Classifying functional time series

We consider the problem of classifying a high-dimensional time series into a number of disjoint classes defined by training data. Techniques of this type are an important component of a number of emerging technologies. These include the use of dense sensor arrays for condition monitoring, brain–computer interfaces for communications and control, the detection of moving pedestrians from sequences of images and the study of cognitive function using high-resolution electroencephalography (EEG). We propose a novel approach to problems of this type using the parameters of an underlying functional auto-regression model. We compare the performance of this approach using two contrasting data sets. The first is based on simulated series with different characteristics and sampling schemes and a second based on high-dimensional times series generated by multi-channel EEG. Both experiments show that our approach outperforms conventional time series methods by exploiting low-intrinsic dimensionality (smoothness). In addition, our simulation experiments show that good performance can be maintained for data generated by non-stationary sampling schemes, the latter causing large reductions in the performance of conventional procedures. These experiments suggest that meaningful information can be extracted from high-resolution EEG.