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A broad class of stochastic volatility models are defined by systems of stochastic differential equations. While these models have seen widespread success in domains such as finance and statistical climatology, they typically lack an…

In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the model are estimated using Expectation Maximization (EM) algorithm. The efficacy of the EM algorithm is shown using simulated and real…

Rate-distortion formulation is the information-theoretic approach to the study of signal encoding systems. Since a more general approach to model the nonstationarity exhibited by real-world signals is to use appropriately fitted time…

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing…

Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…

A threshold autoregressive (TAR) model is a powerful tool for analyzing nonlinear multivariate time series, which includes special cases like self-exciting threshold autoregressive (SETAR) models and vector autoregressive (VAR) models. In…

In this article there is no intention to repeat basic concepts about risk management, but we will try to define why often is usefull the time series analysis during the assessment of risks, and how is possible to compute a significative…

This article shortly introduces Gaussian processes (GP) as a new approach for modelling time series in the field of blazar physics. In the second part of the paper, recent results from an application of GP modelling to the multi-wavelength…

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method…

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…

Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…

Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…

We introduce a new smooth transition vector autoregressive model with a Gaussian conditional distribution and transition weights that, for a $p$th order model, depend on the full distribution of the preceding $p$ observations. Specifically,…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

While the generalized Langevin equation (GLE) is a powerful tool to understand the behavior of complex dissipative systems, driving by external fields renders standard GLE construction workflows invalid. Filtering approaches that separate…

Probabilistic forecasting of time series is an important matter in many applications and research fields. In order to draw conclusions from a probabilistic forecast, we must ensure that the model class used to approximate the true…