Related papers: Conditional Autoregressive Hilbertian processes
AutoRegressive Conditional Heteroscedasticity (ARCH) models are standard for modeling time series exhibiting volatility, with a rich literature in univariate and multivariate settings. In recent years, these models have been extended to…
The autoregressive Hilbertian model (ARH) was introduced in the early 90's by Denis Bosq. It was the subject of a vast literature and gave birth to numerous extensions. The model generalizes the classical multidimensional autoregressive…
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…
A special class of standard Gaussian Autoregressive Hilbertian processes of order one (Gaussian ARH(1) processes), with bounded linear autocorrelation operator, which does not satisfy the usual Hilbert-Schmidt assumption, is considered. To…
This paper presents new results on prediction of linear processes in function spaces. The autoregressive Hilbertian process framework of order one (ARH(1) process framework) is adopted. A componentwise estimator of the autocorrelation…
We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its…
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…
Events in spatiotemporal systems are ubiquitous, yet modeling their complex distributions remains challenging. Existing point process models often rely on strong structural assumptions and are typically limited to autoregressive,…
We introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces. As driving noises of these processes we consider Levy processes in Hilbert space. We provide the basic definitions, show relevant…
We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time…
In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an…
A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is…
Functional autoregressive (FAR) models provide a fundamental framework for analyzing temporally dependent functional data. However, the infinite-dimensional nature of the underlying Hilbert space introduces intrinsic ill-posedness, as the…
This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models for nonlinear time series in which we assume a stochastic autoregressive…
In this paper, we introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional…
Time series models aim for accurate predictions of the future given the past, where the forecasts are used for important downstream tasks like business decision making. In practice, deep learning based time series models come in many forms,…
Heteroskedasticity is a common feature of financial time series and is commonly addressed in the model building process through the use of ARCH and GARCH processes. More recently multivariate variants of these processes have been in the…
A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…
The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like R. A potential…
This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…