Time-varying multi-regime models fitting by genetic algorithms

Abstract

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

Finding Starting-Values for the Estimation of Vector STAR Models

“…The central idea of the local search methods is to allow temporary uphill or downhill moves, i.e., a (controlled) impairment of the objective function value. 6 This is done in order to escape local optima. The algorithms 5 In principle, the grid search and heuristics are equally efficient regarding their computational load.…”

“…Recent contributions emphasize the benefit of employing alternative optimization approaches in non-linear models. These include heuristic methods, see for instance Baragona et al [5], Battaglia and Protopapas [6], Chan and McAleer [7], El-Shagi [8], Maringer and Meyer [9], Wu and Chang [10], Yang et al [11], and Baragona and Cucina [12]. The studies concentrate on parameter estimation in univariate or multivariate regime-switching models.…”

Self Adaptive Genetic Algorithms for Automated Linear Modelling of Time Series

“…Nowadays the construction of model for TS is an area of great development as evidenced by the articles of the Journal of Time Series Analysis (http://www.wiley.com/bw/journal.asp?ref=0143-9782&site=1) in addition to the papers presented in international competitions on time series modelling such as NN3. Nevertheless the existence of GA papers in which are used the TS (Alberto et all, 2010;Battaglia & Protopapas, 2011;Chiogna & Gaetan & Masarotto, 2008;Hansen et all, 1999;Mateo & Sovilj & Gadea, 2010;Szpiro, 1997;Yadavalli et all, 1999), it is important to note that it was not found any reference to the use of SAGA for this purpose.…”

Discussion of “Threshold models in time series analysis — 30 years on” by H. Tong

“…A model of such kind, based on a smooth threshold autoregressive form, was studied by [3] and an extension, allowing also for piecewise linear threshold form (where the autoregressive parameters inside each regime are not constant, but linearly dependent on the threshold variable) was recently presented in [2].…”