Advances in Computational Sciences and Technology

This paper presents a forecast method for chaotic time series. Since only one single time series is available, the state space needs to be reconstructed to embed the time series using delay coordinates. By gradually increasing the dimension of the state space, the fractal dimension of the chaotic attractor in each state space is found. As the dimension of the state space becomes increasingly larger, the fractal dimension of the chaotic attractor will approach an asymptote, from which its embedding dimension can be found by an experimental formula. Due to short-time analogue behaviors of nearby states in the state space, their delayed coordinates are collected and serve as data set to which a multiple linear regression forecast model is fitted. Traffic flows of three different time intervals: 5-min, 10-min and 15-min are taken as examples to show the effectiveness of this forecast model. Numerical results show that the correlation coefficients between the predicted and observed 5-min, 10-min, and 15-min traffic volumes are 0.850, 0.932 and 0.951, respectively. It is also found that using more than the appropriate number of nearby states doesn't improve the accuracy significantly. In addition, the choice of time delay is not crucial when reconstructing the state space, because different time delay will all lead to identical embedding dimension of the chaotic attractor.