GARCH PROCESS WITH SHOWED-'t' AND STABLE CONDITIONAL DISTRIBUTION. BAYESIAN ANALYSIS FOR PLN/USD EXCHANHE RATE
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The paper presents application of Bayesian model comparison, which is based on the posterior probabilities and posterior odds ratio. We considered AR(1)-GARCH(1,1) framework for daily returns of PLN/USD exchange rate, proposed and adopted by Bauwens and Lubrano (1997), Bauwens et al. (1999) and Osiewalski and Pipien (2003), with two types of conditional distribution. In the first model (M1) we assumed conditionally Skewed-'t' distribution while in the second specification (M2) we used conditionally Stable distriburion. We observe the lack of flexibility of the Stable family in modelling financial data. The data give substantial support for the hypothesis that the GARCH model with Skewed-'t' condistional distribution explain the data better than model with Stable conditional distribution. In the paper we also compare predictive distribution of the daily growth rates for several forecasts horizons. Both models generated different type of uncertainty about future daily returns. For each forecast horizon the predictive distribution obtained form model M1 had greatest dispersion and was less leptokurtotic than predictive distribution generated by GARCH with Stable conditional distribution. However, the predictive distributions become more and more similar as the forecast horizon grows.
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