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We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…

Time series forecasting is an important problem across many domains, playing a crucial role in multiple real-world applications. In this paper, we propose a forecasting architecture that combines deep autoregressive models with a Spectral…

Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process…

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…

We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time…

The sparsity-ranked lasso (SRL) has been developed for model selection and estimation in the presence of interactions and polynomials. The main tenet of the SRL is that an algorithm should be more skeptical of higher-order polynomials and…

Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of…

SVR-GARCH model tends to "backward eavesdrop" when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good…

The non-linear autoregressive (NLAR) model plays an important role in modeling and predicting time series. One-step ahead prediction is straightforward using the NLAR model, but the multi-step ahead prediction is cumbersome. For instance,…

Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…

Many important problems can be modeled as a system of interconnected entities, where each entity is recording time-dependent observations or measurements. In order to spot trends, detect anomalies, and interpret the temporal dynamics of…

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

Current time-series forecasting models are primarily based on transformer-style neural networks. These models achieve long-term forecasting mainly by scaling up the model size rather than through genuinely autoregressive (AR) rollout. From…

In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic…

In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning…

Non-autoregressive (NAR) modeling has gained more and more attention in speech processing. With recent state-of-the-art attention-based automatic speech recognition (ASR) structure, NAR can realize promising real-time factor (RTF)…

Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress…

The evolution of images with physics-based dynamics is often spatially localized and nonlinear. A switching linear dynamic system (SLDS) is a natural model under which to pose such problems when the system's evolution randomly switches over…

We present a new method for causal discovery in linear structural vector autoregressive models. We adapt an idea designed for independent observations to the case of time series while retaining its favorable properties, i.e., explicit error…