Box-Cox transforms for realized volatility

The main goal of this paper is to study the accuracy of a new class of transformations for realized volatility based on the Box-Cox transformation. This transformation is indexed by a parameter β and contains as special cases the log (when β=0) and the raw (when β=1) versions of realized volatility. Based on the theory of Edgeworth expansions, we study the accuracy of the Box-Cox transforms across different values of β. We derive an optimal value of β that approximately eliminates skewness. We then show that the corresponding Box-Cox transformed statistic outperforms other choices of β, including β=0 (the log transformation). We provide extensive Monte Carlo simulation results to compare the finite sample properties of different Box-Cox transforms. Across the models considered in this paper, one of our conclusions is that β=−1 (i.e. relying on the inverse of realized volatility also known as realized precision) is the best choice if we want to control the coverage probability of 95% level confidence intervals for integrated volatility.