Least squares (LS) estimation of canonical cointegrating regression (CCR) is explored allowing for potential misspecification from singularity in the system and multicointegration among the variables. The following properties are established: (i) superconsistent estimation with increased rates of convergence in degenerate directions; and (ii) limit theory that is nuisance parameter dependent in degenerate directions. Importantly for practitioners, inference for testing coefficient restrictions is shown to remain valid under certain conditions in CCR despite potential misspecification from singularity in the system.
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Kheifets et al. (2026) studied this question.
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