I'm very new to time series analysis and I've been tasked with trying to make sense of some data and was hoping you smart folks out there could provide some guidance. I have some data relating to complaint rates of a product over time. There is a strong trend over time and the task is to explain why. There are a number of different versions of this product that have come out, and at any point in time, some but not all of the versions are active in the field by different users. If you disregard time and just look at how long the average user has been subscribed to the product family on a given day, there is a very strong correlation with the complaint rate. There are a few other potentially relevant covariates.
What I'd like to do is quantify the effects of version and these covariates. But since this is a time series, and in particular because not all the versions are active together, I'm not entirely sure what the correct method is. Visually it looks fairly obvious what is happening, but I'm looking for a statistical method to really tie it all together and make sure I don't fall into any bad practices. Thank you all!