Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models

Abstract

There has been an increasing interest in the financial econometrics literature on the properties of non-linear transformations of returns. In this paper, we focus on power transformations and analyze which powers of returns provide stronger autocorrelations in the context of stochastic volatility (SV) models. We show that the sample and theoretical autocorrelations implied by short and long memory SV models peak at the same power transformation, which is close to one for realistic values of the model parameters. Consequently, we suggest that the power that maximizes the sample autocorrelations could be used as an additional descriptive tool for the adequacy of a SV model. The results are illustrated with three real series of financial returns.