Mixed-frequency Cointegrating Regressions with Parsimonious Distributed Lag Structures

Parsimoniously specified distributed lag models have enjoyed a resurgence under the MIDAS moniker (Mixed Data Sampling) as a feasible way to model time series observed at very different sampling frequencies. I introduce cointegrating mixed data sampling regressions. I derive asymptotic limits under substantially more general conditions than the extant theoretical literature allows. In addition to the possibility of cointegrated series, I allow for regressors and an error term with general correlation patterns, both serially and mutually. The nonlinear least squares estimator still obtains consistency to the minimum mean-squared forecast error parameter vector, and the asymptotic distribution of the coefficient vector is Gaussian with a possibly singular variance. I propose a novel test of a MIDAS null against a more general and possibly infeasible alternative mixed-frequency specification. An empirical application to nowcasting global real economic activity using monthly financial covariates illustrates the utility of the approach.