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

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Abstract
We propose extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed by Foster and Nelson (1996) for estimating the quadratic variation of asset returns, which is also referred to as integrated or realized volatility. The new approach treats integrated volatility as a continuous time stochastic process sampled at high frequencies and suggests rolling sample estimators which share many features with spot volatility estimators. We also discuss asymptotically efficient window lengths and optimal weighting schemes for estimators of the quadratic variation and establish the links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation.

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