Limit theorems for moving averages of discretized processes plus noise
Jean Jacod, Mark Podolskij, Mathias Vetter
The Annals of Statistics · 2010 · Volume 38 · Issue 3
Abstract
This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634–658, Stochastic Process. Appl. 119 (2009) 2249–2276]) and provides consistent estimates for various characteristics of general semimartingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we find central limit theorems with a convergence rate n−1/4, if n is the number of observations.
Keywords
60F05, 60G42, 60G44, 62G20, 62M09, central limit theorem, high-frequency observations, microstructure noise, Quadratic Variation, Semimartingale, stable convergence
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