Identification of embedding dimension is helpful to the reconstruction of phase space. However, it is difficult to calculate the proper embedding dimension for the financial time series of dynamics. By this Letter, we suggest a new method based on Manhattan distance and recurrence quantification analysis for determining the embedding dimension. By the advantages of the above two tools, the new method can calculate the proper embedding dimension with the feature of stability, accuracy and rigor. Besides, it also has a good performance on the chaotic time series which has a high-dimensional attractors.

In this paper, we mainly use recurrence plot, recurrence quantification analysis and cross recurrence plot to investigate the potential nonlinear dynamical characteristics of the stock market. In addition, we introduce and analyze the capital asset pricing model (CAPM), which can analyze the correlation between returns and risks of stock price data. In particular, we selected the large-cap stocks represented by SSE 50 index and the small-cap stocks represented by CSI 500 index as our research objects. Through the recurrence plot analysis of the time series of [Formula: see text] factor of CAPM and the time series of the stock market, we can find the advantages of large-cap stocks, such as stronger stationarity and long-term certainty, the disadvantages of small-cap stocks, such as greater risk and information, and nonlinear cross recurrence with the stock market.