引入投资者关注的中国股市协方差预测——基于多元HAR类模型

众多经济事实表明投资者并非完全理性。一方面，投资者由于有限关注，无法及时掌握市场上所有投资决策相关信息，可能导致资产价格对信息的反应不足；另一方面，某些信息会诱导投资者过度关注和过度交易，导致价格信号中包含更多噪声。这些都会造成短暂的错误定价，引起资产价格波动和资产间相关性的变化。鉴于此，本文认为投资者关注是影响资产多元波动率的一个重要外生因素，用百度指数衡量中国市场个体投资者关注，将其引入已实现协方差的多元异质自回归类模型，刻画个体投资者关注的变化对资产协方差的非对称影响，同时区分电脑端和移动端百度指数对协方差预测的不同贡献。采用2014年1月2日至2018年12月28日的50ETF成分股高频价格，和以股票简称及“50ETF”为关键词的百度指数，对上述模型进行实证。结果表明，百度指数代理的个体投资者关注蕴含对协方差预测有益的信息，将其引入协方差预测模型显著提升拟合性能和样本外预测能力；投资者关注的变化对资产波动及相关性的影响均存在非对称性；引入电脑端百度指数比引入移动端百度指数对协方差预测性能的提升更为显著。研究结果肯定了引入投资者关注对协方差预测的积极作用，对投资者的资产配置和风险管理有实际指导意义。     

Robust PCA for high-dimensional data based on characteristic transformation

In this paper, we propose a novel robust principal component analysis (PCA) for high-dimensional data in the presence of various heterogeneities, in particular strong tailing and outliers. A transformation motivated by the characteristic function is constructed to improve the robustness of the classical PCA. The suggested method has the distinct advantage of dealing with heavy-tail-distributed data, whose covariances may be non-existent (positively infinite, for instance), in addition to the usual outliers. The proposed approach is also a case of kernel principal component analysis (KPCA) and employs the robust and non-linear properties via a bounded and non-linear kernel function. The merits of the new method are illustrated by some statistical properties, including the upper bound of the excess error and the behaviour of the large eigenvalues under a spiked covariance model. Additionally, using a variety of simulations, we demonstrate the benefits of our approach over the classical PCA. Finally, using data on protein expression in mice of various genotypes in a biological study, we apply the novel robust PCA to categorise the mice and find that our approach is more effective at identifying abnormal mice than the classical PCA.