  In this paper we present a new framework for time-series modeling that
combines the best of traditional statistical models and neural networks. We
focus on time-series with long-range dependencies, needed for monitoring fine
granularity data (e.g. minutes, seconds, milliseconds), prevalent in
operational use-cases.
  Traditional models, such as auto-regression fitted with least squares
(Classic-AR) can model time-series with a concise and interpretable model. When
dealing with long-range dependencies, Classic-AR models can become intractably
slow to fit for large data. Recently, sequence-to-sequence models, such as
Recurrent Neural Networks, which were originally intended for natural language
processing, have become popular for time-series. However, they can be overly
complex for typical time-series data and lack interpretability.
  A scalable and interpretable model is needed to bridge the statistical and
deep learning-based approaches. As a first step towards this goal, we propose
modelling AR-process dynamics using a feed-forward neural network approach,
termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also
scales to long-range dependencies.
  Our results lead to three major conclusions: First, AR-Net learns identical
AR-coefficients as Classic-AR, thus being equally interpretable. Second, the
computational complexity with respect to the order of the AR process, is linear
for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to
model long-range dependencies within fine granularity data. Third, by
introducing regularization, AR-Net automatically selects and learns sparse
AR-coefficients. This eliminates the need to know the exact order of the
AR-process and allows to learn sparse weights for a model with long-range
dependencies.
