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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?).

Richard Hardy
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cs0815
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1 Answers1

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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.
Stephan Kolassa
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  • 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. – cs0815 Apr 30 '20 at 11:46
  • 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.) – Stephan Kolassa Apr 30 '20 at 11:58
  • 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? – cs0815 Apr 30 '20 at 12:12
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    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"). – Stephan Kolassa Apr 30 '20 at 12:26
  • 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. – Richard Hardy Apr 30 '20 at 12:47
  • @RichardHardy: interesting. I always believed what I am writing about were panel data. Could you explain a bit? – Stephan Kolassa Apr 30 '20 at 14:11
  • I tried searching for threads discussing the difference between panel data and multivariate time series but did not find anything particularly interesting. FWIW, here are some (in no particular order): [1](https://stats.stackexchange.com/questions/332411), [2](https://stats.stackexchange.com/questions/250967), [3](https://stats.stackexchange.com/questions/122741), [4](https://stats.stackexchange.com/questions/306832), [5](https://stats.stackexchange.com/questions/93461), [6](https://stats.stackexchange.com/questions/7110). – Richard Hardy Apr 30 '20 at 14:52
  • In my understanding, the distinction between the two types of data is probably easiest by looking at the models and asymptotic theory used for them. Models: you would use a VAR for multivariate time series but a panel VAR (PVAR) for panel data. (A panel VAR is a restricted VAR reflecting some structure.) Asymptotic theory: you would look at N-asymptotics (number of individuals going to infinity) for panel data and T-asymptotics (number of time points going to infinity) for time series. Usually, N>>T for panel data but T>>N for time series. (There are cases of both N *and* T asymptotics, too.) – Richard Hardy Apr 30 '20 at 14:55
  • Within economics, multivariate time series are probably more common in macroeconomics and finance, while panel data are probably more common in microeconomics, though there are exceptions. BTW, I think there are plenty of poor answers in the threads I linked to above. – Richard Hardy Apr 30 '20 at 14:57