Related papers: Analytic Moments for GARCH Processes
GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model (which was introduced a few years ago by Kl\"{u}ppelberg, Lindner and Maller)…
Meta-analysis, because of both logistical convenience and statistical efficiency, is widely popular for synthesizing information on common parameters of interest across multiple studies. We propose developing a generalized meta-analysis…
We prove existence and uniqueness of a stationary distribution and absolute regularity for nonlinear GARCH and INGARCH models of order (p,q). In contrast to previous work we impose, besides a geometric drift condition, only a…
This paper develops a general methodology for a posteriori error estimation in time-dependent multiphysics numerical simulations. The methodology builds upon the generalized-structure additive Runge--Kutta (GARK) approach to time…
In this paper, we address the problem of bounding conditional expectations when moment information of the underlying distribution and the random event conditioned upon are given. To this end, we propose an adapted version of the generalized…
The goal of this paper is to generalize most of the moment formulae obtained in [Pri11]. More precisely, we consider a general point process \mu, and show that the relevant quantities to our problem are the so-called Papangelou intensities.…
The log returns of financial time series are usually modeled by means of the stationary GARCH(1,1) stochastic process or its generalizations which can not properly describe the nonstationary deterministic components of the original series.…
Incorporating specific knowledge into large language models via retrieval-augmented generation (RAG) is a widespread technique that fuels many of today's industry AI applications. A fundamental problem is to assess if the context retrieved…
This paper studies a Stieltjes-type moment problem defined by the generalized lognormal distribution, a heavy-tailed distribution with applications in economics, finance and related fields. It arises as the distribution of the exponential…
This paper examines some probabilistic properties of the class of periodic GARCH processes (PGARCH) which feature periodicity in conditional heteroskedasticity. In these models, the parameters are allowed to switch between different…
We consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups. We compute their moments and find that the first few moments are Gaussian, whereas the limiting distribution is…
In large-scale construction projects, the continuous evolution of decisions generates extensive records, most often captured in meeting minutes. Since decisions may override previous ones, professionals often need to reconstruct the history…
We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…
We propose a continuous-time Markov-switching generalized autoregressive conditional heteroskedasticity (COMS-GARCH) process for handling irregularly spaced time series (TS) with multiple volatilities states. We employ a Gibbs sampler in…
In an asset return series there is a conditional asymmetric dependence between current return and past volatility depending on the current return's sign. To take into account the conditional asymmetry, we introduce new models for asset…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Graph retrieval-augmented generation (GraphRAG) has emerged as a powerful paradigm for enhancing large language models (LLMs) with external knowledge. It leverages graphs to model the hierarchical structure between specific concepts,…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
Inspired by the insightful article arXiv:1210.7587, we revisit the Nualart-Peccati-criterion arXiv:math/0503598 (now known as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov diffusion generators. We…