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The Stock–Watson coincident index and its subsequent extensions assume a static linear one-factor model for the component indicators. This restrictive assumption is unnecessary if one defines a coincident index as an estimate of monthly real gross domestic products (GDP). This paper estimates Gaussian vector autoregression (VAR) and factor models for latent monthly real GDP and other coincident indicators using the observable mixed-frequency series. For maximum likelihood estimation of a VAR model, the expectation-maximization (EM) algorithm helps in finding a good starting value for a quasi-Newton method. The smoothed estimate of latent monthly real GDP is a natural extension of the Stock–Watson coincident index.
Mariano et al. (Thu,) studied this question.