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We consider two-state Non-Homogeneous Hidden Markov Models (NHHMMs) for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state dependent coefficients and time-varying…
Environmental time series data observed at high frequencies can be studied with approaches such as hidden Markov and semi-Markov models (HMM and HSMM). HSMMs extend the HMM by explicitly modeling the time spent in each state. In a…
Data assimilation (DA) is a fundamental component of modern weather prediction, yet it remains a major computational bottleneck in machine learning (ML)-based forecasting pipelines due to reliance on traditional variational methods. Recent…
Autoregressive and moving-average (ARMA) models with stable Paretian errors is one of the most studied models for time series with infinite variance. Estimation methods for these models have been studied by many researchers but the problem…
We introduce Galerkin-ARIMA and Galerkin-SARIMA, a projection-based extension of classical ARIMA/SARIMA that replaces rigid linear lag operators with low-dimensional Galerkin basis expansions while preserving the familiar AR-MA…
The problem of Time-series Forecasting is generally addressed by recurrent, Transformer-based and the recently proposed Mamba-based architectures. However, existing architectures generally process their input at a single temporal scale,…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…
In this paper, we use convolutional neural networks to address the problem of model identification for autoregressive moving average time series models. We compare the performance of several neural network architectures, trained on…
Regularly varying space-time processes have proved useful to study extremal dependence in space-time data. We propose a semiparametric estimation procedure based on a closed form expression of the extremogram to estimate parametric models…
Assessing the availability of rainfall water plays a crucial role in rainfed agriculture. Given the substantial proportion of agricultural practices in India being rainfed and considering the potential trends in rainfall amounts across…
The autoregressive moving average (ARMA) model is one of the most important models in time series analysis.We consider the Bayesian estimation of an unknown spectral density in the ARMA model.In the i.i.d. cases, Komaki showed that Bayesian…
Human trajectory forecasting requires capturing the multimodal nature of pedestrian behavior. However, existing approaches suffer from prior misalignment. Their learned or fixed priors often fail to capture the full distribution of…
In this paper, we propose a novel and efficient two-stage variable selection approach for sparse GLARMA models, which are pervasive for modeling discrete-valued time series. Our approach consists in iteratively combining the estimation of…
Nonstationarity of real-life time series requires model adaptation. In classical approaches like ARMA-ARCH there is assumed some arbitrarily chosen dependence type. To avoid their bias, we will focus on novel more agnostic approach: moving…
We consider the issue of performing accurate small sample inference in beta autoregressive moving average model, which is useful for modeling and forecasting continuous variables that assumes values in the interval $(0,1)$. The inferences…
In this paper, we develop a distributionally robust model predictive control framework for the control of wind farms with the goal of power tracking and mechanical stress reduction of the individual wind turbines. We introduce an ARMA model…
Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…
In this paper, we propose SAMBA, a novel framework for safe reinforcement learning that combines aspects from probabilistic modelling, information theory, and statistics. Our method builds upon PILCO to enable active exploration using…
We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…