Feature Extraction Technique - Summarizing a Sequence of Data I often am building a model (classification or regression) where I have some predictor variables that are sequences and I have been trying to find technique recommendations for summarizing them in the best way possible for inclusion as predictors in the model.

As a concrete example, say a model is being built to predict if a customer will leave the company in the next 90 days (anytime between t and t+90; thus a binary outcome). One of the predictors available is the level of the customers financial balance for periods t_0 to t-1. Maybe this represents monthly observations for the prior 12 months (i.e. 12 measurements). 

I am looking for ways to construct features from this series. I use descriptives of each customers series such as the mean, high, low, std dev., fit a OLS regression to get the trend. Are their other methods of calculating features? Other measures of change or volatility? 

ADD:

As mentioned in a response below, I also considered (but forgot to add here) using Dynamic Time Warping (DTW) and then hierarchical clustering on the resulting distance matrix - creating some number of clusters and then using the cluster membership as a feature. Scoring test data would likely have to follow a process where the DTW was done on new cases and the cluster centroids - matching the new data series to their closest centroids...
would LOVE to see a box written which collected case studies on feature engineering / extraction


Please advise if this helps 


Discretization of Time Series Data 
http://arxiv.org/ftp/q-bio/papers/0505/0505028.pdf
Optimizing Time Series Discretization for Knowledge Discovery
https://www.uni-marburg.de/fb12/datenbionik/pdf/pubs/2005/moerchen05optimizing
Experiencing SAX: a Novel Symbolic Representation of Time Series
http://cs.gmu.edu/~jessica/SAX_DAMI_preprint.pdf
Indexing for Interactive Exploration of Big Data Series
http://acs.ict.ac.cn/storage/slides/Indexing_for_Interactive_Exploration_of_Big_Data_Series.pdf
Generalized Feature Extraction for Structural Pattern Recognition in
Time-series Data
http://www.semanticscholar.org/paper/Generalized-Feature-Extraction-for-Structural-Olszewski-Maxion/7838bcd87bb6616e9fd3ffd92d4676a7082da34c
Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package
https://cran.r-project.org/web/packages/dtw/vignettes/dtw.pdf