its adjacency matrix is at most $1$. A vertex $v$ of a graph is non-essential if at least two of the three kinds of vertex-minor reductions at $v$ result in prime graphs. In 1994, Allys proved that every prime graph with at least four vertices has a non-essential vertex unless it is locally equivalent to a cycle graph. We prove that every prime graph with at least four vertices has at least two non-essential vertices unless it is locally equivalent to a cycle graph. As a corollary, we show that for a prime graph $G$ with at least six vertices and a vertex $x$, there is a vertex $v \ne x$ such that $G \setminus v$ or $G * v \setminus v$ is prime, unless $x$ is adjacent to all other vertices and $G$ is isomorphic to a particular graph on odd number of vertices. Furthermore, we show that a prime graph with at least four vertices has at least three non-essential vertices, unless it is locally equivalent to a graph consisting of at least two internally-disjoint paths between two fixed distinct vertices having no common neighbors. We also prove analogous results for pivot-minors.

math.CO↗

arXiv2023

Adaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data

Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order moment assumption for observed log-returns, which cannot account for the heavy-tail phenomenon of stock-returns. Recently, a robust estimator was developed to handle heavy-tailed distributions with some bounded fourth-moment assumption. However, we often observe that log-returns have heavier tail distribution than the finite fourth-moment and that the degrees of heaviness of tails are heterogeneous across asset and over time. In this paper, to deal with the heterogeneous heavy-tailed distributions, we develop an adaptive robust integrated volatility estimator that employs pre-averaging and truncation schemes based on jump-diffusion processes. We call this an adaptive robust pre-averaging realized volatility (ARP) estimator. We show that the ARP estimator has a sub-Weibull tail concentration with only finite 2$α$-th moments for any $α>1$. In addition, we establish matching upper and lower bounds to show that the ARP estimation procedure is optimal. To estimate large integrated volatility matrices using the approximate factor model, the ARP estimator is further regularized using the principal orthogonal complement thresholding (POET) method. The numerical study is conducted to check the finite sample performance of the ARP estimator.

math.ST↗

arXiv2023

Factor Overnight GARCH-Itô Models

This paper introduces a unified factor overnight GARCH-Itô model for large volatility matrix estimation and prediction. To account for whole-day market dynamics, the proposed model has two different instantaneous factor volatility processes for the open-to-close and close-to-open periods, while each embeds the discrete-time multivariate GARCH model structure. To estimate latent factor volatility, we assume the low rank plus sparse structure and employ nonparametric estimation procedures. Then, based on the connection between the discrete-time model structure and the continuous-time diffusion process, we propose a weighted least squares estimation procedure with the non-parametric factor volatility estimator and establish its asymptotic theorems.

stat.ME↗