A Genetic Algorithm Approach to Time Series Models with Thresholds in Two Domains

A new threshold time series model is proposed, whose submodels are extended from AR to SARIMA and whose domains having thresholds are extended to two. By these two extensions, the newly proposed models would offer more flexibility to piecewisely approximate nonstationary time series by a finite number of local stationary models. Genetic algorithm is applied to simultaneously search for appropriate model structures, estimate the optimal model coefficients, as well as to partition space by finding appropriate thresholds. The resulting model is applied to a synthetic multi-frequency sine wave and two financial time series with improved modeling quality. The proposed model is also applied for seismogram analysis to recognize earthquake wave pattern in order to locate arrival time of different waves.