I have a series of $n$ machines that are going to emit some sensor data. The machines are going to be started at some point, telemetry collected every minute for some time and then stopped. So, instead of one long time-series, I have many short time series. Note that some machines might run for an hour, others for 50 minutes, others for 40 minutes and so on. Within the hour, there will be some seasonal patterns.
Now, I want to fit a time-series model that gives me some 95% confidence bands for each time instant since a machine starts (for the sensor value). Also, tomorrow I will get some new machine I haven’t seen before but one that is expected to behave like the $n$ machines I trained on. For each minute and sensor value it produces, I want to estimate the p_value, denoting what the probability of seeing that observation would be if the machine were no different from the $n$ machines I saw in the past.
What time series models can be good fits for this use-case? As a stretch goal, each of the $n$ machines might have some feature vectors associated with them. Is it possible to take the features into account?
Some thoughts: perhaps we can combine the $n$ time series into one long time series and consider the intervals for which the shorter ones don’t have values as missing? But then the question becomes what order we should combine them in?
Some examples of the panel data: