Lag Selection in Stochastic Additive Models

• Activity Number: 28
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shuping Jiang*+
• Keywords: Additive model ; group selection ; selection consistency ; nonlinear time series model ; polynomial spline ; SCAD

Abstract

We consider stochastic additive models (SAM) for nonlinear time series data. We propose a penalized polynomial spline method for estimation and lag selection in SAM. It approximates the nonparametric functions by polynomial splines and performs variable/lag selection by imposing a penalty on the empirical L2 norm of the spline functions. Under geometrically $\alpha$-mixing, we establish that the resulting estimator enjoys the optimal rate of convergence for estimating the nonparametric functions. It also selects the correct model with probability approaching to one as the sample size increases. A coordinate-wise algorithm is developed for finding the solution for the penalized polynomial spline problem. Extensive Monte Carlo studies have been conducted and show the proposed procedure works effectively even with moderate sample size. We also illustrate the proposed method by analyzing the US employment time series.