  Time series forecasting remains a central challenge problem in almost all
scientific disciplines. We introduce a novel load forecasting method in which
observed dynamics are modeled as a forced linear system using Dynamic Mode
Decomposition (DMD) in time delay coordinates. Central to this approach is the
insight that grid load, like many observables on complex real-world systems,
has an "almost-periodic" character, i.e., a continuous Fourier spectrum
punctuated by dominant peaks, which capture regular (e.g., daily or weekly)
recurrences in the dynamics. The forecasting method presented takes advantage
of this property by (i) regressing to a deterministic linear model whose
eigenspectrum maps onto those peaks, and (ii) simultaneously learning a
stochastic Gaussian process regression (GPR) process to actuate this system.
Our forecasting algorithm is compared against state-of-the-art forecasting
techniques not using additional explanatory variables and is shown to produce
superior performance. Moreover, its use of linear intrinsic dynamics offers a
number of desirable properties in terms of interpretability and parsimony.
Results are presented for a test case using load data from an electrical grid.
Load forecasting is an essential challenge in power systems engineering, with
major implications for real-time control, pricing, maintenance, and security
decisions.
