We investigate the theoretical properties of the Generalized Likelihood Ratio (GLR) test (Fan, Zhang and Zhang (2000)) for the time varying coefficient models when the regressors and error are (possibly) nonstationary time series. It is found that, in general, the Wilks phenomenon does not hold under either non-stationarity or temporal dependence. An alternative bootstrap method is proposed for the inference.

Keywords: Nonstationary time series; Generalized likelihood ratio test; time varying coefficient models

Biography: Dr. Zhou received his Ph.D. in Statitics from University of Chicago in 2009. His major research interests are non-stationary and nonlinear time series analysis and non- and semi- parametric methods.