Inference from the Futures: Ranking the Noise Cancelling Accuracy of Realized Measures

We consider the log-linear relationship between futures contracts and their underlying assets and show that in the classical Brownian semi-martingale (BSM) framework the two series must, by no-arbitrage, have the same integrated variance. We then introduce the concept of noise cancelling and propose a generally applicable methodology to assess the performance of realized measures when the variable of interest is latent, overcoming the problem posed by the lack of a true value for the integrated variance. Using E-mini index futures contracts, we carry out formal testing of several realized measures in the presence of noise. Moreover, a thorough simulation analysis is employed to evaluate the estimators' sensitivity to different price and noise processes, and sampling frequencies.