  Forecasting high-dimensional time series plays a crucial role in many
applications such as demand forecasting and financial predictions. Modern
datasets can have millions of correlated time-series that evolve together, i.e
they are extremely high dimensional (one dimension for each individual
time-series). There is a need for exploiting global patterns and coupling them
with local calibration for better prediction. However, most recent deep
learning approaches in the literature are one-dimensional, i.e, even though
they are trained on the whole dataset, during prediction, the future forecast
for a single dimension mainly depends on past values from the same dimension.
In this paper, we seek to correct this deficiency and propose DeepGLO, a deep
forecasting model which thinks globally and acts locally. In particular,
DeepGLO is a hybrid model that combines a global matrix factorization model
regularized by a temporal convolution network, along with another temporal
network that can capture local properties of each time-series and associated
covariates. Our model can be trained effectively on high-dimensional but
diverse time series, where different time series can have vastly different
scales, without a priori normalization or rescaling. Empirical results
demonstrate that DeepGLO can outperform state-of-the-art approaches; for
example, we see more than 25% improvement in WAPE over other methods on a
public dataset that contains more than 100K-dimensional time series.
