When alternatives are compared using an estimated criterion function, this may introduce a discrepancy between the true and the estimated criterion. In this paper, we consider a situation where a preordering (ranking) of stochastic sequences is defined from expected loss/gain, using a parametric...

This paper applies the Model Confidence Set (MCS) procedure of Hansen, Lunde, and Nason (2003) to a set of volatility models. A MCS is analogous to confidence interval of a parameter in the sense that the former contains the best forecasting model with a certain probability. The key to the MCS...

We study the empirical properties of realized volatility of the E-mini S&P 500 futures contract at various time scales, ranging from a few minutes to one day. Our main finding is that intraday volatility is remarkably rough and persistent. What is more, by further studying daily realized...

We introduce a multivariate estimator of financial volatility that is based on the theory of Markov chains. The Markov chain framework takes advantage of the discreteness of high-frequency returns. We study the finite sample properties of the estimation in a simulation study and apply it to...