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Limit theorems for moving averages of discretized processes plus noise. (English) Zbl 1196.60033
The paper presents some limit theorems for suitable functionals of moving averages of semimartingales plus noise which are observed at high frequency (hence the term microstructure noise is used). It generalizes the pre-averaging approach [see J. Jacod, Y. Li, P. Mykland, M. Podolskij and M. Vetter [Stochastic Processes Appl. 119, 2249–2276 (2009; Zbl 1166.62078)] and M. Podolskij and M. Vetter [Bernoulli 15, 634–658 (2009; Zbl 1200.62131)] and provides consistent estimates for various characterictics of general semimartingales. Some associated multidimensional (stable) central limit theorems (CLT) are proved (these CLT have the convergence rate \(n^-1/4\), where \(n\) is the number of observations).

MSC:
60F05 Central limit and other weak theorems
60G44 Martingales with continuous parameter
62M09 Non-Markovian processes: estimation
60G42 Martingales with discrete parameter
62G20 Asymptotic properties of nonparametric inference
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