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There are tons of approaches to model multi-variate time series. For example VAR and FBProphet, to mention a few. The challenge is, how does one predict the future regressors/independent variables (time series). Do people tend to use univariate time series models or do they create multivariate models for each time series and then iterate over them for each future time step (makes more sense embracing the VAR model?).

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It depends on what you are modeling.

  • If you have panel data, where the different time series you are interested in probably drive each other, possibly with lags (very typical for macroeconomic time series, like GDP, workforce, housing starts etc.), a model like VAR is appropriate.
  • If you have an intervention time series that you can set externally, you just use the future settings. An example would be future promotions in forecasting retail sales.
  • You may also have a time series $X$ that drives your focal time series $Y$, but not vice versa. An example would be the influence of weather on your retail sales. (Can you tell what I do for a living?) In this case, you can use whatever is appropriate to forecast your driver $X$, in this case your favorite meteorological forecast.
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  • $\begingroup$ Thanks. In the VAR setting, would you run a VAR model for each time step and then feed the predictions into each other and then iterate into the future? Points 1 + 3 apply in our scenario and we try to use granger causality to establish some form of "causality" network. $\endgroup$
    – cs0815
    Apr 30 '20 at 11:46
  • $\begingroup$ Well, you have one VAR model which you then typically iterate into the future one step at a time. (Another model I didn't mention would be state space models. Same here.) $\endgroup$ Apr 30 '20 at 11:58
  • $\begingroup$ sorry but how can you only have one model. How are the future regressors/independent variables/time series generated? Or does the VAR model do (e.g. R implementation) do this automagically? $\endgroup$
    – cs0815
    Apr 30 '20 at 12:12
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    $\begingroup$ Yes, you have one large VAR model, which includes all time series you feed into it, and when you forecast, it will forecast all series (step by step, but in any implementation, this will happen "under the hood"). $\endgroup$ Apr 30 '20 at 12:26
  • $\begingroup$ The difference between panel data and multivariate time series is subtle, but what you refer to in the first bullet point seems more like multivariate time series. $\endgroup$ Apr 30 '20 at 12:47

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