Estimation of Vector Error Correction Models with Mixed‐Frequency Data

Vector autoregressive (VAR) models with error‐correction structures (VECMs) that account for cointegrated variables have been studied extensively and used for further analyses such as forecasting, but only with single‐frequency data. Both unstructured and structured VAR models have been estimated and used with mixed‐frequency data. However, VECMs have not been studied or used with mixed‐frequency data. The article aims partly to fill this gap by estimating a VECM using the expectation‐maximization (EM) algorithm and US data on four monthly coincident indicators and quarterly real GDP and, then, using the estimated model to compute in‐sample monthly smoothed estimates and out‐of‐sample monthly forecasts of GDP. Because the model is treated as operating at the highest monthly frequency and the monthly‐quarterly data are used as given (neither interpolated to all‐monthly data, nor aggregated to all‐quarterly data), the application is expected to be unbiased and efficient. A Monte Carlo analysis compares the accuracy of VECMs estimated with the given mixed‐frequency data vs. with their single‐frequency temporal aggregate.