Related papers: Conditional Autoregressive Hilbertian processes
Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is…
A mathematical framework for Continuous Time Finance based on operator algebraic methods offers a new direct and entirely constructive perspective on the field and leads to new numerical analysis techniques. This is partly a review paper as…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but…
We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The process is a natural extension of a complex-valued autoregressive process, extended to include a widely linear autoregressive term. This…
Spatial autoregressive model, introduced by Clif and Ord in 1970s has been widely applied in many areas of science and econometrics such as regional economics, public finance, political sciences, agricultural economics, environmental…
Probabilistic forecasting, i.e. estimating the probability distribution of a time series' future given its past, is a key enabler for optimizing business processes. In retail businesses, for example, forecasting demand is crucial for having…
A joint conditional autoregressive expectile and Expected Shortfall framework is proposed. The framework is extended through incorporating a measurement equation which models the contemporaneous dependence between the realized measures and…
This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by…
We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations,…
In this article, we discuss some geometric infinitely divisible (gid) random variables using the Laplace exponents which are Bernstein functions and study their properties. The distributional properties and limiting behavior of the…
Recent progress in panoramic image generation has underscored two critical limitations in existing approaches. First, most methods are built upon diffusion models, which are inherently ill-suited for equirectangular projection (ERP)…
Linear processes on functional spaces were born about fifteen years ago. And this original topic went through the same fast development as the other areas of functional data modeling such as PCA or regression. They aim at generalizing to…
We investigate precursors and predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of…
This research attempts to model the stochastic process of trades in a limit order book market as a marked point process. We propose a semi-parametric model for the conditional distribution given the past, attempting to capture the effect of…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
Invertible processes are central to functional time series analysis, making the estimation of their defining operators a key problem. While asymptotic error bounds have been established for specific ARMA models on $L^2[0,1]$, a general…
Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility,…
Generative models are often trained with a next-token prediction objective, yet many downstream applications require the ability to estimate or control sequence-level properties. Next-token prediction can lead to overfitting of local…
Point processes offer a versatile framework for sequential event modeling. However, the computational challenges and constrained representational power of the existing point process models have impeded their potential for wider…