Fractional order time-delay multivariable discrete grey model for short-term online public opinion prediction

•The multivariable grey model predicts short-term online public opinion is proposed.•The parameter estimation and time response formula are expressed as discrete form.•The time-delay parameters are introduced to model considering the time-lag effect.•The fractional-order operator is introduced to reduce the influence of randomness. Aiming at the rapid fermentation characteristics of the online public opinion, this paper established the fractional order multivariable time-delayed discrete grey model to predict the trend of short-term online public opinion. Considering the dynamic time-varying delays of each driving factor in online public opinion, the time-delay parameters are introduced, and the lag time are determined by the maximum grey correlation theory. In order to reduce the influence of uncertainty between short-term public opinion data, the integer order accumulation is extended to the fractional order one, and the parameters are calculated by optimization model. Furthermore, the model is applied to forecast real event on microblog, and the results show that the new grey model has higher prediction accuracy compared with related grey models.