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In this paper, we propose the realized Hyperbolic GARCH model for the joint-dynamics of lowfrequency returns and realized measures that generalizes the realized GARCH model of Hansen et al.(2012) as well as the FLoGARCH model introduced by…

Methodology · Statistics 2021-04-27 El Hadji Mamadou Sall , El Hadji Deme , Abdou Ka Diongue

This paper proposes a novel hybrid model, termed GARCH-FIS, for recursive rolling multi-step forecasting of financial time series. It integrates a Fuzzy Inference System (FIS) with a Generalized Autoregressive Conditional Heteroskedasticity…

Machine Learning · Computer Science 2026-03-17 Wen-Jing Li , Da-Qing Zhang

In order to calculate the unobserved volatility in conditional heteroscedastic time series models, the natural recursive approximation is very often used. Following \cite{StraumannMikosch2006}, we will call the model \emph{invertible} if…

Statistics Theory · Mathematics 2012-12-18 Alexey Sorokin

Improvements in data acquisition and processing techniques have lead to an almost continuous flow of information for financial data. High resolution tick data are available and can be quite conveniently described by a continuous time…

Statistics Theory · Mathematics 2011-05-03 Siegfried Hormann , Lajos Horvath , Ron Reeder

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

HYGARCH process is the commonly used long memory process in modeling the long-rang dependence in volatility. Financial time series are characterized by transition between phases of different volatility levels. The smooth transition HYGARCH…

Computation · Statistics 2017-01-24 Ferdous Mohammadi , Saeid Rezakhah

Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling features commonly found in observed financial returns. The extremal properties of these processes are of considerable interest for…

Computation · Statistics 2019-08-20 Fabrizio Laurini , Paul Fearnhead , Jonathan A. Tawn

Price range contains important information about the asset volatility, and has long been considered an important indicator for it. In this paper, we propose to jointly model the [low, high] price range as a random interval and introduce an…

Methodology · Statistics 2015-02-18 Yan Sun , Jennifer Loveland , Isaac Blackhurst

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…

Systems and Control · Electrical Eng. & Systems 2025-05-28 Hongpei Shao , Da-Qing Zhang , Feilong Lu

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

This paper proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(\infty) form of the GARCH model. This model can provide varying structures for conditional…

Methodology · Statistics 2023-11-14 Qianqian Zhu , Songhua Tan , Yao Zheng , Guodong Li

The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…

Statistical Finance · Quantitative Finance 2015-05-08 Gordon J. Ross

One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time…

Methodology · Statistics 2021-05-13 Tingguo Zheng , Han Xiao , Rong Chen

The discrete-time GARCH methodology which has had such a profound influence on the modelling of heteroscedasticity in time series is intuitively well motivated in capturing many `stylized facts' concerning financial series, and is now…

Statistical Finance · Quantitative Finance 2008-12-18 Ross A. Maller , Gernot Müller , Alex Szimayer

Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with…

Econometrics · Economics 2020-10-09 Yuta Yamauchi , Yasuhiro Omori

This paper presents a novel dynamic network autoregressive conditional heteroscedasticity (ARCH) model based on spatiotemporal ARCH models to forecast volatility in the US stock market. To improve the forecasting accuracy, the model…

Applications · Statistics 2023-03-21 Raffaele Mattera , Philipp Otto

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…

Probability · Mathematics 2007-09-20 Abdelouahab Bibi , Abdelhakim Aknouche

There is a serious and long-standing restriction in the literature on heavy-tailed phenomena in that moment conditions, which are unrealistic, are almost always assumed in modelling such phenomena. Further, the issue of stability is often…

Methodology · Statistics 2024-10-02 Yuxin Tao , Dong Li

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…

Statistical Finance · Quantitative Finance 2009-11-13 L. Gazola , C. Fernandes , A. Pizzinga , R. Riera

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…

Methodology · Statistics 2025-10-22 Peiyi Zhou