It is well known that GM estimators for linear models are consistent and lead to a small loss of efficiency with respect to LS estimator. When they are extended to threshold models, which are
piecewise linear models, the consistency of GM estimators is guaranteed only under certain choices of the objective function.
The loss of consistency of GM-SETAR (Self-Exciting Threshold AutoRegressive) estimator is explored in a simulation experiment under different objective functions, time series length, parameters combinations and type of contaminations. Finally the best robust estimator is applied to study the dynamic of electricity prices where regime switching and high spikes are widely observed features.
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