Abstract: “Big data” is a hot term. However its strict theoretical basis has not been formed yet.The purpose of research in big data is from its application. From their mathematical formulation,big data and massive high-dimensional and high-frequency data have no big difference. From the statistical point of view, the big data study is to find a lower-dimensional stationary time series from the high-dimensional and high-frequency massive data, then use the law of large numbers(the ergodic theorem) to find the value of its application. In finance, that is just statistical arbitrage.

Key words: big data, stationary time series, statistical arbitrage