Vector Autoregressive Model With Dynamic Factors

Abstract

We study semi-parametric inference in a Vector Autoregressive (VAR) model of order p augmented by unobservable common factors with a dynamic described by a VAR process of order q. This state-space specification is useful to define a network of interconnectedness and to measure separately the impulse responses to either systematic, or idiosyncratic, shocks. We show that the state-space parameters are identifiable from the autocovariance function of the observed process. We estimate the model by means of a multi-step procedure in closed-form, which combines an eigenvalue-eigenvector matrix decomposition and Instrumental Variable (IV) estimation allowing for Hansen-Sargan specification tests. We study the asymptotic and finite-sample properties of the parameter estimators and of rank tests for selecting the number of unobservable factors and VAR orders. In an empirical application we investigate which are the dynamic common factors that drive the co-movements in the daily log absolute return series of four sectorial stock market indices of the Chinese economy.