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SVR-GARCH model tends to "backward eavesdrop" when forecasting the financial time series volatility in which case it tends to simply produce the prediction by deviating the previous volatility. Though the SVR-GARCH model has achieved good…

Statistical Finance · Quantitative Finance 2022-06-23 Jun Lu , Shao Yi

We conclude our work [arXiv:2403.07628, arXiv:2503.12644] on asymptotic expansions at the soft edge for the classical $n$-dimensional Gaussian and Laguerre ensembles, now studying the gap-probability generating functions. We show that the…

Probability · Mathematics 2026-05-18 Folkmar Bornemann

It is common for long financial time series to exhibit gradual change in the unconditional volatility. We propose a new model that captures this type of nonstationarity in a parsimonious way. The model augments the volatility equation of a…

Econometrics · Economics 2024-10-15 Niklas Ahlgren , Alexander Back , Timo Teräsvirta

L\'evy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. We propose an essentially asymptotically efficient estimation method for the system parameters of…

Statistics Theory · Mathematics 2014-04-14 Máté Mánfay , László Gerencsér , Zsanett Orlovits

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian…

Statistics Theory · Mathematics 2014-02-04 Audronė Virbickaitė , M. Concepción Ausín , Pedro Galeano

In this paper we study the asymptotic behavior of the Gaussian quasi maximum likelihood estimator of a stationary GARCH process with heavy-tailed innovations. This means that the innovations are regularly varying with index…

Statistics Theory · Mathematics 2007-06-13 Thomas Mikosch , Daniel Straumann

In this study, we develop a unified volatility modeling framework that embeds GARCH dynamics directly within recurrent neural networks. We propose two interpretable hybrid architectures, GARCH-GRU and GARCH-LSTM, that integrate the…

Statistical Finance · Quantitative Finance 2025-11-25 Jingyi Wei , Steve Yang , Zhenyu Cui

Strong mixing property holds for a broad class of linear and nonlinear time series models such as ARMA and GARCH models. In this article we study correlation structure of strong mixing sequences, and some asymptotic properties are…

Statistics Theory · Mathematics 2012-03-02 Fatemeh Azizzadeh , Saeid Rezakhah

We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR…

Statistics Theory · Mathematics 2021-05-17 Jaehyeok Shin , Aaditya Ramdas , Alessandro Rinaldo

We propose a new approach to volatility modeling by combining deep learning (LSTM) and realized volatility measures. This LSTM-enhanced realized GARCH framework incorporates and distills modeling advances from financial econometrics, high…

Econometrics · Economics 2023-10-18 Chen Liu , Chao Wang , Minh-Ngoc Tran , Robert Kohn

In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a…

Statistics Theory · Mathematics 2020-07-03 Sophie Achard , Pierre Borgnat , Irène Gannaz

Generative moment matching networks (GMMNs) are introduced as dependence models for the joint innovation distribution of multivariate time series (MTS). Following the popular copula-GARCH approach for modeling dependent MTS data, a…

Methodology · Statistics 2021-10-05 Marius Hofert , Avinash Prasad , Mu Zhu

Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of…

Methodology · Statistics 2016-10-25 Yao Zheng , Qianqian Zhu , Guodong Li , Zhijie Xiao

In this paper, we use the results in Andrews and Cheng (2012), extended to allow for parameters to be near or at the boundary of the parameter space, to derive the asymptotic distributions of the two test statistics that are used in the…

Econometrics · Economics 2022-10-21 Philipp Ketz

Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…

Statistics Theory · Mathematics 2011-08-19 Martin Wendler

In this paper, we propose an Adaptive Realized Hyperbolic GARCH (A-Realized HYGARCH) process to model the long memory of high-frequency time series with possible structural breaks. The structural change is modeled by allowing the intercept…

Methodology · Statistics 2021-05-03 El Hadji Mamadou Sall , El Hadji Deme , Abdou Kâ Diongue

We develop the theory of a new type of asymptotic expansions for functions of two variables the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined…

Dynamical Systems · Mathematics 2010-04-30 Augustin Fruchard , Reinhard Schäfke

We develop the theory of a new type of asymptotic expansions for functions of two variables the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined…

Dynamical Systems · Mathematics 2010-03-23 Augustin Fruchard , Reinhard Schäfke

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…

Computation · Statistics 2023-08-30 Hanwen Xuan , Luca Maestrini , Feng Chen , Clara Grazian

The AutoRegressive Conditional Heteroskedasticity (ARCH) and its generalized version (GARCH) family of models have grown to encompass a wide range of specifications, each of them is designed to enhance the ability of the model to capture…

Data Analysis, Statistics and Probability · Physics 2007-05-23 G. R. Jafari , A. Bahraminasab , P. Norouzzadeh