Dynamic Chain Graph Models for Ordinal Time Series Data

Abstract: This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional independence among variables at a fixed time point, and an autoregressive coefficient that contains dynamic conditional independences interactions among time series components across consecutive time steps. The proposed model is a Gaussian copula vector autoregressive model, which is used to model sparse interactions in a high-dimensional setting. Estimation is achieved via a penalized EM algorithm. In this paper, we use an efficient coordinate descent algorithm to optimize the penalized log-likelihood with the smoothly clipped absolute deviation penalty. We demonstrate our approach on simulated and genomic datasets. The method is implemented in an R package tsnetwork.