“…Examples include voting records of politicians, discrete health states for a patient over time, or action labels for players on a team. Furthermore, even when the raw recording mechanism produces continuous-valued time series, to facilitate downstream analyses, the series may be quantized into a small set of discrete values; examples include weather data from multiple stations (Doshi-Velez et al, 2011), wind data (Raftery, 1985), stock returns (Nicolau, 2014), or sales volume for a collection of products (Ching et al, 2002). In these cases, the traditional VAR framework for Granger causal analysis, (6), is inappropriate.…”