# Time series explaining the trend

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!

• Could you clarify what you are actually measuring? Is it total complaints; complaints per user; complaints per unit time; something else? After all, how long the average user has been subscribed will be directly related to how long the product has been on the market which will be directly related to how many people are using it, so you should expect complaint rates to increase with time. Indeed, it's possible the product could be improving yet still produce more complaints. I recommend thinking through these issues before considering what statistical methods you could apply. – whuber Aug 23 at 13:26

What you are looking for is called SARMAX https://autobox.com/pdfs/SARMAX.pdf which correctly formed can include a differencing operator and one or more pulses suggesting points of inflection in a stochastic trend AND/OR actual time oriented predictor series called deterministic time trends such 1,2,3,,,,t and 0,0,0,0,1,1,2,3,,,t-4 suggesting a two-trended series IN ADDITION to the effects of the user-specified predictor series (X's).

Only your data knows for sure what the appropriate model is . Employ methods that can adequately identify both kinds of "trends" proxying user-omitted causal series while identifying and employing level/step shift indicators and pulse indicators as needed.

You might post your data in a csv file format and elicit help from the group.