Limit Theorems for Moving Averages of Discretized Processes Plus Noise

Abstract

This paper presents some limit theorems for certain functionals of moving averages of semi-martingales plus noise, which are observed at high frequency. Our method generalizes the pre-averaging approach (see [13],[11]) and provides consistent estimates for various characteristics of general semi-martingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we find central limit theorems with a convergence rate n1=4, if n is the number of observations.

Keywords: central limit theorem, high frequency observations, microstructure noise, quadratic variation, semimartingale, stable convergence

JEL Classification: C10, C13, C14