Limit theorems for moving averages of discretized processes plus noise

• Verfasst von: Jacod, Jean [VerfasserIn]
• Verfasst von: Podolskij, Mark [VerfasserIn]
• Verfasst von: Vetter, Mathias [VerfasserIn]
• Titel: Limit theorems for moving averages of discretized processes plus noise
• Verf.angabe: Jean Jacod, Mark Podolskij and Mathias Vetter
• Umfang: 68 S.
• Fussnoten: Gesehen am 29.05.2018
• Titel Quelle: Enthalten in: The annals of statistics
• Jahr Quelle: 2010
• Band/Heft Quelle: 38(2010), 3, S. 1478-1545
• ISSN Quelle: 2168-8966
• DOI: doi:10.1214/09-AOS756
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1575813335

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.