Related papers: Analytic Moments for GARCH Processes
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
Stochastic Event Timing is a fundamental issue in developing both analytic and simulation models for stochastic systems. Generalized Erlang distributions are quite useful for generating those random events in a quite general way by…
Factorial moments are convenient tools in particle physics to characterize the multiplicity distributions when phase-space resolution ($\Delta$) becomes small. They include all correlations within the system of particles and represent…
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…
The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate…
Existing Moment Retrieval methods face three critical bottlenecks: (1) data scarcity forces models into shallow keyword-feature associations; (2) boundary ambiguity in transition regions between adjacent events; (3) insufficient…
Graph generation generally aims to create new graphs that closely align with a specific graph distribution. Existing works often implicitly capture this distribution through the optimization of generators, potentially overlooking the…
We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…
Retrieval-augmented generation (RAG) enhances large language models (LLMs) with external knowledge but incurs significant inference costs due to lengthy retrieved contexts. While context compression mitigates this issue, existing methods…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.
In this work, we present some recommendations on the evaluation of state-of-the-art generative models for constrained generation tasks. The progress on generative models has been rapid in recent years. These large-scale models have had…
In this paper we study ideals arising from moments of local Dirac measures and their mixtures. We provide generators for the case of first order local Diracs and explain how to obtain the moment ideal of the Pareto distribution from them.…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
GARCH-type time series (characterized by Generalized Autoregressive Conditional Heteroskedasticity) exhibit pronounced volatility, autocorrelation, and heteroskedasticity. To address these challenges and enhance predictive accuracy, this…
This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model…
We provide novel characterizations of multivariate normality that incorporate both the characteristic function and the moment generating function, and we employ these results to construct a class of affine invariant, consistent and…
The generation of multi-step density forecasts for non-Gaussian data mostly relies on Monte Carlo simulations which are computationally intensive. Using aggregated wind power in Ireland, we study two approaches of multi-step density…
This paper introduces an extension of the Markov switching GARCH model where the volatility in each state is a convex combination of two different GARCH components with time varying weights. This model has the dynamic behavior to capture…
We introduce a heterogeneous spatiotemporal GARCH model for geostatistical data or processes on networks, e.g., for modelling and predicting financial return volatility across firms in a latent spatial framework. The model combines…
Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…