Related papers: Analytic Moments for GARCH Processes
Volatility clustering and spillovers are key features of real-world financial time series when there are a lot of cross-sectional financial assets. While network analysis helps connect stocks that are 'similar' or 'correlated', which is…
We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard…
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…
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…
We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH$(r,s)$ (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH…
This study connects two methods for modeling reaction times (RTs) in choice tasks: (1) the first-hitting time of a simple diffusion model with a single barrier, representing the cognitive process leading to a response, and (2) Generalized…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We…
Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include…
We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two…
The argmax theorem is a useful result for deriving the limiting distribution of estimators in many applications. The conclusion of the argmax theorem states that the argmax of a sequence of stochastic processes converges in distribution to…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
Christoffersen, Jacobs, Ornthanalai, and Wang (2008) (CJOW) proposed an improved Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model for valuing European options, where the return volatility is comprised of two distinct…
Models for financial risk often assume that underlying asset returns are stationary. However, there is strong evidence that multivariate financial time series entail changes not only in their within-series dependence structure, but also in…
We introduce a numerical method for solving Grad's moment equations or regularized moment equations for arbitrary order of moments. In our algorithm, we do not need explicitly the moment equations. As an instead, we directly start from the…
{ In this paper we present a natural and comprehensive generalisation of the standard factorial moments ($\clFq$) analysis of a multiplicity distribution. The Generalised Factorial Moments are defined for all $q$ in the complex plane and,…
Retrieval-Augmented Generation (RAG) enhances language models by combining retrieval with generation. However, its current workflow remains largely text-centric, limiting its applicability in geoscience. Many geoscientific tasks are…
For probabilistic programs, it is usually not possible to automatically derive exact information about their properties, such as the distribution of states at a given program point. Instead, one can attempt to derive approximations, such as…