Title: A Unified Framework for Long Range and Cold Start Forecasting of Seasonal Profiles in Time Series,
Abstract: Providing long-range forecasts is a fundamental challenge in time series
modeling, which is only compounded by the challenge of having to form such
forecasts when a time series has never previously been observed. The latter
challenge is the time series version of the cold-start problem seen in
recommender systems which, to our knowledge, has not been addressed in previous
work. A similar problem occurs when a long range forecast is required after
only observing a small number of time points --- a warm start forecast. With
these aims in mind, we focus on forecasting seasonal profiles---or baseline
demand---for periods on the order of a year in three cases: the long range case
with multiple previously observed seasonal profiles, the cold start case with
no previous observed seasonal profiles, and the warm start case with only a
single partially observed profile. Classical time series approaches that
perform iterated step-ahead forecasts based on previous observations struggle
to provide accurate long range predictions; in settings with little to no
observed data, such approaches are simply not applicable. Instead, we present a
straightforward framework which combines ideas from high-dimensional regression
and matrix factorization on a carefully constructed data matrix. Key to our
formulation and resulting performance is leveraging (1) repeated patterns over
fixed periods of time and across series, and (2) metadata associated with the
individual series; without this additional data, the cold-start/warm-start
problems are nearly impossible to solve. We demonstrate that our framework can
accurately forecast an array of seasonal profiles on multiple large scale
datasets.