Clarification on the Global Models and Univariate / Multivariate Forecasting.

[CWrecker]

In the NeuralForecast model overview, it is stated that:

Univariate / Multivariate: A multivariate model explicitly models the interactions between multiple time series in a dataset and will provide predictions for multiple time series concurrently. In contrast, a univariate model trained on multiple time series implicitly models interactions between multiple time series and provides predictions for single time series concurrently. Multivariate models are typically computationally expensive and empirically do not necessarily offer better forecasting performance compared to using a univariate model.

1. Is it possible to train a single global model for multivariate forecasting using this library?
   For instance, If I have a dataset with 10 instances (e.g. 10 farms) and each example has 4 variables (e.g. temp, sun, water, yield), how is this organized?

From what I can tell, the multivariate models treat each time series (unique_id) as belonging to the same instance.
Reference: https://nixtlaverse.nixtla.io/neuralforecast/docs/tutorials/multivariate_tsmixer.html (Here each unique_id represents a different measured quantity (i.e. Oil Temp, High UseLess Load, Middle UseFul Load, etc.) In this example, what if the dataset contains more than one transformer?

2. How are interactions "implicitly modeled" in the univariate case? Is this referring to the same thing as a single global model being trained over each time series?

[CWrecker]

Hello! Univariate vs multivariate can be seen as channel independence vs channel dependence.

Basically, a univariate model applies channel independence, meaning that a global model is trained, but the inter-dependency of each series is not learned. In your scenario with 4 farms, it means that the impact farm 1 can have on farm 2 will not be learned by the model.

A multivariate model uses channel dependence, meaning that it will learn the inter-dependency of each series. In your scenario, that means that the impact of farm 1 may have on farm 2 will be learned.

Then, both univariate and multivariate models can handle exogenous features. Those are features that are not measured in your target series.

So, in your case, you should have 10 unique ids, since you have 10 farms, and the other variables (temp, sun, water, yield) are exogenous features. Now, it's up to you to decide if you want a multivariate (channel dependence) or univariate (channel independence) model. Of course, if you want to use exogenous features, make sure that the model supports them. The complete list of models and their capabilities is here.

Courtesy of @marcopeix!