A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation
AbstractFinancial 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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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws103822.
Date of creation: Sep 2010
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Bayesian estimation; Deviance information criterion; Dirichlet process mixture; Financial time series; Location-scale Gaussian mixture; Markov chain Monte Carlo;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-02 (All new papers)
- NEP-BAN-2010-10-02 (Banking)
- NEP-ECM-2010-10-02 (Econometrics)
- NEP-ETS-2010-10-02 (Econometric Time Series)
- NEP-RMG-2010-10-02 (Risk Management)
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