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Time series imputation is one of the most challenge problems and has broad applications in various fields like health care and the Internet of Things. Existing methods mainly aim to model the temporally latent dependencies and the…

We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…

Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such…

Large Language Models (LLMs) have gained popularity in time series forecasting, but their potential for anomaly detection remains largely unexplored. Our study investigates whether LLMs can understand and detect anomalies in time series…

Diffusion Language Models (DLMs) are rapidly emerging as a powerful and promising alternative to the dominant autoregressive (AR) paradigm. By generating tokens in parallel through an iterative denoising process, DLMs possess inherent…

This paper presents a comparative analysis evaluating the accuracy of Large Language Models (LLMs) against traditional macro time series forecasting approaches. In recent times, LLMs have surged in popularity for forecasting due to their…

Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…

Ecological systems are governed by complex interactions which are mainly nonlinear. In order to capture this complexity and nonlinearity, statistical models recently gained popularity. However, although these models are commonly applied in…

Recent research has shown that large language models (LLMs) can be effectively used for real-world time series forecasting due to their strong natural language understanding capabilities. However, aligning time series into semantic spaces…

These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…

Generative models for network time series (also known as dynamic graphs) have tremendous potential in fields such as epidemiology, biology and economics, where complex graph-based dynamics are core objects of study. Designing flexible and…

Recently, there has been great success in leveraging pre-trained large language models (LLMs) for time series analysis. The core idea lies in effectively aligning the modality between natural language and time series. However, the…

Distributed lag models (DLMs) express the cumulative and delayed dependence between pairs of time-indexed response and explanatory variables. In practical application, users of DLMs examine the estimated influence of a series of lagged…

Time series anomaly detection is critical for supply chain management to take proactive operations, but faces challenges: classical unsupervised anomaly detection based on exploiting data patterns often yields results misaligned with…

Time series forecasting is critical across multiple domains, where time series data exhibit both local patterns and global dependencies. While Transformer-based methods effectively capture global dependencies, they often overlook short-term…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

This paper explores the potential of large language models (LLMs) to generate financial reports from time series data. We propose a framework encompassing prompt engineering, model selection, and evaluation. We introduce an automated…

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…

In the current context of Big Data, the nature of many forecasting problems has changed from predicting isolated time series to predicting many time series from similar sources. This has opened up the opportunity to develop competitive…

We study the problem of estimating the parameters of a regression model from a set of observations, each consisting of a response and a predictor. The response is assumed to be related to the predictor via a regression model of unknown…