Time series often exhibit seasonal patterns, and identification of these patterns is essential to understanding the data and predicting future behavior. Most methods train on large datasets and can fail to predict far past the training data. This limitation becomes more pronounced when data is sparse. This paper presents a method to fit a model to seasonal time series data that maintains predictive power when data is limited. This method, called \textit{SINAPSE}, combines statistical model fitting with an information criteria to search for disjoint, and possibly nonconsecutive, regimes underlying the data, allowing for a sparse representation resistant to overfitting.