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

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  • Concepción Ausín

    ()

  • Pedro Galeano

    ()

  • Pulak Ghosh

    ()

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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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws103822.

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Date of creation: Sep 2010
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Handle: RePEc:cte:wsrepe:ws103822

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Keywords: Bayesian estimation; Deviance information criterion; Dirichlet process mixture; Financial time series; Location-scale Gaussian mixture; Markov chain Monte Carlo;

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
  3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
  4. Bhattacharyya, Malay & Chaudhary, Abhishek & Yadav, Gaurav, 2008. "Conditional VaR estimation using Pearson's type IV distribution," European Journal of Operational Research, Elsevier, vol. 191(2), pages 386-397, December.
  5. Ghosh, Pulak & Basu, Sanjib & Tiwari, Ram C., 2009. "Bayesian Analysis of Cancer Rates From SEER Program Using Parametric and Semiparametric Joinpoint Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 439-452.
  6. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344.
  7. María Concepcion Ausin & Pedro Galeano, 2005. "Bayesian Estimation Of The Gaussian Mixture Garch Model," Statistics and Econometrics Working Papers ws053605, Universidad Carlos III, Departamento de Estadística y Econometría.
  8. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  9. Galeano, Pedro & Ausín, M. Concepción, 2010. "The Gaussian Mixture Dynamic Conditional Correlation Model: Parameter Estimation, Value at Risk Calculation, and Portfolio Selection," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 559-571.
  10. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
  11. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  12. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
  13. Basu S. & Chib S., 2003. "Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 224-235, January.
  14. Damien, Paul & Galenko, Alexander & Popova, Elmira & Hanson, Timothy, 2007. "Bayesian semiparametric analysis for a single item maintenance optimization," European Journal of Operational Research, Elsevier, vol. 182(2), pages 794-805, October.
  15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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Cited by:
  1. Mark J Jensen & John M Maheu, 2012. "Bayesian semiparametric multivariate GARCH modeling," Working Papers tecipa-458, University of Toronto, Department of Economics.
  2. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.

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