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Keywords:

  • Missing data;
  • cointegration;
  • state-space model;
  • Kalman filter;
  • expectation maximization algorithm;
  • smoothing
  • C13;
  • C22;
  • C32

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.