Asymptotic F test in regressions with observations collected at high frequency over long span

This paper proposes tests of linear hypotheses when the variables may be continuous-time processes with observations collected at a high sampling frequency over long span. Utilizing series run variance (LRV) estimation in place traditional kernel LRV estimation, we develop easy-to-implement and more accurate F both stationary nonstationary environments. The environment accommodates exogenous regressors that are general semimartingales. Endogenous allowed similar to cointegration models usual discrete-time setting. can implemented exactly same way as are, therefore, robust or nature data. Simulations demonstrate improved size accuracy competitive power relative existing testing procedures their versions. practical interest recent work by Chang et al. (2021) demonstrates inference methods become invalid produce spurious results observed on finer grids