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BAYESIAN SV MODELS IN THE ANALYSIS OF CONDITIONAL CORRELATION

100%

Pajor A.

Przegląd Statystyczny

2006

vol. 53

issue 1

69-89

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.

INTRODUCING SKEWNESS INTO CONDITIONALLY FAT TAILED GARCH PROCESSES: A BAYESIAN COMPARISON

100%

Pipien M.

Przegląd Statystyczny

2008

vol. 55

issue 2

89-116

The main goal of this paper is an application of Bayesian model comparison, based on the posterior probabilities and posterior odds ratios, in testing the explanatory power of the set of competing GARCH (Generalised Autoregressive Conditionally Heteroscedastic) specifications, all with asymmetric and heavy tailed conditional distributions. In building competing volatility models we consider, as an initial specification, GARCH process with conditional Student-t distribution with unknown degrees of freedom parameter, proposed by Bollerslev. By introducing skewness into Student-t family and by application the resulting class as a conditional distribution we generated various GARCH models, which compete in explaining possible asymmetry of both conditional and unconditional distribution of financial data. In order to make Student-t family skewed we consider various alternative methods recently proposed in the literature. In particular, we apply the hidden truncation mechanism, an approach based on the inverse scale factors in the positive and the negative orthant, order statistics concept, Beta distribution transformation and Bernstein density transformation. Additionally, we consider GARCH process with conditional a-Stable distribution. Based on the daily returns of hypothetical financial time series, we discuss the results of Bayesian comparison of alternative skewing mechanisms applied in the initial Student -t GARCH framework. We also check the sensitivity of model ranking with respect to structural changes in dynamics of considered time series. Additionally, we present formal Bayesian inference about conditional asymmetry of the distribution of the daily returns in all competing specifications on the basis of the skewness measure defined by Arnold and Groenveld.

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2 Przegląd Statystyczny

1 Pajor A.

1 Pipien M.

1 2008

1 2006

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BAYESIAN SV MODELS IN THE ANALYSIS OF CONDITIONAL CORRELATION

INTRODUCING SKEWNESS INTO CONDITIONALLY FAT TAILED GARCH PROCESSES: A BAYESIAN COMPARISON