Stability Analysis of Deep Belief Network: Based SD-AR Model for Nonlinear Time Series

Abstract

As for nonlinear time series prediction, many different kinds of varying-coefficient models have been proposed and analysised in recent years. A kind of varying functional-coefficient autoregressive model, called the deep belief network-based state-dependent autoregressive (DBN-AR) model is considered in this paper. The stability conditions and existing conditions of limit cycle of the DBN-AR model are also studied. An especial designed parameter estimation method is used to identify the DBN-AR model. The DBN-AR model is used to predict the famous Canadian lynx data and Henon chaotic series, the prediction capability of the DBN-AR model is compared with other prediction models, the experimental results show that the DBN-AR model obtains better prediction accuracy.