Bayesian Stochastic Method Research Articles

On tree-structured linear and quantile regression-based asset pricing

PurposeThis study aims to introduce a tree-structured linear and quantile regression framework to the analysis and modeling of equity returns, within the context of asset pricing.Design/Methodology/ApproachThe approach is based on the idea of a binary tree, where every terminal node parameterizes a local regression model for a specific partition of the data. A Bayesian stochastic method is developed including model selection and estimation of the tree structure parameters. The framework is applied on numerous U.S. asset pricing models, using alternative mimicking factor portfolios, frequency of data, market indices, and equity portfolios.FindingsThe findings reveal strong evidence that asset returns exhibit asymmetric effects and non- linear patterns to different common factors, but, more importantly, that there are multiple thresholds that create several partitions in the common factor space.Originality/ValueTo the best of the authors' knowledge, this paper is the first to explore and apply a tree-structured and quantile regression framework in an asset pricing context.

On Tree-Structured Linear and Quantile Regression Based Asset Pricing

A tree-structured linear and quantile regression framework is proposed for the analysis and modeling of equity market returns. The approach is based on the idea of a binary tree, where every terminal node parameterizes a local regression model for a specific partition of the data. A Bayesian stochastic method is developed including model selection and estimation of the tree structure parameters. The modeling framework is applied on numerous asset pricing models related to the whole U.S. equity market, using alternative mimicking factor portfolios, frequency of data and widely followed market indices. The findings reveal strong evidence that asset returns exhibit asymmetric effects and nonlinear patterns to different common factors.

Bayesian approach to magnetotelluric tensor decomposition

Normal.dotm 0 0 1 210 1198 INGV BO 9 2 1471 12.0 0 false 14 18 pt 18 pt 0 0 false false false Magnetotelluric directional analysis and impedance tensor decomposition are basic tools to validate a local/regional composite electrical model of the underlying structure. Bayesian stochastic methods approach the problem of the parameter estimation and their uncertainty characterization in a fully probabilistic fashion, through the use of posterior model probabilities.We use the standard Groom­Bailey 3­D local/2­D regional composite model in our bayesian approach. We assume that the experimental impedance estimates are contamined with the Gaussian noise and define the likelihood of a particular composite model with respect to the observed data. We use non­informative, flat priors over physically reasonable intervals for the standard Groom­Bailey decomposition parameters. We apply two numerical methods, the Markov chain Monte Carlo procedure based on the Gibbs sampler and a single­component adaptive Metropolis algorithm. From the posterior samples, we characterize the estimates and uncertainties of the individual decomposition parameters by using the respective marginal posterior probabilities. We conclude that the stochastic scheme performs reliably for a variety of models, including the multisite and multifrequency case with up to several hundreds of parameters. Though the Monte Carlo samplers are computationally very intensive, the adaptive Metropolis algorithm increase the speed of the simulations for large­scale problems.

Modelling volatility asymmetries: a Bayesian analysis of a class of tree structured multivariate GARCH models

A new class of multivariate threshold GARCH models is proposed for the analysis and modelling of volatility asymmetries in financial time series. The approach is based on the idea of a binary tree where every terminal node parametrizes a (local) multivariate GARCH model for a specific partition of the data. A Bayesian stochastic method is developed and presented for the analysis of the proposed model consisting of parameter estimation, model selection and volatility prediction. A computationally feasible algorithm that explores the posterior distribution of the tree structure is designed using Markov chain Monte Carlo stochastic search methods. Simulation experiments are conducted to assess the performance of the proposed method, and an empirical application of the proposed model is illustrated using real financial time series.

Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models

A new class of flexible threshold normal mixture GARCH models is proposed for the analysis and modelling of the stylized facts appeared in many financial time series. A Bayesian stochastic method is developed and presented for the analysis of the proposed model allowing for automatic model determination and estimation of the thresholds and their unknown number. A computationally feasible algorithm that explores the posterior distribution of the threshold models is designed using Markov chain Monte Carlo stochastic search methods. A simulation study is conducted to assess the performance of the proposed method, and an empirical application of the proposed model is illustrated using real data.

Application of a Bayesian approach to stochastic delineation of capture zones.

This paper presents a Bayesian Monte Carlo method for evaluating the uncertainty in the delineation of well capture zones and its application to a wellfield in a heterogeneous, multiaquifer system. In the method presented, Bayes' rule is used to update prior distributions for the unknown parameters of the stochastic model for the hydraulic conductivity, and to calculate probability-based weights for parameter realizations using head residuals. These weights are then assigned to the corresponding capture zones obtained using forward particle tracking. Statistical analysis of the set of weighted protection zones results in a probability distribution for the capture zones. The suitability of the Bayesian stochastic method for a multilayered system is investigated, using the wellfield Het Rot at Nieuwrode, Belgium, located in a three-layered aquifer system, as an example. The hydraulic conductivity of the production aquifer is modeled as a spatially correlated random function with uncertain parameters. The aquitard and overlying unconfined aquifer are assigned random, homogeneous conductivities. The stochastic results are compared with deterministic capture zones obtained with a calibrated model for the area. The predictions of the stochastic approach are more conservative and indicate that parameter uncertainty should be taken into account in the delineation of well capture zones.