RTSF

A simplified write up of a paper on linear mapping for long term time series forecasting. The main claim: a seasonal series with a period condition always admits an analytical linear solution.

RTSF is a simplified documentation of a paper called Revisiting Long-term Time Series Forecasting: An Investigation on Linear Mapping. Simplified means the full paper is condensed into the problem definition and the theoretical results, as a quick reference for the core idea rather than the full treatment.

The problem is defined for linear mapping on long term time series forecasting. A historical observation has c channels and n time steps, and a weight matrix plus a bias maps that history to the forecast output. The setup is minimal: one weight matrix, one bias, applied to the historical window.

The core result is a theorem. Given a seasonal time series that satisfies the periodic condition where the value at time t equals the value at time t minus the period, an analytical solution for the linear model always exists. That is the central claim of the paper, and it is the reason a plain linear mapping can handle seasonal forecasting.

The linear model is formalized with a transition matrix as the weight and a bias vector, applied to the historical observation window. The period assumption is stated as a condition for the analytical solution, which ties the theorem directly back to the model definition.

The whole argument rests on one theorem: a periodic seasonal series guarantees an analytical solution for a linear forecast model. Everything else in the README builds the notation around that claim.

• Source 1 · Project repository
• Source 2 · README