Bayesian Comparison of GARCH Processes with Skewness Mechanism in Conditional Distributions
Abstract
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 a set of competing GARCH (Generalized Autoregressive Conditionally Heteroscedastic) specifications, all with asymmetric and heavy tailed conditional distributions. In building competing volatility models we consider, as an initial specification, conditionally Student-t GARCH process with unknown degrees of freedom parameter. By introducing skewness into Student-t family and incorporating 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 mechanisms 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 alpha -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. 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.
- Publication:
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Acta Physica Polonica B
- Pub Date:
- November 2006
- DOI:
- 10.48550/arXiv.physics/0606253
- arXiv:
- arXiv:physics/0606253
- Bibcode:
- 2006AcPPB..37.3105P
- Keywords:
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- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- Presented at 2nd Symposium on Socio- and Econophysics, Cracow 21-22 April 2006. Research supported by a grant from Cracow University of Economics. To be published in Acta Physica Polonica B