Related papers: Edge-indexed network time series with graph Ornste…

The paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The noise is specified by the Ornstein-Uhlenbeck process driven by the mixture of a Brownian motion…

Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval $I$ such that the process starting…

Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of…

L\'evy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current…

This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…

This paper is a survey of recent results on the adaptive robust non parametric methods for the continuous time regression model with the semi - martingale noises with jumps. The noises are modeled by the L\'evy processes, the Ornstein --…

This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional…

We study a recent class of models which uses graph neural networks (GNNs) to improve forecasting in multivariate time series. The core assumption behind these models is that there is a latent graph between the time series (nodes) that…

In this paper, we use variational recurrent neural network to investigate the anomaly detection problem on graph time series. The temporal correlation is modeled by the combination of recurrent neural network (RNN) and variational inference…

We combine earlier investigations of linear systems with L\'{e}vy fluctuations [Physica {\bf 113A}, 203, (1982)] with recent discussions of L\'{e}vy flights in external force fields [Phys.Rev. {\bf E 59},2736, (1999)]. We give a complete…

In recent years there have been many proposals as flexible alternatives to Gaussian based continuous time stochastic volatility models. A great deal of these models employ positive L\'evy processes. Among these are the attractive…

Real-time adaptive control of nonlinear systems with unknown dynamics and time-varying disturbances demands precise modeling and robust parameter adaptation. While existing neural network-based strategies struggle with computational…

The performance of mobile ad hoc networks in general and that of the routing algorithm, in particular, can be heavily affected by the intrinsic dynamic nature of the underlying topology. In this paper, we build a new analytical/numerical…

Reconstructing time-varying graph signals (or graph time-series imputation) is a critical problem in machine learning and signal processing with broad applications, ranging from missing data imputation in sensor networks to time-series…

In this paper, we present a novel approach to modeling long-term dependencies in sequential data by introducing a gated recurrent unit (GRU) with a weighted time-delay feedback mechanism. Our proposed model, named $\tau$-GRU, is a…

We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean…

When stock prices are observed at high frequencies, more information can be utilized in estimation of parameters of the price process. However, high-frequency data are contaminated by the market microstructure noise which causes significant…

Modeling irregularly sampled multivariate time series is a persistent challenge in domains like healthcare and sensor networks. While recent works have explored a variety of complex learning architectures to solve the prediction problems…

Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…

We study high-dimensional drift estimation for L\'evy-driven Ornstein--Uhlenbeck processes based on discrete observations. Assuming sparsity of the drift matrix, we analyze Lasso and Slope estimators constructed from approximate likelihoods…