Estimation of structural changes in nonlinear time series models by using particle filters and genetic programming

AbstractSeveral works have demonstrated detection of changes of state equations called structural changes based on statistical measures but have given no suggestions regarding the functional forms of the state equations after changes. This paper deals with the estimation of structural changes in nonlinear time series models by using particle filters, genetic programming GP, and its applications. We consider the problems of state estimation from the observed time series that are generated based on nonlinear state equations. It is assumed that structural changes can be detected by some measure of likelihood and that the state equation after changes is modified from its current functional form. Individuals corresponding to functional forms in the GP pool are generated at random, and we apply the crossover operation between the current functional form and the individuals by giving possible multiple functional forms. Then, we have the optimal functional form among the possible functional forms generated by GP from the current form. As an application, we show the estimation of structural change for an artificially generated time series and also discuss the estimation of functional forms for a real economic time series before and after structural changes. Copyright © 2015 John Wiley & Sons, Ltd.