Statistics and Its Interface

Volume 13 (2020)

Number 2

Non-Gaussian stochastic volatility model with jumps via Gibbs sampler

Pages: 209 – 219

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n2.a6

Authors

Arthur T. Rego (Department of Statistics, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil)

Thiago R. dos Santos (Department of Statistics, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil)

Abstract

In this work we propose a model for estimating volatility from financial time series, extending the non-Gaussian family of space-state models with exact marginal likelihood proposed by [6]. On the literature there are models focused on estimating financial assets risk, however, most of them rely on MCMC methods based on Metropolis algorithms, since full conditional posterior distributions are not known. We present an alternative model capable of automatically estimating the volatility, since all full conditional posterior distributions are known, and it is possible to obtain an exact sample of volatility parameters via Gibbs Sampler. The incorporation of jumps in returns allows the model to capture speculative movements of the data so that their influence does not propagate to volatility. We evaluate the performance of the algorithm using synthetic and real data time series and the results are satisfactory.

Keywords

financial time series, stochastic volatility, Gibbs Sampler, dynamic linear models

2010 Mathematics Subject Classification

Primary 62M10, 62P20. Secondary 91B70.

Received 5 October 2018

Received revised 23 September 2019

Accepted 25 October 2019