Sampling Frequency and Window Length Trade-offs in Data-Driven Volatility Estimation: Appraising the Accuracy of Asymptotic Approximations

Despite the difference in information sets, we are able to compare the asymptotic distribution of volatility estimators involving data sampled at different frequencies. To do so, we propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed by Foster and Nelson (1996, Econometrica, 64, 139–174). We focus on traditional historical volatility filters involving monthly, daily and intradaily observations. Theoretical results are complemented with Monte Carlo simulations in order to assess the validity of the asymptotics for sample sizes and filters encountered in empirical studies.