We examine the relationship between MIDAS regressions and the estimation of state space models applied to mixed frequency data. While in some cases the binding function is known, in general it is not, and therefore indirect inference is called for. The approach is appealing when we consider state space models which feature stochastic volatility, or other non-Gaussian and nonlinear settings where maximum likelihood methods require computationally demanding approximate filters. The stochastic volatility feature is particularly relevant when considering high frequency financial series. In addition, we propose a filtering scheme which relies on a combination of re-projection methods and now-casting MIDAS regressions with ARCH models. We assess the efficiency of our indirect inference estimator for the stochastic volatility model by comparing it with the Maximum Likelihood (ML) estimator in Monte Carlo simulation experiments. The ML estimate is computed with a simulation-based Expectation-Maximization (EM) algorithm, in which the smoothing distribution required in the E step is obtained via a particle forward-filtering/backward-smoothing algorithm. Our Monte Carlo simulations show that the Indirect Inference procedure is very appealing, as its statistical accuracy is close to that of MLE but the former procedure has clear advantages in terms of computational efficiency. An application to forecasting quarterly GDP growth in the Euro area with monthly macroeconomic indicators illustrates the usefulness of our procedure in empirical analysis.
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