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European Central Bank (ECB) Working Paper - INFINITE-DIMENSIONAL VARS & Factor Models

Vector autoregressive models (VARs) provide a flexible framework for the analysis of complex dynamics and interactions that exist between variables in the national and global economy. However, the application of the approach in practice is often limited to a handful of variables which could lead to misleading inference if important variables are omitted merely to accommodate the VAR modelling strategy. Number of parameters to be estimated grows at the quadratic rate with the number of variables, which is limited by the size of typical data sets to no more than 5 to 7. In many empirical applications, this is not satisfactory.

This paper introduces a novel approach for dealing with the curse of dimensionality in the case of large linear dynamic systems. Restrictions on the coeficients of an unrestricted VAR are proposed that are binding only in a limit as the number of endogenous variables tends to in…nity. It is shown that under such restrictions, an infinite-dimensional VAR (or IVAR) can be arbitrarily well characterized by a large number of infinite-dimensional models. The paper also considers IVAR models with dominant individual units and shows that this will lead to a dynamic factor model with the dominant unit acting as the factor. The problems of estimation and inference in a stationary IVAR with unknown number of unobserved common factors are also investigated. A cross section augmented least squares estimator is proposed and its asymptotic distribution is derived. Satisfactory small sample properties are documented by Monte Carlo experiments.

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