I am currently working with time series data. My objective is to predict the a certain value at time t given some other variables that we will know the same day ( but prior to our objective variable). After trying several models I have managed to obtain a relatively good prediction using lasso regression.
However, given the importance of the problem, I would like to have some kind of confidence interval for my predictions, it would be very important to understand how accurate my prediction would be given a certain probability.
One solution I have though about is using a certain number of past MAE to compute the standard deviation and with that, and assuming they errors have a normal distribution compute a confidence interval at 95% with +-2 s.d.
One important consideration is that my dependent variable does not behave the same through the years, it is not stationary.
Would this be a robust way of computing this intervals or are there better alternatives?