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The interacting impact between the crude oil prices and the stock market indices in China is investigated in the present paper, and the corresponding statistical behaviors are also analyzed. The database is based on the crude oil prices of Daqing and Shengli in the 7-year period from January 2003 to December 2009 and also on the indices of SHCI, SZCI, SZPI, and SINOPEC with the same time period. A jump stochastic time effective neural network model is introduced and applied to forecast the fluctuations of the time series for the crude oil prices and the stock indices, and we study the corresponding statistical properties by comparison. The experiment analysis shows that when the price fluctuation is small, the predictive values are close to the actual values, andwhen the price fluctuation is large, the predictive values deviate from the actual values to some degree. Moreover, the correlation properties are studied by the detrended fluctuation analysis, and the results illustrate that there are positive correlations both in the absolute returns of actual data and predictive data. [ABSTRACT FROM AUTHOR]