  Multivariate time series are routinely encountered in real-world
applications, and in many cases, these time series are strongly correlated. In
this paper, we present a deep learning structural time series model which can
(i) handle correlated multivariate time series input, and (ii) forecast the
targeted temporal sequence by explicitly learning/extracting the trend,
seasonality, and event components. The trend is learned via a 1D and 2D
temporal CNN and LSTM hierarchical neural net. The CNN-LSTM architecture can
(i) seamlessly leverage the dependency among multiple correlated time series in
a natural way, (ii) extract the weighted differencing feature for better trend
learning, and (iii) memorize the long-term sequential pattern. The seasonality
component is approximated via a non-liner function of a set of Fourier terms,
and the event components are learned by a simple linear function of regressor
encoding the event dates. We compare our model with several state-of-the-art
methods through a comprehensive set of experiments on a variety of time series
data sets, such as forecasts of Amazon AWS Simple Storage Service (S3) and
Elastic Compute Cloud (EC2) billings, and the closing prices for corporate
stocks in the same category.
