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Vector autoregressive (VAR) models are popularly adopted for modelling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modelling, the number of parameters grow quadratically with…

We develop a procedure for forecasting the volatility of a time series immediately following a news shock. Adapting the similarity-based framework of Lin and Eck (2020), we exploit series that have experienced similar shocks. We aggregate…

Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in…

The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…

We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…

Price range contains important information about the asset volatility, and has long been considered an important indicator for it. In this paper, we propose to jointly model the [low, high] price range as a random interval and introduce an…

One of the most important features of financial time series data is volatility. There are often structural changes in volatility over time, and an accurate estimation of the volatility of financial time series requires careful…

Estimating the covariance structure of multivariate time series is a fundamental problem with a wide-range of real-world applications -- from financial modeling to fMRI analysis. Despite significant recent advances, current state-of-the-art…

Large language models (LLMs) have revolutionized natural language processing, yet their practical utility is often limited by persistent issues of hallucinations and outdated parametric knowledge. Although post-training model editing offers…

The frozen Gaussian approximation (FGA) is an effective tool for modeling high frequency wave propagation. In previous works, the convergence of the FGA has established for strict hyperbolic systems. In this work, we derive the frozen…

Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…

Adaptive Retrieval-Augmented Generation (RAG) promises accuracy and efficiency by dynamically triggering retrieval only when needed and is widely used in practice. However, real-world queries vary in surface form even with the same intent,…

Retrieval-augmented generation (RAG) enables large language models (LLMs) to access external knowledge, helping mitigate hallucinations and enhance domain-specific expertise. Graph-based RAG enhances structural reasoning by introducing…

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index…

In this paper we propose an identification method for latent-variable graphical models associated to autoregressive (AR) Gaussian stationary processes. The identification procedure exploits the approximation of AR processes through…

The bivariate copulas that describe the dependencies and partial dependencies of lagged variables in strictly stationary, first-order GARCH-type processes are investigated. It is shown that the copulas of symmetric GARCH processes are…

Despite recent remarkable achievements in quadruped control, it remains challenging to ensure robust and compliant locomotion in the presence of unforeseen external disturbances. Existing methods prioritize locomotion robustness over…

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound…

Graph-based Retrieval-Augmented Generation (Graph-RAG) enhances large language models (LLMs) by structuring retrieval over an external corpus. However, existing approaches typically assume a static corpus, requiring expensive full-graph…

Retrieval-Augmented Generation (RAG) has emerged as a powerful approach for enhancing large language models' question-answering capabilities through the integration of external knowledge. However, when adapting RAG systems to specialized…