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I am trying to understand the underlying fundamental/statistical differences between vector autoregression models and Facebook's Prophet, with regards to multivariate time series forecasting.

I am very new to time series forecasting, but I am really looking to understand the differences between these models in terms of how they approach fitting a trend and forecasting future values. Most comparisons I can find online are in terms of their actual performance differences, that is not what I am looking for.

This is all very new so any pointers to resources which explain how Prophet and VAR work – for someone without a deep mathematical background – would be excellent, and then I can derive the answer myself from there. I cannot find very much about what Prophet really is, beyond the description.

My experience is in machine learning methods as opposed to time series forecasting, so I would appreciate any explanation which accounts for my very basic subject matter knowledge.

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    $\begingroup$ More details on the Prophet model can be found in their paper, "Forecasting at scale" doi.org/10.7287/peerj.preprints.3190v2. Simply put, the Prophet model is a generalized additive model (GAM) which uses predictors commonly used in time series forecasting problems. The model using three time series components - growth: $g(t)$, seasonality: $s(t)$, and holidays: $h(t)$. The terms are added with an Normal error $\varepsilon(t)$ to give: $y(t) = g(t) + s(t) + h(t) + \varepsilon(t)$. $g(t)$ is modelled using piecewise linear trends, $s(t)$ with fourier terms, and $h(t)$ as dummies. $\endgroup$
    – Mitchell O'Hara-Wild
    Aug 2, 2020 at 9:11
  • $\begingroup$ Thank you @MitchellO'Hara-Wild, I know this is beyond the scope of my original question and I can create a new question if that would be more appropriate: why/when would someone choose to use VAR instead of Prophet and vice versa? $\endgroup$
    – Darcey BM
    Aug 2, 2020 at 10:30
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    $\begingroup$ VAR and Prophet models are different model classes, and one is not always better than the other. A simple approach to choosing models for forecasting, is to try both and use which one produces the most accurate results on test data. To touch on your original question, a VAR is a multivariate model while Prophet is a univariate model. So a VAR will produce multivariate forecasts with uncertainty jointly determined by errors of multiple series (covariance matrix), while Prophet will produce univariate forecasts with uncertainty based on errors from a single series (variance scalar). $\endgroup$
    – Mitchell O'Hara-Wild
    Aug 2, 2020 at 11:49
  • $\begingroup$ Thanks @MitchellO'Hara-Wild, it is interesting to learn a bit more about the differences. I believe Prophet can be implemented as a multivariate forecast using the add_regressor method: facebook.github.io/prophet/docs/… $\endgroup$
    – Darcey BM
    Aug 3, 2020 at 6:58
  • $\begingroup$ By multivariate model above, I am referring to models that have multiple response variables. Using add_regressor with Prophet will use an additional time series variable(s) to predict a single response variable. $\endgroup$
    – Mitchell O'Hara-Wild
    Aug 4, 2020 at 0:01

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VAR can add regressors for multivariate series (exogen variables) and Prophet can add regressors for univariate series. thats the main difference. So first make a test (Granger test for example) to see if ur target variables are exogen or endogen and after that, you can use both of them in some cases (univariate series) and in other cases (multivariate series) you just can use VAR. Sorry for my english.

Just remember, if u wanna predict with exogen variables, both of them VAR and Prophet need the future values of those variables for ur target.

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