题 目:How many common driving Brownian motions latent in high dimensional Ito process with high frequency data ?

报告人：孔新兵教授 (苏州大学必赢国际bwin登录）

摘要：In this paper, we find a novel approach to determine the number of common driving Brownian motions latent in the high dimensional Ito process using high frequency data. The high dimensional Ito process is first approximated locally on a shrinking block by discrete-time approximate factor model. We then estimate the number of common driving Brownian motions by minimizing the penalized aggregated mean-squared residual error. It turns out the estimated number is consistent to the true number. While the local mean-squared residual error on each block converges at the rate of $n^{1/4} /wedge /sqrt{p} $ where $n$ is the sample size and $p$ is the dimensionality, it is interesting that the aggregated mean-squared residual error converges at a higher rate of $/sqrt{n}/wedge p$. It is also shown that the model discretization error does not affect the estimation at all when the block length shrinks to zero. Simulation results justify the performance of our estimator. A real financial data is also analyzed.

时间：2015年11月27日（周五）下午14:30开始

地点：数学系致远楼102室

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