Empirical Likelihood Confidence Intervals for Nonlinear Nonstationary Model

• Activity Number: 32
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Ryota Yabe*+
• Companies: Hitotsubashi University
• Keywords: Empirical likelihood ; Time Series ; Nonparametric ; Unit root ; Kernel Estimator

Abstract

We construct the empirical likelihood (EL) based confidence interval for a nonparametric nonstationary nonlinear regression model.

Much attention has been paid to the case where the observed process is assumed to be stationary. However, the stationary assumption seems very restrictive to analyze economic and financial data. The nonparametric nonlinear nonstationary model recently receives so much attention. For example, Wang and Phillips (2009, 2011) have developed the asymptotic theory of the local constant and linear estimators and constructed the confidence interval of the regression function based on the asymptotic distributions of the estimators. The confidence interval based on the asymptotic distribution of the estimators is always symmetry around the estimates. This limitation is crucial if the distribution of the error term is asymmetric.

Since the EL based confidence interval is data-dependent and flexible, this procedure can avoid the symmetric restriction. We show that the Wilks theorem holds even if the covariate process is nonstationary. The asymptotic distribution is same as that of the case where the covariate process is stationary.