Studying the methodology of analyzing non-stationary time series by taking high-frequency price data as an example

本文研究了利用高频价格时间序列分析非平稳时间序列的方法。为了处理价格序列的强随机性和时间依赖性，我们避免了对数据取平均值，而是直接对原始时间序列进行处理，通过求解价格序列间互相关矩阵的特征值问题，将其特征值分布与相应的RMT公式进行比较。在本研究中，我们成功地建立了“RMT-PCA”在股票市场上的应用，并发明了一种新的工具来衡量随机性，我们称之为“RMT-test”，并证明了它的有效性，通过比较各种随机发生器的随机性水平，测量散列函数的质量，以及选择股票投资。

We examined the methods of analyzing non-stationary time series by using high frequency price time series. In order to treat the strong randomness and the time dependence, we avoided taking averages of the data but treated the original time series directly by solving the eigenvalue problem of the cross correlation matrix between pairs of price time series to compare its eigenvalue distribution to the corresponding RMT formula. In this study, we have successfully established the application of "RMT-PCA" on stock markets, and also invented a new tool to measure the randomness, that we call the "RMT-test", and proved its effectiveness by comparing the levels of randomness of various random generators, measuring the quality of hash functions, and also the choice of stocks to invest.