Related papers: Introduction to Dynamic Linear Models for Time Ser…
Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time…
Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis…
Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to…
Large Language Models (LLMs) offer the potential for automatic time series analysis and reporting, which is a critical task across many domains, spanning healthcare, finance, climate, energy, and many more. In this paper, we propose a…
Traditional time series analysis has long relied on pattern recognition, trained on static and well-established benchmarks. However, in real-world settings -- where policies shift, human behavior adapts, and unexpected events unfold --…
Time series analysis is pivotal in domains like financial forecasting and biomedical monitoring, yet traditional methods are constrained by limited nonlinear feature representation and long-term dependency capture. The emergence of Large…
This paper introduces a new data analysis method for big data using a newly defined regression model named multiple model linear regression(MMLR), which separates input datasets into subsets and construct local linear regression models of…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
Time series data plays a critical role across diverse domains such as healthcare, energy, and finance, where tasks like classification, anomaly detection, and forecasting are essential for informed decision-making. Recently, large language…
We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
In this paper we discuss dynamic ARMA-type regression models for time series taking values in $(0,\infty)$. In the proposed model, the conditional mean is modeled by a dynamic structure containing autoregressive and moving average terms,…
Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when…
Large Language Models (LLMs) have emerged as a promising paradigm for time series analytics, leveraging their massive parameters and the shared sequential nature of textual and time series data. However, a cross-modality gap exists between…
A rich supply of data and innovative algorithms have made data-driven modeling a popular technique in modern industry. Among various data-driven methods, latent variable models (LVMs) and their counterparts account for a major share and…
Time series analysis is critical for emerging net- work intelligent control and management functions. However, existing statistical-based and shallow machine learning models have shown limited prediction capabilities on multivariate time…
Linear processes on functional spaces were born about fifteen years ago. And this original topic went through the same fast development as the other areas of functional data modeling such as PCA or regression. They aim at generalizing to…
Accurate prediction of travel time is an essential feature to support Intelligent Transportation Systems (ITS). The non-linearity of traffic states, however, makes this prediction a challenging task. Here we propose to use dynamic linear…
Time series analysis is essential for comprehending the complexities inherent in various realworld systems and applications. Although large language models (LLMs) have recently made significant strides, the development of artificial general…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
Recently, remarkable progress has been made over large language models (LLMs), demonstrating their unprecedented capability in varieties of natural language tasks. However, completely training a large general-purpose model from the scratch…