# Predict Variables in Multivariate Time Series

I have a time series of some $p$ variables and $n$ observations (going back several years and with resolution of approximately 15 minutes). The variables are the numbers of product $p_i$ sold, and each sale has its own observation; not all products are sold at the same time and some products may frequently be sold together. It is as yet unclear if any products are only sold conditional on some other product also being sold.
If it is helpful we can think of my data a $p$ x $n$ matrix whose rows are vectors with $p$ entries representing sales per 15 minutes.
I understand that I can separately analyze each of my $p$ products using a variety of methods and forecast future sales separately. However, in my (admittedly beginner's) research I have seen no discussion of how to develop a model that can predict all $p_i$ at once. Is there such a technique? Or should I form $p$ models separately?