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Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…
Vector autoregressive (VAR) models are widely used in multivariate time series analysis for describing the short-time dynamics of the data. The reduced-rank VAR models are of particular interest when dealing with high-dimensional and highly…
We propose a Weighted Autoregressive Varying gatE (WAVE) attention mechanism equipped with both Autoregressive (AR) and Moving-average (MA) components. It can adapt to various attention mechanisms, enhancing and decoupling their ability to…
The spatio-temporal autoregressive moving average (STARMA) model is frequently used in several studies of multivariate time series data, where the assumption of stationarity is important, but it is not always guaranteed in practice. One way…
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…
We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model with oblique projections. This model partitions the measurement space into a dynamic subspace and a static subspace that do not need to be…
We introduce a variational approach to learning and inference of temporally hierarchical structure and representation for sequential data. We propose the Variational Temporal Abstraction (VTA), a hierarchical recurrent state space model…
We reinterpret Visual Autoregressive (VAR) models as iterative refinement models to identify which design choices drive their quality-efficiency trade-off. Instead of treating VAR only as next-scale autoregression, we formalise it as a…
Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to…
The variational autoencoder (VAE) is a popular deep latent variable model used to analyse high-dimensional datasets by learning a low-dimensional latent representation of the data. It simultaneously learns a generative model and an…
As evidenced by various recent and significant papers within the frequentist literature, along with numerous applications in macroeconomics, genomics, and neuroscience, there continues to be substantial interest to understand the…
Visual Autoregressive (VAR) modeling inefficiently applies a fixed computational depth to each position when generating high-resolution images. While existing methods accelerate inference by pruning tokens using frequency maps, their binary…
Auto-regressive moving-average (ARMA) models are ubiquitous forecasting tools. Parsimony in such models is highly valued for their interpretability and computational tractability, and as such the identification of model orders remains a…
Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature…
Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. In this article, the problem of detecting…
Vector Auto-Regressive (VAR) models capture lead-lag temporal dynamics of multivariate time series data. They have been widely used in macroeconomics, financial econometrics, neuroscience and functional genomics. In many applications, the…
The time series with periodic behavior, such as the periodic autoregressive (PAR) models belonging to the class of the periodically correlated processes, are present in various real applications. In the literature, such processes were…
Fitting sparse models to high-dimensional time series is an important area of statistical inference. In this paper we consider sparse vector autoregressive models and develop appropriate bootstrap methods to infer properties of such…
Threshold autoregressive moving-average (TARMA) models are popular in time series analysis due to their ability to parsimoniously describe several complex dynamical features. However, neither theory nor estimation methods are currently…