We consider Particle Gibbs (PG) as a tool for Bayesian analysis of non-linear non-Gaussian state-space models. PG is a Monte Carlo (MC) approximation of the standard Gibbs procedure which uses sequential MC (SMC) importance sampling inside the Gibbs procedure to update the latent and potentially...

A Bayesian analysis is presented of a time series which is the sum of a stationary component with a smooth spectral density and a deterministic component consisting of a linear combination of a trend and periodic terms. The periodic terms may have known or unknown frequencies. The advantage of...

Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility with piecewise constant realisations on bins forming a...

We are comparing two approaches for stochastic volatility and jumps estimation in the EUR/USD time series - the non-parametric power-variation approach using high-frequency returns, and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We find that both of...

This paper develops a sampling algorithm for bandwidth estimation in a nonparametric regression model with continuous and discrete regressors under an unknown error density. The error density is approximated by the kernel density estimator of the unobserved errors, while the regression function...

This note presents a nonparametric Bayesian approach to fitting a distribution to the survey data provided in Kilian and Zha (2002) regarding the prior for the half-life of deviations from purchasing power parity (PPP). A point mass at infinity is included. The unknown density is represented as...

The goal of this article is an exact Bayesian analysis of the Heston (1993) stochastic volatility model. We carefully study the effect different parameterizations of the latent volatility process and the parameters of the volatility process have on the convergence and the mixing behavior of the...

Non-parametric approach to financial time series jump estimation, using the L-Estimator, is compared with the parametric approach utilizing a Stochastic-Volatility-Jump-Diffusion (SVJD) model, estimated with MCMC and extended with Particle Filters to estimate the out-sample evolution of its...

Methodology is proposed of how to utilize high-frequency power-variation estimators in the Bayesian estimation of Stochastic-Volatility Jump-Diffusion (SVJD) models. Realized variance is used as an additional source of information for the estimation of stochastic variances, while the Z-Estimator...