Threshold models for high-dimensional time series with network structure

Abstract

Threshold autoregressive (TAR) models form an important class of nonlinear time series models and have attracted great attentions in the literature. In order to extend threshold modeling to high-dimensional nonlinear time series, a threshold network autoregressive (TNAR) model is proposed in this paper to overcome the difficulty of over-parameterization by exploiting the available information of network relations. The proposed model can characterize the regime-switching feature in nonlinear complex network systems. Sufficient conditions for the strict stationarity and the ergodicity of the TNAR model are established. A computationally efficient method based on group LASSO is developed to estimate the multiple thresholds and the parameters. A grouped TNAR model is also proposed to further reduce the number of the parameters. The asymptotic behavior of the proposed method is explored and the estimation consistency of both number of groups and group membership structure is established.