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Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which…

Applications · Statistics 2023-02-15 Junhyeon Kwon , Yingcai Zheng , Mikyoung Jun

Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…

Statistical Mechanics · Physics 2014-08-25 Yon Visell , Guillaume Millet

The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we…

Computational Finance · Quantitative Finance 2010-12-30 Tetsuya Takaishi

The Constant Elasticity of Variance (CEV) model is mathematically presented and then used in a Credit-Equity hybrid framework. Next, we propose extensions to the CEV model with default: firstly by adding a stochastic volatility diffusion…

Probability · Mathematics 2007-05-23 Marc Atlan , Boris Leblanc

We introduce a new smooth transition vector autoregressive model with a Gaussian conditional distribution and transition weights that, for a $p$th order model, depend on the full distribution of the preceding $p$ observations. Specifically,…

Econometrics · Economics 2026-02-10 Markku Lanne , Savi Virolainen

This paper proposes a semiparametric stochastic volatility (SV) model that relaxes the restrictive Gaussian assumption in both the return and volatility error terms, allowing them to follow flexible, nonparametric distributions with…

Computation · Statistics 2025-06-03 Yudong Feng , Ashis Gangopadhyay

Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of…

Applications · Statistics 2016-03-10 Worapree Maneesoonthorn , Catherine S. Forbes , Gael M. Martin

A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an…

Statistics Theory · Mathematics 2024-08-19 Nicolas-Domenic Reiter , Jonas Wahl , Andreas Gerhardus , Jakob Runge

Our article considers a regression model with observed factors. The observed factors have a flexible stochastic volatility structure that has separate dynamics for the volatilities and the correlation matrix. The correlation matrix of the…

Other Statistics · Statistics 2011-07-14 Yu-Cheng Ku , Peter Bloomfield , Robert Kohn

We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and…

Risk Management · Quantitative Finance 2014-10-30 Pedro Lencastre , Frank Raischel , Pedro G. Lind , Tim Rogers

We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and…

Methodology · Statistics 2021-02-19 Wei-Ting Lai , Ray-Bing Chen , Ying Chen , Thorsten Koch

The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse…

Applications · Statistics 2017-02-07 Yong Huang , James L. Beck , Hui Li

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

We propose a sparse vector autoregressive (VAR) hidden semi-Markov model (HSMM) for modeling temporal and contemporaneous (e.g. spatial) dependencies in multivariate nonstationary time series. The HSMM's generic state distribution is…

Applications · Statistics 2024-04-30 Beniamino Hadj-Amar , Jack Jewson , Marina Vannucci

We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…

Probability · Mathematics 2018-07-12 Łukasz Treszczotko

Multivariate data sources with components of different information value seem to appear frequently in practice. Models in which the components change their homogeneity at different times are of significant importance. The fact whether any…

Optimization and Control · Mathematics 2020-11-04 Krzysztof Szajowski

This paper studies Markov-switching (MS) models with time-varying transition probabilities (TVTP) under various specifications of the transition probability matrix. Especially, we extend the two-regime common-variance setting of the…

Methodology · Statistics 2026-05-15 Samuel Modée , Yushu Li , Sjur Westgaard , Stein Andreas Bethuelsen

We consider structural vector autoregressions subject to 'narrative restrictions', which are inequality restrictions on functions of the structural shocks in specific periods. These restrictions raise novel problems related to…

Econometrics · Economics 2021-02-15 Raffaella Giacomini , Toru Kitagawa , Matthew Read

In a real life process evolving over time, the relationship between its relevant variables may change. Therefore, it is advantageous to have different inference models for each state of the process. Asymmetric hidden Markov models fulfil…

Machine Learning · Computer Science 2023-05-16 Carlos Puerto-Santana , Pedro Larrañaga , Concha Bielza

Demographic heterogeneity is often studied through the geographical lens. Therefore it is considered at a predetermined spatial resolution, which is a suitable choice to understand scalefull phenomena. Spatial autocorrelation indices are…

Physics and Society · Physics 2024-04-01 Aleksejus Kononovicius , Justas Kvedaravicius