Conditionally Efficient Estimation of Long-Run Relationships Using Mixed-Frequency Time Series

I analyze efficient estimation of a cointegrating vector when the regressand and regressor are observed at different frequencies. Previous authors have examined the effects of specific temporal aggregation or sampling schemes, finding conventionally efficient techniques to be efficient only when both the regressand and the regressors are average sampled. Using an alternative method for analyzing aggregation under more general weighting schemes, I derive an efficiency bound that is conditional on the type of aggregation used on the low-frequency series and differs from the unconditional bound defined by the full-information high-frequency data-generating process, which is infeasible due to aggregation of at least one series. I modify a conventional estimator, canonical cointegrating regression (CCR), to accommodate cases in which the aggregation weights are known. The correlation structure may be utilized to offset the potential information loss from aggregation, resulting in a conditionally efficient estimator. In the case of unknown weights, the correlation structure of the error term generally confounds identification of conditionally efficient weights. Efficiency is illustrated using a simulation study and an application to estimating a gasoline demand equation.