A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation

Abstract

Financial time series analysis deals with the understanding of data collected on financial markets. Several parametric distribution models have been entertained for describing, estimating and predicting the dynamics of financial time series. Alternatively, this article considers a Bayesian semiparametric approach. In particular, the usual parametric distributional assumptions of the GARCH-type models are relaxed by entertaining the class of location-scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution, leading to a Dirichlet process mixture model. The proposed specification allows for a greater exibility in capturing both the skewness and kurtosis frequently observed in financial returns. The Bayesian model provides statistical inference with finite sample validity. Furthermore, it is also possible to obtain predictive distributions for the Value at Risk (VaR), which has become the most widely used measure of market risk for practitioners. Through a simulation study, we demonstrate the performance of the proposed semiparametric method and compare results with the ones from a normal distribution assumption. We also demonstrate the superiority of our proposed semiparametric method using real data from the Bombay Stock Exchange Index (BSE-30) and the Hang Seng Index (HSI). In particular, the usual parametric distributional assumptions of the GARCH-type models are relaxed by entertaining the class of location-scale mixtures of Gaussian distributions with a Dirichlet process prior on the mixing distribution, leading to a Dirichlet process mixture model. The proposed specification allows for a greater flexibility in capturing both the skewness and kurtosis frequently observed in financial returns. The Bayesian model provide statistical inference with finite sample validity. Furthermore, it is also possible to obtain predictive distributions for the Value at Risk (VaR), which has become the most widely used measure of market risk for practitioners. Through a simulation study, we demonstrate the performance of the proposed semiparametric method and compare results with the ones from a normal distribution assumption. We also demonstrate the superiority of our proposed semiparametric method using real data from the Bombay Stock Exchange Index (BSE-30) and the Hang Seng Index (HSI).

A Bayesian non-parametric approach to asymmetric dynamic conditional correlation model with application to portfolio selection

“…Also, we present an application of Bayesian non-parametric techniques in portfolio decision problems and explore the differences in uncertainty between the proposed approach and conventional restrictive distributional assumptions, where the objective is to provide a more realistic evaluation of risk of financial decisions. As commented before, this study extends the work by Ausín et al (2014) to the multivariate framework and the recent work by Jensen & Maheu (2013) to the asymmetric setting. Also, differently from the work of Jensen & Maheu (2013), we always assume a conjugate prior specification and we use a different sampling approach.…”

“…This is a very flexible model that can be viewed as an infinite location-scale mixture of Gaussian distributions which includes, among others, the Gaussian, Student-t, logistic, double exponential, Cauchy and generalized hyperbolic distributions, among others. We follow closely the works of Ausín et al (2014), who have applied the DPM models for univariate GJR-GARCH, and Jensen & Maheu (2013), who have used DPM models for the multivariate symmetric DVEC by Ding & Engle (2001).…”

Bayesian semiparametric multivariate GARCH modeling

“…Our semiparametric MGARCH model is closely related to the semiparametric univariate volatility models of Jensen & Maheu (2010, 2012 and Ausín et al (2010). These earlier semiparametric models were based on modeling the dynamics of conditional volatility parametrically and on a nonparametric Dirichlet process mixture (DPM) prior for the distribution of the standardized returns.…”

Bayesian semiparametric Markov switching stochastic volatility model

“…Delatola and Griffin 21,22 proposed to approximate the distribution of t as an infinite mixture of Normals by relying on DPM models. Dirichlet process mixture models, firstly introduced by Lo, 26 have been widely used for modeling time-varying volatilities with univariate and multivariate SV and GARCH-type models (see other works [19][20][21][22][23][49][50][51][52].…”