2013/05/06 by Yuta Koike, Koike, Yuta · 1 citation
Mathematics · #60F17 #62M10 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:60F17 #msc:62M10 #stat.TH
paper · pdf · doi:10.48550/arxiv.1305.1229
39 pages, 2 figures, 7 tables. arXiv admin note: text overlap with arXiv:1302.4887
arxiv created 2013/07/03 · arxiv updated 2013/07/04
We consider two continuous Itô semimartingales observed with noise and sampled at stopping times in a nonsynchronous manner. In this article we establish a central limit theorem for the pre-averaged Hayashi-Yoshida estimator of their integrated covariance in a general endogenous time setting. In particular, we show that the time endogeneity has no impact on the asymptotic distribution of the pre-averaged Hayashi-Yoshida estimator, which contrasts the case for the realized volatility in a pure diffusion setting. We also establish a central limit theorem for the modulated realized covariance, which is another pre-averaging based integrated covariance estimator, and demonstrate the above property seems to be a special feature of the pre-averaging technique.