Abstract: We present a linearly regressive prediction model for noisy chaotic time series phase space based on variational Bayesian and phase space reconstructive theory. Time series phase space is constructed. The variational Bayesian method estimates the linear regressive coefficient. We use the model to predict the Mackey-Glass chaotic time series with additive Gaussian noise. The results show that the model is robust to noise and can effectively control over-fitting. The prediction effect is not sensitive to the change of embedding dimension and time delay.

Key words: chaotic time series, variational Bayesian, phase space, linear regressive model, prediction