  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.
