Limit theorems for moving averages of discretized processes plus noise

Details Limit theorems for moving averages of discretized processes plus noise Limit theorems for moving averages of discretized processes plus noise

2010-10-02

arxiv.org/abs/1010.0335v1

Annals of Statistics 2010, Vol. 38, No. 3, 1478-1545

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS756 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS756

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.

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