Multiple-regime Self-excited Vector Threshold Autoregressive Models with Multivariate Threshold Variables
Yuan Gan, The Chinese University of Hong Kong, Hong Kong
This talk proposes a multivariate extension of the well-known threshold autoregressive (TAR) model in nonlinear time series literature. We consider k dimensional multiple-regime self-excited vector threshold autoregressive models with multivariate threshold variables, where the regime switches are governed by the lag d series. Specifically, the regimes are the subsets partitioned by unknown threshold hyperplanes in the k dimensional space, and the time series follows different models when the lag d series falls into different partitioning subsets. One challenge in estimating such models arises from the great complexity of regimes under high dimensional settings. We formulate the task of model estimation into a minimization problem based on minimum description length (MDL) principle and develop a genetic algorithm that can estimate the number of threshold hyperplanes, the parametric equations of threshold hyperplanes and vector autoregressive (VAR) model parameters in each regime simultaneously. The consistency of such estimators is established theoretically with an illustration by numerical simulations.