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Many bubble test methods do not have the ability to predict multiple bubbles in a high dimensional space now. Therefore, we propose a data-driven, self-adaptive evolutionary bubble prediction algorithm named WSADF. First, according to the invariance principle, we speculate that if there are inherent degrees of freedom for high dimensional time series, then comovement causality analysis (CCA) can be improved to select the decisive high dimensional time series that must reflect the prominent comovement causality. The optimization problem of the high dimensional space can be solved in the low dimensional space and maintain the inherent relationships among the time series by using CCA. Second, the learning parameters of hidden neurons have the ability of self-adaptive differential evolution. The neurons in the network are used to model the individuals’ signals from the perspective of evolution. Third, a self-adaptive evolutionary neural network can be used to simulate the operation of the entire market’s signals. The generalized sup augmented Dickey–Fuller test is improved to suit changing market environmental conditions. Thus, the WSADF algorithm has the ability to predict multiple bubbles in high dimensional space. An empirical application of the methodology is conducted on different types of markets (e.g., the USDCNH and CSI300 closing prices), which has successfully identified and forecasted multiple bubbles from 2015 to 2017.

High-Dimensional Multiple Bubbles Prediction Based on Sparse Constraints