  Time series are an interesting frontier for kernel-based methods, for the
simple reason that there is no kernel designed to represent them and their
unique characteristics in full generality. Existing sequential kernels ignore
the time indices, with many assuming that the series must be regularly-spaced;
some such kernels are not even psd. In this manuscript, we show that a "series
kernel" that is general enough to represent irregularly-spaced multivariate
time series may be built out of well-known "vector kernels". We also show that
all series kernels constructed using our methodology are psd, and are thus
widely applicable. We demonstrate this point by formulating a Gaussian
process-based strategy - with our series kernel at its heart - to make
predictions about test series when given a training set. We validate the
strategy experimentally by estimating its generalisation error on multiple
datasets and comparing it to relevant baselines. We also demonstrate that our
series kernel may be used for the more traditional setting of time series
classification, where its performance is broadly in line with alternative
methods.
