  Non-stationary time series with non-linear trends are frequently encountered
in applications. We consider here the feasibility of accurately forecasting the
signals of multiple such time series considering jointly when the number of
historic samples is inadequate for accurately forecasting the signal of each
considered in isolation. We develop a new forecasting methodology based on
Gaussian process regression that is successful in doing so in examples for
which the method of generalized least-squares is not. The new method employs a
form of deep machine learning.
