Abstract: The research on the causal prediction of multivariate time series is a hot issue to explore the relationship between complex network-driven responses.This paper proposes a hierarchical filter method that combines and improves the lower bound constraints of dynamic time warping(DTW).This method was combined with Granger causality to verify the causal statistics,so that it dug out effective value information to achieve effective dimensionality reduction.And it was inputted into LSTM prediction model to make causal predictions.The simulation experiment used open-source air quality time series data sets for quantitative and qualitative comparison and verification.It is found that the training curve and the test curve in its loss function curve have a better fit,which shows that the causal prediction method is feasible and effective.