Sequence / Foundations
verifiedSeasonality
Electricity demand has a daily shape, a weekly shape and a yearly shape, all at once. Seasonality is that repetition at known periods, and it is the easiest structure in a series to exploit and the easiest to destroy — aggregate to the wrong resolution and a pattern that dominated the signal disappears entirely.
Two representations compete. Fourier terms are compact and assume the shape is smooth; dummies per period are flexible and cost a parameter each. The practical trap is resolution: summing hourly data to daily removes the daily cycle by construction, and a model then reports that no such cycle exists. Multiple seasonalities interacting — a holiday landing on a weekend — are what break the simple approaches.
A period-m season contributes energy at frequency 1/m and its harmonics, so a spectrum shows it as isolated peaks rather than spread mass. Averaging over a window of length w acts as a low-pass filter with zeros at multiples of 1/w — which is why aggregating at exactly the seasonal period annihilates it rather than attenuating it.
16 values. The left group decays steeply; the right group is 28% of the way to flat, and reads flatter than the left.
Energy across frequencies, as measured and after aggregating to a coarser interval. Drag the aggregation up to watch the seasonal peaks flatten into the noise floor — at the wrong resolution the cycle is not weakened, it is gone.
Reviewed by opendroid · 2026-08-18
- arXiv:1905.10437 — N-BEATS: Neural basis expansion analysis for interpretable time series forecasting