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This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…
The main focus of this work is to understand the dynamics of non regulated markets. The present model can describe the dynamics of any market where the pricing is based on supply and demand. It will be applied here, as an example, for the…
Forecasting the number of trips in bike-sharing systems and its volatility over time is crucial for planning and optimizing such systems. This paper develops timeseries models to forecast hourly count timeseries data, and estimate its…
Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…
In this paper, we propose a regression model where the response variable is beta prime distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The proposed regression model is useful…
In this paper we describe a framework for model-based diagnosis of dynamic systems, which extends previous work in this field by using and expressing temporal uncertainty in the form of qualitative interval relations a la Allen. Based on a…
This article introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents…
We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
In this paper we present a theoretical analysis of a recently proposed two-dimensional Cellular Automata model for traffic flow in cities with the novel ingredient of turning capability. Numerical simulations of this model show that there…
The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models…
In this paper we apply the techniques of symbolic dynamics to the analysis of a labor market which shows large volatility in employment flows. In a recent paper, Bhattacharya and Bunzel \cite{BB} have found that the discrete time version of…
Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…