This time, at ISF2026, I presented the paper that I have worked on together with Juan Ramon Trapero and Diego Pedregal. The idea of the paper is to introduce a taxonomy of the models in the Multiple Sources of Error (MSOE) framework. In the Single Source of Errors one, there is ETS, in the MSOE, there is nothing. So, we have united the existing research in one taxonomy of “Power transform, Trend, and Seasonal” model – analogue of ETS, but in the MSOE world. We are now finalising the paper about this, hoping to submit to a peer reviewed journal soon.

Abstract: State space models for time series forecasting have been dominated by the single source of error (SSOE) framework, most notably the ETS family of models. The idea of SSOE is to use the same error across all equations in the model. Multiple source of error (MSOE) models, by contrast, assign independent stochastic disturbances to each component – level, trend, and seasonality – offering a richer and more flexible representation of uncertainty, yet they lack a systematic, unifying taxonomy. This paper introduces the PTS taxonomy, a structured classification of MSOE state space models tailored to the specific properties of the MSOE setting. The taxonomy organises models along three dimensions: P (Power transform, based on the Box-Cox transformation), T (Trend, with options for none, local, global, or damped), and S (Seasonality, with options for none, discrete, or trigonometric), yielding up to 24 well-defined model variants. All models are cast within a general state space system and estimated via the Kalman filter using maximum likelihood, with model selection performed through standard information criteria. The framework also incorporates a robust outlier detection procedure covering additive outliers, level shifts, and slope changes, as well as natural handling of missing observations through the Kalman smoother. We illustrate the practical utility of the taxonomy through empirical experiments on the real life dataset, demonstrating that the PTS family is both theoretically coherent and empirically competitive with established alternatives.

Slides are here.
Package that implements PTS: muse