The approach delay has close relationship with the first vehicle’s arriving time at the signalized intersections. The research parameter is the difference time between the red light beginning time and the first vehicle’s arriving time, and the parameter has been forecasted. Considering the volatile of the first vehicle’ arrival time series, the mutual information and Cao method has been used to calculate the parameter that needed in the maximum Lyapunov index discrimination, and the chaotic characteristics has been proved. Then, the time has been forecasted using the wavelet-Elman neural network method. It is proved that the average error is 3.13s. The research result can provide reliable data for the delay extraction and signal time optimization.