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.