Threshold autoregressive model blind identification based on array clustering

In this paper, we propose a new algorithm to estimate all the parameters of a Self Exited Threshold AutoRegressive (SETAR) model from an observed time series. The aim of this algorithm is to relax all the hypotheses concerning the SETAR model for instance, the knowledge (or assumption) of the number of regimes, the switching variables, as well as of the switching function. For this, we reverse the usual framework of SETAR model identification of the previous papers, by first identifying the AR models using array clustering (instead of the switching variables and function) and second the switching conditions (instead of the AR models). The proposed algorithm is a pipeline of well-known algorithms in image/data processing allowing us to deal with the statistical non-stationarity of the observed time series. We pay a special attention on the results of each step over the possible discrepancies over the following step. Since we do not assume any SETAR model property, asymptotical properties of the identification results are difficult to derive. Thus, we validate our approach on several experiment sets. In order to assess the performance of our algorithm, we introduce global metrics and ancillary metrics to validate each step of the proposed algorithm.