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In this paper we propose the Single-equation Penalized Error CorrectionSelector (SPECS) as an automated estimation procedure for dynamicsingle-equation models with a large number of potentially (co)integratedvariables. By extending the classical single-equation error correction model,SPECS enables the researcher to model large cointegrated datasets withoutnecessitating any form of pre-testing for the order of integration orcointegrating rank. Under an asymptotic regime in which both the number ofparameters and time series observations jointly diverge to infinity, we showthat SPECS is able to consistently estimate an appropriate linear combinationof the cointegrating vectors that may occur in the underlying DGP. In addition,SPECS is shown to enable the correct recovery of sparsity patterns in theparameter space and to posses the same limiting distribution as the OLS oracleprocedure. A simulation study shows strong selective capabilities, as well assuperior predictive performance in the context of nowcasting compared tohigh-dimensional models that ignore cointegration. An empirical application tonowcasting Dutch unemployment rates using Google Trends confirms the strongpractical performance of our procedure.

An Automated Approach Towards Sparse Single-Equation Cointegration Modelling