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Time-varying multi-regime models fitting by genetic algorithms


Correspondence to: Francesco Battaglia, Dipartimento di Statistica Probabilita e Statistiche Applicate, Universita La Sapienza, Piazzale Aldo Moro, 5, 00100 Rome, Italy.


Many time series exhibit both nonlinearity and non-stationarity. Though both features have been often taken into account separately, few attempts have been proposed for modelling them simultaneously. We consider threshold models, and present a general model allowing for different regimes both in time and in levels, where regime transitions may happen according to self-exciting, or smoothly varying or piecewise linear threshold modelling. Since fitting such a model involves the choice of a large number of structural parameters, we propose a procedure based on genetic algorithms, evaluating models by means of a generalized identification criterion. The performance of the proposed procedure is illustrated with a simulation study and applications to some real data.