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.
Citation
Jean Jacod. Mark Podolskij. Mathias Vetter. "Limit theorems for moving averages of discretized processes plus noise." Ann. Statist. 38 (3) 1478 - 1545, June 2010. https://doi.org/10.1214/09-AOS756
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