In a Time Series Problem, is it possible to forecast quantities by learning the patterns of other items? What are my options? Suppose I own a store that sells a variety of apples and I have the following stats each month.


Report Date 
Type of Apple (TA) 
Quantity Available(QA) 
Quantity Sold in the Past 30 days(QS30) 
Quantity Shipping In (QSI) 
Quantity Needed to Order(QN)


Lets make the following assumptions/givens:


There are three types of apples: red apples, green apples and yellow apples.
T(1) denotes the first month and T(60) denotes the 60th month.
QA @ T(i + 1) = QA@T(i) + QSI@T(i) - QS30@T(i+1)




I can provide all the data from T1-60 for each apple.

I can also provide all the data for T61 besides QN for each apple.

My goal is predict QN at T61, or the 61st month for each apple.



If I am only concerned about Red Apples, I can just use ARIMAX with data pertaining to only red apples or VAR right? 

But what if I suddenly introduce a new apple type such as orange apples and only have a history from T1-4?

Given I need to use T1-4 for the orange apples...
Is it possible to use other data from the red, green and yellow to aid in properly calculating a QN value for orange apples at T5?
If I am only concerned about Red Apples, I can just use ARIMAX with data pertaining to only red apples or VAR right?

Yes, is possible, you will lose information (perhaps valuable) but you can work with it.

But what if I suddenly introduce a new apple type such as orange apples and only have a history from T1-4?

Given I need to use T1-4 for the orange apples... Is it possible to use other data from the red, green and yellow to aid in properly calculating a QN value for orange apples at T5?

You will be limited to the knowledge of the orange apples but the other variables might help you obtain enough information until you could have a more robust model, 4 entries might not be enough, but the model might help you obtain an estimation