An Automated Approach Towards Sparse Single-Equation Cointegration Modelling

TL;DR

This paper introduces SPECS, an automated method for estimating large cointegrated single-equation models that avoids pre-testing, accurately estimates cointegrating relationships, and outperforms traditional models in nowcasting tasks.

Contribution

SPECS extends classical error correction models to high-dimensional settings, enabling automated estimation and accurate recovery of cointegration and sparsity without pre-testing.

Findings

SPECS consistently estimates cointegrating vectors in high-dimensional settings.

The method accurately recovers sparsity patterns in parameters.

SPECS outperforms high-dimensional models in nowcasting accuracy.

Abstract

In this paper we propose the Single-equation Penalized Error Correction Selector (SPECS) as an automated estimation procedure for dynamic single-equation models with a large number of potentially (co)integrated variables. By extending the classical single-equation error correction model, SPECS enables the researcher to model large cointegrated datasets without necessitating any form of pre-testing for the order of integration or cointegrating rank. Under an asymptotic regime in which both the number of parameters and time series observations jointly diverge to infinity, we show that SPECS is able to consistently estimate an appropriate linear combination of the cointegrating vectors that may occur in the underlying DGP. In addition, SPECS is shown to enable the correct recovery of sparsity patterns in the parameter space and to posses the same limiting distribution as the OLS oracle procedure. A simulation study shows strong selective capabilities, as well as superior predictive performance in the context of nowcasting compared to high-dimensional models that ignore cointegration. An empirical application to nowcasting Dutch unemployment rates using Google Trends confirms the strong practical performance of our procedure.