  The variety of complex algorithmic approaches for tackling time-series
classification problems has grown considerably over the past decades, including
the development of sophisticated but challenging-to-interpret
deep-learning-based methods. But without comparison to simpler methods it can
be difficult to determine when such complexity is required to obtain strong
performance on a given problem. Here we evaluate the performance of an
extremely simple classification approach -- a linear classifier in the space of
two simple features that ignore the sequential ordering of the data: the mean
and standard deviation of time-series values. Across a large repository of 128
univariate time-series classification problems, this simple distributional
moment-based approach outperformed chance on 69 problems, and reached 100%
accuracy on two problems. With a neuroimaging time-series case study, we find
that a simple linear model based on the mean and standard deviation performs
better at classifying individuals with schizophrenia than a model that
additionally includes features of the time-series dynamics. Comparing the
performance of simple distributional features of a time series provides
important context for interpreting the performance of complex time-series
classification models, which may not always be required to obtain high
accuracy.
