Statistical Inference for Independent Component Analysis
Christian Gouriéroux, Alain Monfort · RePEc: Research Papers in Economics · 2015
The modelling of error terms in multivariate dynamic models by independent component analysis (ICA) is required for reliable impulse response analysis in macroeconomic applications. Since the introduction of ICA by Comon (1994), a large number of semi-parametric estimation methods have been proposed for "orthogonalizing" the error terms. These methods can be pseudo-maximum likelihood (PML) approaches, recursive PML, or moment methods. However several of these approaches are not consistent, and the other ones can be signi cantly sube cient. The aim of our paper is to derive the asymptotic properties of the PML approaches, in particular to study their consistency (or lack of consistency). Moreover we introduce covariance estimators and explain how to improve their e ciency. Finally we discuss the empirical likelihood approach.