Limit theorems for moving averages of discretized processes plus noise
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 co...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
24 March 2010
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| In: |
The annals of statistics
Year: 2010, Volume: 38, Issue: 3, Pages: 1478-1545 |
| ISSN: | 2168-8966 |
| DOI: | 10.1214/09-AOS756 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/09-AOS756 Verlag, Volltext: http://projecteuclid.org/euclid.aos/1269452645 
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| Author Notes: | Jean Jacod, Mark Podolskij and Mathias Vetter |
MARC
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| 520 | |a 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. | ||
| 650 | 4 | |a Central limit theorem | |
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| 650 | 4 | |a quadratic variation | |
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| 650 | 4 | |a stable convergence | |
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