Fitting piecewise linear threshold autoregressive models by means of genetic algorithms

A GRASP method for building classification trees

“…There are several works and applications in the last years. For example: in variable selection for classification (Garcia et al 2005;Pacheco et al, 2006), in clustering (Belacel N, Hansen P and Mladenović, 2003;Pacheco and Valencia, 2003;Pacheco, 2005;Woodruff and Reiners, 2004), in Principal Components, (Cadima, Cerdeira and Minhoto, 2004), Regression and Prediction models Kontoghiorghes, 2003, 2005;Hofmann, Gatu and Kontoghiorghes, 2007;Baragona, Battaglia and Cucina, 2004;Kapetanios, 2007), etc.…”

Multi–regime models for nonlinear nonstationary time series

“…The SETAR model may be interpreted as a special case of the STAR model, when γ L tends to infinity. A different proposal, where the autoregressive coefficients change linearly and continuously with the driving variable X t−d , but with different slope in each regime, is the piecewise linear threshold model (Baragona et al 2004), described by…”

“…Lundberg et al (2003) proposed a model based on a first order autoregressive structure with the parameter changing both according to time and to a driving variable alternating between two regimes only, with smooth change (in the same way as smooth transition autoregressive models of Teräsvirta (1994)). Battaglia and Protopapas (2011) extended this framework to allow also change of the autoregressive parameters in a piecewise linear fashion (piecewise linear threshold multi-regime model, Baragona et al 2004) and proposed a genetic algorithm for building such a model, but also limited to two regimes.…”

An analysis of global warming in the Alpine region based on nonlinear nonstationary time series models

“…Lundbergh et al (2003) proposed a model based on a first order autoregressive structure with the parameter changing both according to time and to a driving variable alternating between two regimes only, with smooth change (in the same way as smooth transition autoregressive models (STARs) of Teräsvirta 1994). Battaglia and Protopapas (2011) extended this framework to allow also change of the autoregressive parameters in a piecewise linear fashion (piecewise linear threshold multi-regime model, Baragona et al 2004) and proposed a genetic algorithm for building such a model, but also limited to two regimes. Finally, Battaglia and Protopapas (2012) completed this procedure to allow for more than two regimes.…”