We present a general framework for optimal nonparametric spot volatility estimation based on intraday range data, comprised of the first, highest, lowest, and last price over a given time interval. We rely on a decision-theoretic approach together with a coupling-type argument to directly tailor...

This paper concerns the uniform inference for nonparametric series estimators in time-series applications. We develop a strong approximation theory of sample averages of serially dependent random vectors with dimensions growing with the sample size. The strong approximation is first proved for...