Series Estimator for Dependent Processes

• Activity Number: 623
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yinxiao Huang*+ and Wei Wu
• Companies: The University of Chicago and The University of Chicago
• Keywords: series estimator ; dependent processes ; long memory ; gaussian processes ; series estimator ; dependent processes ; long memory ; gaussian processes

Abstract

Series estimators are least-squares fits of a regression function where the number of regressors $K$ depends on sample size $n$. Newey(1997), de Jong (2002) obtained uniform convergence rate and asymptotic normality under certain conditions for iid data. However, limiting behavior of series estimator for dependent processes has not been touched yet. We considers series estimator for nonparametric regression estimation problems for a wide class of nonlinear time series models under the short-range-dependent assumption. Asymptotic normality and uniform convergence rates of series estimators are established under mild regularity conditions. Further more, we study the series estimator for long memory processes and, as a starting point, consider Gaussian subordinates where properties of the Hermite polynomials could be utilized.