Smooth transition autoregressive models and fuzzy rule-based systems: Functional equivalence and consequences

In this work we will explore the theoretical connections existing between fuzzy rule-based systems (FRBS) applied on univariate time series and two statistical reference tools, the autoregressive (AR) models and the smooth transition autoregressive (STAR) model. We will show that a TSK fuzzy rule happens to be a localised AR model and that a STAR model can hence be interpreted as a restricted FRBS. Several consequences derive from this fact, and we will explore some of them, including a statistical inference-based procedure to incrementally build FRBS or the linguistic interpretation of STAR models. Finally an econometric example is given to illustrate the core idea.