Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error

We consider a cointegrating regression in which the integrated regressors are messy in the sense that they contain data that may be mismeasured, missing, observed at mixed frequencies, or have other irregularities that cause the econometrician to observe them with mildly nonstationary noise. Least squares estimation of the cointegrating vector is consistent. Existing prototypical variancebased estimation techniques, such as canonical cointegrating regression (CCR), are both consistent and asymptotically mixed normal. This result is robust to weakly dependent but possibly nonstationary disturbances.