We conduct inference on volatility with noisy high‐frequency data. We assume the observed transaction price follows a continuous‐time Itô‐semimartingale, contaminated by a discrete‐time moving‐average noise process associated with the arrival of trades. We estimate volatility, defined as the quadratic variation of the semimartingale, by maximizing the likelihood of a misspecified moving‐average model, with its order selected based on an information criterion. Our inference is uniformly valid over a large class of noise processes whose magnitude and dependence structure vary with sample size. We show that the convergence rate of our estimator dominates n 1/4 as noise vanishes, and is determined by the selected order of noise dependence when noise is sufficiently small. Our implementation guarantees positive estimates in finite samples.

Standard estimators of risk premia in linear asset pricing models are biased if some priced factors are omitted. We propose a three-pass method to estimate the risk premium of an observable factor, which is valid even when not all factors in the model are specified or observed. The risk premium of the observable factor can be identified regardless of the rotation of the other control factors if together they span the true factor space. Our approach uses principal components of test asset returns to recover the factor space and additional regressions to obtain the risk premium of the observed factor.

Data snooping is a major concern in empirical asset pricing. We develop a new framework to rigorously perform multiple hypothesis testing in linear asset pricing models, while limiting the occurrence of false positive results typically associated with data snooping. By exploiting a variety of machine learning techniques, our multiple-testing procedure is robust to omitted factors and missing data. We also prove its asymptotic validity when the number of tests is large relative to the sample size, as in many finance applications. To improve the finite sample performance, we also provide a wild-bootstrap procedure for inference and prove its validity in this setting. Finally, we illustrate the empirical relevance in the context of hedge fund performance evaluation.