Open Access
June 2010 Limit theorems for moving averages of discretized processes plus noise
Jean Jacod, Mark Podolskij, Mathias Vetter
Ann. Statist. 38(3): 1478-1545 (June 2010). DOI: 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.


Download 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.


Published: June 2010
First available in Project Euclid: 24 March 2010

zbMATH: 1196.60033
MathSciNet: MR2662350
Digital Object Identifier: 10.1214/09-AOS756

Primary: 60F05 , 60G44 , 62M09
Secondary: 60G42 , 62G20

Keywords: central limit theorem , high-frequency observations , microstructure noise , Quadratic Variation , Semimartingale , stable convergence

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • June 2010
Back to Top