Title: Regularized estimation and testing for high-dimensional multi-block VAR models
Authors: Jiahe Lin - University of Michigan (United States) [presenting]
George Michailidis - University of Florida (United States)
Abstract: Dynamical systems comprising of multiple components that can be partitioned into distinct blocks originate in many scientific areas. A pertinent example is the interactions between financial assets and selected macroeconomic indicators, e.g. a stock index and an employment index. A key shortcoming of this approach is that it ignores potential influences from other related components that may exert influence on the system's dynamics. To mitigate this issue, we consider a multi-block linear dynamical system with Granger-causal ordering between blocks. We derive the MLE for the posited model for Gaussian data in the high-dimensional setting based on appropriate regularization schemes. To optimize the underlying non-convex likelihood function, we develop an iterative algorithm with convergence guarantees. We establish theoretical properties of the MLE, leveraging the decomposability of the regularizers and a careful analysis of the iterates. Finally, we develop testing procedures for the null hypothesis of whether a block ``Granger-causes'' another block of variables. The performance of the model and the testing procedures are evaluated on synthetic data, and illustrated on a data set involving log-returns of the US S\&P 100 component stocks and key macroeconomic variables.