Forecasting stock of product is forecasting sells.
Because normally you should know how much stock you're going to buy for the stock.
[current stock = stock you buy(you should know) - sells]
So I just focus on sells of products. You don't mention about the period.
So I assume you're trying to predict tomorrow sales(as whole day) from past data.
Sales data should have seasonal and long span trend. But it might be independent relationship tomorrow and today. Because customer wouldn't buy product in a row due to the waste of energy.
I can't tell correctly without taking a look your data. This case doesn't fit ARIMA, LSTM.
It should fit regression or Decompose model.
Choose the model by the dimension(OlS ~ Xgboost). Preprocess to reduce the dimension can be more effective for large dimension data.
As a first step, try to model except special case like promotion and vacation season..
Then try to combine those behavior or separate model.
1.Certain stocks are in compete of each other
This phenomenon is vague, so it is hard to tell relationship.
2.Certain stocks are normally buy together.
In happening this, products have been already bought. So it is no meaning for forecast. But you could find some theory sells goes down if other product is not in stock.
It can be used regression.
3.They are different promotion structure for a stock
This kind of human behavior is hard to apply model because it is not constant. Promotion effects will decrease over time.
Anyhow it should be possible to use in regression.
4.Certain stock are new and there is no existing record
If you have new data may effects current model, let see the model output error before and after. And significant error is happened by new data. You have to update model to include new data.