BAYESIAN SV MODELS IN THE ANALYSIS OF CONDITIONAL CORRELATION
The paper presents four specifications of Bivariate Stochastic Volatility process: the Basic Stochastic Volatility process (BSV), the Stochastic Discount Factor process (SDF), the SV with the Cholesky decomposition (TSV), and the SV with the spectral decomposition (JSV). The multivariate SV models are characterised by treating the volatilities (the conditional variances) as unobserved variables. The SDF model assumes that the conditional covariances are stochastic but the conditional correlations among the series are constant over time - the dynamic of the conditional variances and covariance is described by one stochastic process. The TSV and JSV models assume that the conditional correlation is time-varying and stochastic. In the TSV model the conditional covariance matrix is modelled using three separate stochastic processes, while in the JSV model there are only two separate processes. In this paper the bivariate stochastic volatility models are used to describe the daily exchange rate of the euro against the Polish zloty and the daily exchange rate of the US dollar against the Polish zloty. The general methods of the Bayesian inference and model selection are used to select the best bivariate SV model. The results presented here indicate that the conditional correlation coefficient changes over .time. The TSV model outperforms other models. The assumption of zero conditional correlation is strongly rejected by the data. The BSV model turned out to be the worst one. The results presented in this paper are obtained by Monte Carlo Markov chain. The Metropolis-Hastings algorithm is used within the Gibbs sampler.
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