Publication: A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation
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2010-09
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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).
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Keywords
Bayesian estimation, Deviance information criterion, Dirichlet process mixture, Financial time series, Location-scale Gaussian mixture, Markov chain Monte Carlo