I'm working on a time series problem, with additional predictors. While I'm exploring various ways to approach the problem, one possible way is to turn the time series problem into a supervised machine learning problem, i.e. use $(t-k), ..., (t-1)$ to predict $t$, where $k$ is the number of lagged values (as described here). I also plan to use additional predictor (binary variables) such as holidays, days of the week, months of the year, etc.
For now, I need to determine variable importance of each predictor (including lagged values). Is it valid to use Random Forests to determine variable importance in such a problem? If not, what are other (better) ways to approach the problem?
Note that I understand that there are methods specifically for investigating the correlation of a $t$ and its lagged values $(t-k), ..., (t-1)$ (e.g. ACF, PACF). However, I'm also interested in the importance of the exogenous variables.