In this work, we consider signals on graphs whose structure is motivated by time series analysis. In typical models for time series data, the values that occur closely together in time show a stronger dependence than observations that are spaced further apart. However, this property may need to be modified to explain recurring patterns, such as daily or weekly periodicities in traffic intensities. We assume that the underlying periodicities are known and encoded in a graph structure, where neighboring vertices are immediate successors in time or related by a shift in time corresponding to a period of the observed process. Based on the graph structure, one may devise a type of scattering transform in the spirit of Mallat’s scattering transform to generate feature vectors with convolutional networks in a non-adaptive way, for example as in the work by Zou and Lehrman based on graph wavelets. Here, we pursue a parallel, adaptive strategy that is based on heat kernels. Encoding known statistics from the training data in a type of graph Laplacian permits to obtain desirable properties of the graph convolutional network and, in turn, to detect anomalies in the time series. The main example consists of traffic intensities with daily and weekly periodicities and anomalous events that disrupt the regular pattern. This is joint work with Iris Emilsdottir.