Abstract
A new tool to measure the degree of randomness of a given sequence, named as the RMT-test, is introduced and applied on machine-generated random numbers as well as real-world data sequences. The tool consists of two parts: the qualitative evaluation that is aimed to visualize the degree of randomness, and the quantitative evaluation that is aimed to distinguish subtle differences of randomness among highly random sequences based on moment analysis, in which the moments of the actual eigenvalue distributions of the correlation matrix to the corresponding theoretical expression derived by the random matrix theory. The RMT-test is applied to solve practical problems by comparing the randomness of real data, such as the output of cryptographic hash functions MD5 and SHA-1, and high-frequency time series of stock prices. It is found that the stock of higher randomness tends to perform better than the stock of lower randomness in the following time period.
