Open Conference Systems, ICQQMEAS2013

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AUXIALIRY VARIABLE SAMPLER FOR ARCH AND GARCH MODELS
Stefanos G. Giakoumatos

Last modified: 2015-09-24

Abstract


In financial time series such as stock returns and exchange rates, it is often met the phenomenon of "volatility clustering". To model this financial phenomenon the Autoregressive Conditional Heteroskedasticity (ARCH) model (Engle, 1982) and the Stochastic Volatility model (Taylor 1986) have been proposed. For the case of ARCH type model, a variety of extensions have been proposed such as the GARCH model (Bollerslev (1986)), EGARCH (Nelson, (1991)), etc.; see Francq and Zakoian (2010). From the Bayesian perspective, a number of MCMC algorithms have been proposed (Vrontos et al 2001) that produce sample from the posterior distribution of the parameters of the models. However, these algorithms are not easily applied, mainly because the full conditional densities of the parameters are not of the known forms. In this paper we adopt the methodology of Auxiliary Variable Sampler (Neal (2003), Giakoumatos (2010. 2005), Damien et al. (1999)) and we propose MCMC algorithms for the ARCH and GARCH model where all the full conditionals are of known form. This has as a result that the proposed algorithms to be easily applied by financial practitioners

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