Feature selection for time series data I am looking for methods for feature selection (or feature extraction) for time series data. Of course I did some research before, but it was not satisfying.
I am aware of methods like PCA, importance matrix from random forest, linear regression, etc. for feature selection or extraction, but are those methods also applicable to time series data?
The task would be to find a set of variables which is a good predictor of a certain time series variable.
Thanks for any suggestions!
 A: I was also on the search for a list of time series features quite a while ago. There are publications inspecting individual features but I was not able to find a comprehensive list of features.
 tsfresh automates extraction of features 
While working on industrial machine learning projects I made my own list of features that proved helpful in different applications.
This list is contained in the python package tsfresh, which allows to automatically extract a huge of number of features and filter them for their importance.
 Comprehensive list of time series features 
So regarding your question: You can find inspiration about other features in the comprehensive documentation about the calculated features of tsfresh here. There are simple features such as the mean, time series related features such as the coefficients of an AR model or highly sophisticated features such as the test statistic of the augmented dickey fuller hypothesis test.
I am sure you will find some interesting features for your application there.
Disclaimer: I am one of the authors of tsfresh.
A: The Cross Correlation function will help you identify relationships in your X variables.  Box-Jenkins discussed this in their text book. Time Series Analysis: Forecasting and Control
Of course, you will also need to identify outliers as the relationship can be impacted by these events along with changes in trend and level.
Plotting the Y and X in standardized form in a scatterplot and line plot will also support your hypothesis.
