Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results

We propose different extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed by Foster and Nelson (1996). First, despite the difference in information sets we are able to compare the asymptotic distribution of volatility estimators involving data sampled at different frequencies. We focus on traditional historical volatility filters involving monthly, daily and intra-daily observations. Second, we introduce a continuous record asymptotics approach for estimating the so called integrated volatility, which represents the cumulative integral of instantaneous volatility. The new approach treats integrated volatility as a stochastic process sampled at high frequencies and suggests rolling sample estimators which share many features with spot volatility estimators. We discuss optimal weighting schemes for integrated volatility estimators. Thirdly, we establish the links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation. Nous proposons des extensions de la théorie asymptotique de Foster et Nelson pour l'estimation de variance. Nous proposons une approximation asymptotique qui permet de comparer des estimateurs obtenus à partir de données avec fréquences d'échantillonnage différentes. Une autre extension consiste à appliquer les arguments de Foster et Nelson à des processus plus généraux tels que la volatilité intégrée.