  Periodic time series (PTS) forecasting plays a crucial role in a variety of
industries to foster critical tasks, such as early warning, pre-planning,
resource scheduling, etc. However, the complicated dependencies of the PTS
signal on its inherent periodicity as well as the sophisticated composition of
various periods hinder the performance of PTS forecasting. In this paper, we
introduce a deep expansion learning framework, DEPTS, for PTS forecasting.
DEPTS starts with a decoupled formulation by introducing the periodic state as
a hidden variable, which stimulates us to make two dedicated modules to tackle
the aforementioned two challenges. First, we develop an expansion module on top
of residual learning to perform a layer-by-layer expansion of those complicated
dependencies. Second, we introduce a periodicity module with a parameterized
periodic function that holds sufficient capacity to capture diversified
periods. Moreover, our two customized modules also have certain interpretable
capabilities, such as attributing the forecasts to either local momenta or
global periodicity and characterizing certain core periodic properties, e.g.,
amplitudes and frequencies. Extensive experiments on both synthetic data and
real-world data demonstrate the effectiveness of DEPTS on handling PTS. In most
cases, DEPTS achieves significant improvements over the best baseline.
Specifically, the error reduction can even reach up to 20% for a few cases.
Finally, all codes are publicly available.
