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.
@article{1269452645,
author = {Jacod, Jean and Podolskij, Mark and Vetter, Mathias},
title = {Limit theorems for moving averages of discretized processes plus noise},
journal = {Ann. Statist.},
volume = {38},
number = {1},
year = {2010},
pages = { 1478-1545},
language = {en},
url = {http://dml.mathdoc.fr/item/1269452645}
}
Jacod, Jean; Podolskij, Mark; Vetter, Mathias. Limit theorems for moving averages of discretized processes plus noise. Ann. Statist., Tome 38 (2010) no. 1, pp. 1478-1545. http://gdmltest.u-ga.fr/item/1269452645/