Bayesian Estimation and Prediction of Stochastic Volatility Models via INLA

Ehlers, Ricardo S.; Zevallos, Mauricio

doi:10.1080/03610918.2013.790444

Cited by 10 publications

(17 citation statements)

References 9 publications

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“…INLA has found its applications in many fields in the models where high-dimensional problems arise. Stochastic volatility models have been analyzed using INLA in [ 37 , 38 ]. Bivariate stochastic volatility model has been considered in [ 39 ], where the authors present and solve some issues that arise in using INLA in the multivariate case of the model.…”

Section: Methodsmentioning

confidence: 99%

“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

Shapovalova

2021

Entropy

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We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application.

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Section: Methodsmentioning

confidence: 99%

“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

Shapovalova

2021

Entropy

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“…Moreover, the most important objective of this work is to show the benefits of using Stochastic Partial Differential Equation (SPDE) with Integrated Nested Laplace Approximation (INLA) for spatial data (Ehlers and Zevallos, 2015;Lindgren et al, 2011;Martins, et al 2013;Neyens et al, 2018;R-INLA, 2015;Rue et al, 2009;Ruiz-Cárdenas et al, 2012). Previous studies (Taylor and Diggle, 2013) have described the difficulty of working with INLA for specific parameters, i.e., spatial parameters, but this problem could be solved with the use of SPDE in the majority of scenarios.…”

Section: Introductionmentioning

confidence: 99%

Enhancing the SPDE modeling of spatial point processes with INLA, applied to wildfires. Choosing the best mesh for each database

Paz

2019

Communications in Statistics - Simulation and Computation

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Wildfires play an important role in shaping landscapes and as a source of CO 2 and particulate matter, and are a typical spatial point process studied in many papers. Modeling the spatial variability of a wildfire could be performed in different ways and an important issue is the computational facilities that the new techniques afford us. The most common approaches have been through point pattern analysis or by Markov random fields. These methods have made it possible to build risk maps, but for many forest managers it is very useful to know the size of the fire as well as its location. In this work, we use Stochastic Partial Differential Equation (SPDE) with Integrated Nested Laplace Approximation (INLA) to model the size of the forest fires observed in the Valencian Community, Spain. But the most important element in this paper is the process that needs to be carried out prior to simulating and analyzing the different point patterns, namely, the choice of the most suitable mesh for the database. We describe and take advantage of the Bayesian methodology by including INLA and SPDE in the modeling process in all the scenarios.

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“…We extend simulation study provided in Ehlers and Zevallos (2015) by analyzing data generating processes with some different values of µ and σ η , in particular it is of interest when the values of σ η are relatively small since that is one of the cases where some of the estimation methods fail and this case has not been studied with respect to INLA.…”

Section: Approximate Methodsmentioning

confidence: 99%

“…INLA has found its applications in many fields which tend to have high-dimensional problems. Stochastic volatility models have been analyzed using INLA in Martino et al (2011) and Ehlers and Zevallos (2015).…”

Section: Integrated Nested Laplace Approximation (Inla)mentioning

confidence: 99%

Bayesian inference in multivariate nonlinear state-space models

Shapovalova

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Bayesian Estimation and Prediction of Stochastic Volatility Models via INLA

Cited by 10 publications

References 9 publications

“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

Enhancing the SPDE modeling of spatial point processes with INLA, applied to wildfires. Choosing the best mesh for each database

Bayesian inference in multivariate nonlinear state-space models

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