Can you provide examples of business application of vector autoregressive model?

Vector Autoregressive models are exploited at Economics faculties all around the world. They are just another statistical model that solves problem of forecasting, although in a deeply complexity-uncovering manner.

Yet to my surprise, there is no evidence it has been used outside pure economics domain, namely, to solve business problems like we all - Data Scientists - do.

Can you share either your experience with application of VAR to solve business problem, a scenario in which it could hypothetically be used or state why it cannot be easily applied in business environment (if this is an objective, mathematically/empirically grounded reason, I am not looking for opinions on why this method has slow adoption)?

The question can apply as well to VECM models of course.

• VAR is a multivariate counterpart of AR. Sep 23, 2020 at 17:18

Caveat: I have a doctorate in economics and that is why I knew how, and where, and when to apply this type of model.

Sure, I used a vecm model last year to figure out how many credit cards get compromised per month given how much activity we see. (I work for a financial institution). We were looking for a long-run relationship and a short-run relationship. From this model, a survival analysis, and a couple of other techniques we were able to determine the optimal time to set the expiration date on a card. I applied this technique because I was afraid I was getting the wrong answer, namely because the number of transactions and number of fraud transactions were cointegrated.(All of the models I tried gave similar results which was comforting). Given that we are talking about fraud strategies I don't feel comfortable giving more details than this, hopefully, that gives you a flavor of what I was trying to accomplish. Basically, I was trying to do a robustness check.

It isn't easily applied in a business context because this model isn't intuitive, it isn't easily explained, and it takes great skill to interpret it. The "mathematical" answer probably has something to go like this, ask an average data scientist what the impulse-response function for their model looks like and you will get a blank stare. Ask them what the FEVD looks like for their model, and you will get a blank stare. Data scientists tend to be trained in non-linear models (read machine learning), not cointegrated time-series models. It isn't that they aren't capable, they've just never been trained to think in those terms. I know technically not math, and technically that is an opinion but it is probably the truth.

Also doing the math, I can probably get a better fit out of a non-linear model like an LSTM network(?). So if I only care about pure prediction, it wouldn't be worth my time. Where VAR and VECM shine is that although complicated, they are essentially linear, and therefore, fairly interpretable. So perhaps what you are looking for is a business setting that requires causally valid, interpretable, multivariate time-series models. If you look hard enough, I'm sure you can come up with a couple of interelated KPIs being tracked in your business where it would make sense.

But in my experience, if you need a fast dirty answer, forgive me econometrics teachers everywhere, you can just plug the differenced series into a linear regression. (Warning not best practices, but it does alright).

• Thank you. This is probably much better wording of my initial thoughts that I could have made myself! Still, I am curious on more examples, maybe with model specification, so I will accept this as an answer if nothing more appropriate to the core question will arise. Jun 2, 2018 at 21:33

Vector autoregression, just like plain autoregression, applies to linear problems. Linearity is an assumption that barely applies to everyday scenarios, especially with disturbance sources, such as human sentiment, being nonlinear.

Models that capture temporal nonlinearities, such as LSTM-RNNs, are much more useful in such problems.

A business application of VAR that I can think of would be to forecast the sales of a product based on its past values.