Bayesian Analysis of the Box-Cox Transformation in Stochastic Volatility Models

In the paper, we consider the Box-Cox transformation of financial time series in Stochastic Volatility models. Bayesian approach is applied to make inference about the Box-Cox transformation parameter (l). Using daily data (quotations of stock indices), we show that in the Stochastic Volatility models with fat tails and correlated errors (FCSV), the posterior distribution of parameter l strongly depends on the prior assumption about this parameter. In the majority of cases the values of l close to 0 are more probable a posteriori than the ones close to 1.