均值函数相等检验及在高频股指收益率中应用

Equality Test of Mean Functions and Its Application in High Frequency Stock Index Return

针对具有相依特征的函数型数据样本,提出利用经典的Newey-West估计式对它们的长期协方差函数进行估计,从而可以得到更加准确的函数主成分,进而对独立同分布条件下的均值函数相等检验统计量进行改进,并通过模特卡罗模拟和实例分析与现有独立同分布和相依条件下的检验方法进行比较。模特卡罗模拟结果表明,相比于现有检验方法,文中所提改进方法的检验水平与显著性水平更接近,而检验功效更高。实例分析结果表明,2018年沪深300和上证180股指1分钟和5分钟累积收益率的均值函数相等,即这两个金融市场的投资收益水平相当。

For functional data samples with dependent characteristics,it is proposed to use the classical Newey-West estimator to estimate their long-run covariance function,so as to obtain more accurate functional principal components.Furthermore,the equality test statistic of mean functions under independent and identically distributed is improved,and compared with existing test methods under independent and identically distributed and dependent conditions through Monte Carlo simulation and empirical analysis.The Monte Carlo simulation results show that compared to existing testing methods,the improved method proposed in the article has a testing level closer to the significance level and higher testing power.The example analysis results show that the mean functions of the 1-minute and 5-minute cumulative returns of the CSI 300 and SSE 180 stock indexes in 2018 are equal,indicating that the investment returns of these two financial markets are equivalent.