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Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be…

This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…

When globally optimal solutions of complicated optimization problems cannot be located by evolutionary algorithms (EAs) in polynomial expected running time, the hitting time/running time analysis is not flexible enough to accommodate the…

We propose a parsimonious quantile regression framework to learn the dynamic tail behaviors of financial asset returns. Our model captures well both the time-varying characteristic and the asymmetrical heavy-tail property of financial time…

Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the…

We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…

Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…

In large-scale systems, complex internal relationships are often present. Such interconnected systems can be effectively described by low rank stochastic processes. When identifying a predictive model of low rank processes from sampling…

High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and…

Prediction for high dimensional time series is a challenging task due to the curse of dimensionality problem. Classical parametric models like ARIMA or VAR require strong modeling assumptions and time stationarity and are often…

Online (also called "recursive" or "adaptive") estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modelling. In this work, we propose an online parameter estimation algorithm that…

While recent advancements in foundation models have significantly impacted machine learning, rigorous tests on the performance of time series foundation models (TSFMs) remain largely underexplored. This paper presents an empirical study…

We propose a parsimonious spatiotemporal model for time series data on a spatial grid. Our model is capable of dealing with high-dimensional time series data that may be collected at hundreds of locations and capturing the spatial…

Variational Autoencoders (VAEs) have recently been highly successful at imputing and acquiring heterogeneous missing data. However, within this specific application domain, existing VAE methods are restricted by using only one layer of…

Handling missing data in time series classification remains a significant challenge in various domains. Traditional methods often rely on imputation, which may introduce bias or fail to capture the underlying temporal dynamics. In this…

This paper proposes a recursive interval-valued estimation framework for identifying the parameters of linearly parameterized systems which may be slowly time-varying. It is assumed that the model error (which may consist in measurement…

Missing values challenge data analysis because many supervised and unsupervised learning methods cannot be applied directly to incomplete data. Matrix completion based on low-rank assumptions are very powerful solution for dealing with…

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…