We further derive an exact expectation-maximization algorithm for inference in both subsampled and mixed-frequency settings. By studying the structural case, we develop identifiability and estimation methods for the causal structure of lagged and instantaneous effects at the desired time scale. We present a unifying framework for parameter identifiability and estimation under subsampling and mixed frequencies when the noise, or shocks, is non-Gaussian. To determine instantaneous and lagged effects between series at the causal scale, we take a model-based approach that relies on structural vector autoregressive models. Furthermore, series may be observed at different sampling rates, yielding mixed-frequency series. Causal inference in multivariate time series is challenging because the sampling rate may not be as fast as the time scale of the causal interactions, so the observed series is a subsampled version of the desired series.
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