Supplemental Material for “Automated Estimation of Vector Error Correction Models”

This supplement has two sections. Section 1 contains proofs of some auxiliary lemmas used in the main text. Section 2 provides some further simulation results which complement those reported in the main text. 1 Proofs of Auxiliary Lemmas This section provides proofs of some lemmas which are used in the main text to derive the asymptotic properties of the LS shrinkage estimator. For ease of exposition, we separate the lemmas and their proofs that relate to different sections of the main text into different subsections within this Supplemental Appendix. The same notation is used here as in the main text, where the definitions may be found. 1.1 Proofs of Some Lemmas in Section 3 Assumption 1.1 (WN) {ut}t≥1 is an m-dimensional iid process with zero mean and nonsingular covariance matrix Ωu. ∗Department of Economics, UC Los Angeles, 8379 Bunche Hall, Mail Stop: 147703, Los Angeles, CA 90095. Email: [email protected] †Yale University, University of Auckland, University of Southampton and Singapore Management University. Support from the NSF under Grant Nos SES 09-56687 and SES 12-58258 is gratefully acknowledged. Email: [email protected]