I have a situation where the outcome variable is measured monthly from 1975-current and then multiple predictors with varying start dates and end dates. My question is what is the best approach to take with this data? I'm working with another statistician who has more experience with time series data in these situations and he tells me the common practice is to delete the data up to the shortest predictor. For example, if predictor 1 is measured from 1975-current and predictor 2 is measured from 2001-current, he tells me the best approach and only option is to use data for both predictors from 2001-current. So, essentially deleting all the data for predictor 1 from 1975-2000. He also said this often results in better prediction. I'm a bit skeptical of all this and was wondering if an ML or Bayesian approach in Mplus might be able to handle this and use all available data.