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. (C) 2007 Elsevier B.V. All rights reserved.