Bayesowska analiza transformacji Boxa i Coxa dla ilorazu cen w modelach FCSV

Abstract

The continuously compounded rates of return (or logarithmic returns) and the simple rates of return are commonly used in econometric analyses of financial data. These two types of data transformation are applied arbitrarily. However, both are variants of the well-known Box- Cox transformation of the xt/xt-1 ratio (where xt denotes the asset price at time t) with parameter 0 and 1, respectively. In the paper, we consider the Box-Cox transformation of financial time series in Stochastic Volatility (SV) models. Bayesian approach is applied to make inference about the Box-Cox transformation parameter (λ). As parameter λ is estimated along with other unknown parameters, information in the data is used to determine which transformation is appropriate for the data. 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 λ strongly depends on the prior assumption about this parameter. It seems that in more cases the values of λ close to 0 are more probable a posteriori than the one close to 1.