Ajieh, Frank
A methodology that transforms time into a spiral coordinate system to separate and internalize trend and seasonality, dramatically improving time series forecasting performance.
Existing time series models treat time as a simple scalar (1D) or rely on manually engineered sine/cosine features. This fails to effectively capture the interaction between trend and seasonality, especially in data with multiple periodicities.
Time is represented as a point on a 2D Archimedean spiral. The radial coordinate encodes cumulative progression (trend), and the angular coordinate encodes phase within a recurring cycle (seasonality). This decomposition is geometric and a priori. Single-period and multi-period embeddings are defined, designed to replace positional encodings in Transformers. Experiments are conducted on US Monthly Retail Sales (RSXFS) with 10 LSTM ablations.
The optimal multi-period spiral time embedding achieves 1.69% MAPE, outperforming scalar time (9.76%) by 83% and hand-engineered sinusoidal features (4.62%) by 63%. All 10 experiments show monotonic performance improvement with each geometric addition. Key finding: the radial term contributes only when linear in θ and z-score normalized; incorrect normalization yields worse results than omitting the trend term entirely. Code is open-source.