View Submission - COMPSTAT

A0428
**Title: **On constrained estimation of graphical time series models
**Authors: **Heung Wong - The Hong Kong Polytechnic University (Hong Kong) **[presenting]**

**Abstract: **Graphical models represent the conditional independence relations between random variables in multivariate data. These independence relationships can be visualized by an undirected graph where vertices represent the variables and edges between vertices illustrate that the corresponding variables of the connected vertices are conditionally dependent. The increasing interest in data science has heightened the need for the development of Gaussian graphical models with sparse coefficients on high dimensional data. The use of graphical models has been extended to multivariate time series to explore the interrelationship between components of a multivariate time series process. We propose a method to estimate a graphical time series model, which is based on a sparse vector autoregressive process. Both the autoregressive coefficients and the entries of the inverse of the noise covariance matrix will be estimated. To impose sparsity on both the coefficients and the inverse covariance matrix, we propose an iterative algorithm to estimate a sparse VAR model by considering the maximum likelihood estimation with the sparsity constraints as a biconvex problem in the sense that the optimization problem becomes convex when either the autoregressive coefficients or the inverse covariance matrix is fixed.