Bayesian estimation and the application of long memory stochastic volatility models

A new sampling-based Bayesian approach to the long memory stochastic volatility (LMSV) process is presented; the method is motivated by the GPH-estimator in fractionally integrated autoregressive moving average (ARFIMA) processes, which was originally proposed by J. Geweke and S. Porter-Hudak [The estimation and application of long memory time series models, Journal of Time Series Analysis, 4 (1983) 221–238]. In this work, we perform an estimation of the memory parameter in the Bayesian framework; an estimator is obtained by maximizing the posterior density of the memory parameter. Finally, we compare the GPH-estimator and the Bayes-estimator by means of a simulation study and our new approach is illustrated using several stock market indices; the new estimator is proved to be relatively stable for the various choices of frequencies used in the regression.     

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leão Pinto Jr, Bayesian analysis of a multivariate null intercept error-in-variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763–771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161–178].     

Bayesian analysis of stochastic volatility models with flexible tails

An alternative distributional assumption is proposed for the stochastic volatility model. This results in extremely flexible tail behaviour of the sampling distribution for the observables, as well as in the availability of a simple Markov Chain Monte Carlo strategy for posterior analysis. By allowing the tail behaviour to be determined by a separate parameter, we reserve the parameters of the volatility process to dictate the degree of volatility clustering. Treatment of a mean function is formally integrated in the analysis.

Some empirical examples on both stock prices and exchange rates clearly indicate the presence of fat tails, in combination with high levels of volatility clustering. In addition, predictive distributions indicate a good fit with these typical financial data sets.     

Bayesian analysis of stochastic volatility models with flexible tails

An alternative distributional assumption is proposed for the stochastic volatility model. This results in extremely flexible tail behaviour of the sampling distribution for the observables, as well as in the availability of a simple Markov Chain Monte Carlo strategy for posterior analysis. By allowing the tail behaviour to be determined by a separate parameter, we reserve the parameters of the volatility process to dictate the degree of volatility clustering. Treatment of a mean function is formally integrated in the analysis.

Some empirical examples on both stock prices and exchange rates clearly indicate the presence of fat tails, in combination with high levels of volatility clustering. In addition, predictive distributions indicate a good fit with these typical financial data sets.     

GMM estimation of a realized stochastic volatility model: A Monte Carlo study

This article investigates alternative generalized method of moments (GMM) estimation procedures of a stochastic volatility model with realized volatility measures. The extended model can accommodate a more general correlation structure. General closed form moment conditions are derived to examine the model properties and to evaluate the performance of various GMM estimation procedures under Monte Carlo environment, including standard GMM, principal component GMM, robust GMM and regularized GMM. An application to five company stocks and one stock index is also provided for an empirical demonstration.     

Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes

This paper develops Bayesian inference of extreme value models with a flexible time-dependent latent structure. The generalized extreme value distribution is utilized to incorporate state variables that follow an autoregressive moving average (ARMA) process with Gumbel-distributed innovations. The time-dependent extreme value distribution is combined with heavy-tailed error terms. An efficient Markov chain Monte Carlo algorithm is proposed using a state-space representation with a finite mixture of normal distributions to approximate the Gumbel distribution. The methodology is illustrated by simulated data and two different sets of real data. Monthly minima of daily returns of stock price index, and monthly maxima of hourly electricity demand are fit to the proposed model and used for model comparison. Estimation results show the usefulness of the proposed model and methodology, and provide evidence that the latent autoregressive process and heavy-tailed errors play an important role to describe the monthly series of minimum stock returns and maximum electricity demand.     

Bayesian analysis of multivariate threshold autoregressive models with missing data

In some fields, we are forced to work with missing data in multivariate time series. Unfortunately, the data analysis in this context cannot be carried out in the same way as in the case of complete data. To deal with this problem, a Bayesian analysis of multivariate threshold autoregressive models with exogenous inputs and missing data is carried out. In this paper, Markov chain Monte Carlo methods are used to obtain samples from the involved posterior distributions, including threshold values and missing data. In order to identify autoregressive orders, we adapt the Bayesian variable selection method in this class of multivariate process. The number of regimes is estimated using marginal likelihood or product parameter-space strategies.     

Bayesian analysis of multivariate mortality data with large families

This paper presents a Bayesian method for the analysis of toxicological multivariate mortality data when the discrete mortality rate for each family of subjects at a given time depends on familial random effects and the toxicity level experienced by the family. Our aim is to model and analyse one set of such multivariate mortality data with large family sizes: the potassium thiocyanate (KSCN) tainted fish tank data of O'Hara Hines. The model used is based on a discretized hazard with additional time-varying familial random effects. A similar previous study (using sodium thiocyanate (NaSCN)) is used to construct a prior for the parameters in the current study. A simulation-based approach is used to compute posterior estimates of the model parameters and mortality rates and several other quantities of interest. Recent tools in Bayesian model diagnostics and variable subset selection have been incorporated to verify important modelling assumptions regarding the effects of time and heterogeneity among the families on the mortality rate. Further, Bayesian methods using predictive distributions are used for comparing several plausible models.     

Conjugate analysis of multivariate normal data with incomplete observations

The authors discuss prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. They present a general class of priors for incorporating information about unidentified parameters in the covariance matrix. They analyze the special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distribution resulting from a conjugate prior distribution. They develop an importance sampling and a Gibbs sampling approach to sample from a general posterior distribution and compare the two methods.     

Dynamic Bayesian analysis of generalized odds ratios assuming multivariate skew-normal distribution for the error terms in the system equation

In this paper, we develop a methodology for the dynamic Bayesian analysis of generalized odds ratios in contingency tables. It is a standard practice to assume a normal distribution for the random effects in the dynamic system equations. Nevertheless, the normality assumption may be unrealistic in some applications and hence the validity of inferences can be dubious. Therefore, we assume a multivariate skew-normal distribution for the error terms in the system equation at each step. Moreover, we introduce a moving average approach to elicit the hyperparameters. Both simulated data and real data are analyzed to illustrate the application of this methodology.     

Bayesian analysis of the linear regression model with an edgeworth series prior distribution

The purpose of the present investigation 1s to observe the effect of departure from normahty of the prior distribution of regresslon parameters on the Bayman analysis of a h e a r regresslon model Assuming an Edgeworth serles prior distribution for the regresslon coefficients and gamma prior for the disturbances precision, the expressions for the posterlor distribution, posterlor mean and Bayes risk under a quadratic loss function are obtalned The results of a numerical evaluation are also analyzed     

Joint analysis of occurrence and time to stability after entrance into the Italian labour market: an approach based on a Bayesian cure model with structured stochastic search variable selection

Precarious employment is a serious social problem, especially in those countries, such as Italy, where there are limited benefits from social security. We investigate this phenomenon by analysing the initial part of the career of employees starting with unstable contracts for a panel of Italian workers. Our aim is to estimate the probability of getting a stable job and to detect factors influencing both this probability and the duration of precariousness. To answer these questions, we use an ad hoc mixture cure rate model in a Bayesian framework.