Bayesian Nonparametric Graphical Models for Time-Varying Parameters VAR

Abstract

Over the last decade, big data have poured into econometrics, demanding new statistical methods for analysing high-dimensional data and complex non-linear relationships. A common approach for addressing dimensionality issues relies on the use of static graphical structures for extracting the most significant dependence interrelationships between the variables of interest. Recently, Bayesian nonparametric techniques have become popular for modelling complex phenomena in a flexible and efficient manner, but only few attempts have been made in econometrics. In this paper, we provide an innovative Bayesian nonparametric (BNP) time-varying graphical framework for making inference in high-dimensional time series. We include a Bayesian nonparametric dependent prior specification on the matrix of coefficients and the covariance matrix by mean of a Time-Series DPP as in Nieto-Barajas et al. (2012). Following Billio et al. (2019), our hierarchical prior overcomes over-parametrization and over-fitting issues by clustering the vector autoregressive (VAR) coefficients into groups and by shrinking the coefficients of each group toward a common location. Our BNP timevarying VAR model is based on a spike-and-slab construction coupled with dependent Dirichlet Process prior (DPP) and allows to: (i) infer time-varying Granger causality networks from time series; (ii) flexibly model and cluster non-zero time-varying coefficients; (iii) accommodate for potential non-linearities. In order to assess the performance of the model, we study the merits of our approach by considering a well-known macroeconomic dataset. Moreover, we check the robustness of the method by comparing two alternative specifications, with Dirac and diffuse spike prior distributions.