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In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process. In particular, there may be certain time intervals exhibiting rapid changes and others in which changes are slow. If…
Time series forecasting plays a crucial role in various applications, particularly in healthcare, where accurate predictions of future health trajectories can significantly impact clinical decision-making. Ensuring transparency and…
The probability prediction of multivariate time series is a notoriously challenging but practical task. On the one hand, the challenge is how to effectively capture the cross-series correlations between interacting time series, to achieve…
Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…
Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There…
This paper proposes a new methodological framework for estimating inferential models with latent variables. It also introduces a new latent variable regression model called LARX: an extension of the ubiquitous autoregressive model with…
The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications,…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the…
Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…
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…
There has been a recent surge of interest in time series modeling using the Transformer architecture. However, forecasting multivariate time series with Transformer presents a unique challenge as it requires modeling both temporal…
As a special infinite-order vector autoregressive (VAR) model, the vector autoregressive moving average (VARMA) model can capture much richer temporal patterns than the widely used finite-order VAR model. However, its practicality has long…
We introduce a method which enables a recurrent dynamics model to be temporally abstract. Our approach, which we call Adaptive Skip Intervals (ASI), is based on the observation that in many sequential prediction tasks, the exact time at…
We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development…
In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity…
Irregularly sampled time series are increasingly prevalent, particularly in medical domains. While various specialized methods have been developed to handle these irregularities, effectively modeling their complex dynamics and pronounced…
A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows…
Although numerical weather forecasting methods have dominated the field, recent advances in deep learning methods, such as diffusion models, have shown promise in ensemble weather forecasting. However, such models are typically…
The paper examines the problem of representing the dynamics of low order autoregressive (AR) models with time varying (TV) coefficients. The existing literature computes the forecasts of the series from a recursion relation. Instead, we…