Estimation of Sparse Single Index Vector Autoregression Models

Stimulated by the analysis of a data set about house price variance in the USA, we propose a sparse single-index vector autoregressive model (SSIVARM). In order to solve the model, we develop an iterative algorithm based on least squares es- timation procedure (PLSEP) to simultaneously identify the zero components and estimate the non-zero unknown parame- ters and unknown functions in the model. Not only providing concrete methodology for the implementation of the proposed algorithm, we also conduct intensive simulation studies to investigate the performance of the proposed PLSEP and the iterative algorithm when the sample size is finite. Finally, we apply the proposed SSIVARM together with the proposed PLSEP and iterative algorithm to the data set mentioned above. Our results reveal some interesting connections be- tween some variables and the house price. Although the pro- posed SSIVARM is stimulated by a data set about house price, our findings suggest it can be applied to any multivariate time series.