Lag selection in stochastic additive models

Abstract

We studied stochastic additive models (SAM) for nonlinear time series data. We proposed a penalised polynomial spline (PPS) method for estimation and lag selection in SAM. This method approximated the nonparametric functions by polynomial splines and performed variable/lag selection by imposing a penalty on the empirical L ₂ norm of the spline functions. Under geometrically α-mixing condition, we established that the resulting estimator converges at the same rate as in univariate smoothing. Our method also selected the correct model with probability approaching to one as the sample size increased. A coordinate-wise algorithm was developed for finding the solution of the PPS problem. Extensive Monte Carlo studies had been conducted and showed that the proposed procedure worked effectively even with moderate sample size. We also illustrated the proposed method by analysing the US employment time series.

Keywords:

• additive model
• model selection
• nonlinear time series model
• polynomial spline
• selection consistency

Acknowledgements

This work is supported in part by National Science Foundation grants.