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This work delves into presenting a probabilistic method for analyzing linear process data with weakly dependent innovations, focusing on detecting change-points in the mean and estimating its spectral density. We develop a test for…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
We propose here a framework to model real-time components consisting of concurrent real-time tasks running on a single processor, using parametric timed automata. Our framework is generic and modular, so as to be easily adapted to different…
A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as {\it…
In the domain of multivariate time series analysis, the concept of channel independence has been increasingly adopted, demonstrating excellent performance due to its ability to eliminate noise and the influence of irrelevant variables.…
This article proposes a new approach to modeling high-dimensional time series by treating a $p$-dimensional time series as a nonsingular linear transformation of certain common factors and idiosyncratic components. Unlike the approximate…
We propose a new and easy-to-use method for identifying cointegrated components of nonstationary time series, consisting of an eigenanalysis for a certain non-negative definite matrix. Our setting is model-free, and we allow the…
Over the last decade, nonparametric methods have gained increasing attention for modeling complex data structures due to their flexibility and minimal structural assumptions. In this paper, we study a general multivariate nonparametric…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…
Analyzing sequential data is crucial in many domains, particularly due to the abundance of data collected from the Internet of Things paradigm. Time series classification, the task of categorizing sequential data, has gained prominence,…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension $d$ to scale with the series length $T$. We treat the transition matrix of…
This paper considers a structural-factor approach to modeling high-dimensional time series and space-time data by decomposing individual series into trend, seasonal, and irregular components. For ease in analyzing many time series, we…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
This paper shows how a time series of measurements of an evolving system can be processed to create an inner time series that is unaffected by any instantaneous invertible, possibly nonlinear transformation of the measurements. An inner…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…