Multivariate time series with additional features I am dealing with a problem that contains multiple categorical features and different time series depending on these variables. So, for example the dataset can be represented as:




Day
catA
catB
catC
productA




1
A
B
B
1.8


2
A
B
B
2.4


3
A
B
B
2.8


4
A
B
B
3.8


5
A
B
B
4.4


6
A
B
B
4.8


7
A
B
B
5.4




...
...
With n days recorded.
The fact is that during this same time, in parallel, another product is being registered with some of the categorical features in common:




Day
catA
catB
catC
productB




1
A
B
C
1.1


2
A
B
C
1.4


3
A
B
C
1.8


4
A
B
C
1.8


5
A
B
C
1.2


6
A
B
C
3.8


7
A
B
C
3.4




...
...
And this process is done for multiple products. All the categorical space of combinations is being explored during n days for different products.
The ideal forecasting will be something like predicting the next 5 days for the given categorical combination i.e catA=A, catB=B and catB=B, and it will forecast different results depending on the categorical input.
I have been looking for something to model this problem and Prophet (with its additional regressors) looks interesting but I do not know if it is the (best) approach.
I have also thought of a Bayesian regression due to I can introduce some prior knowledge on the distribution that the categorical features follow:
y = catA + catB + catC where y are the different time series as mentioned before.
What kind of model/framework/approach do you think I must follow to solve this?
Thanks

Since you have multiple items and for a given item the category is static then you won't get much benefit from models like prophet / arima as they only fit single time series. Your best bet would be using LightGBM/XGBoost and creating lagged features of your target and moving averages as well as date features.
You could give mlforecast a shot.
