PARTIALLY LINEAR MODELS WITH UNIT ROOTS
研究了非平稳部分线性回归模型的渐近性质，允许协变量以非参数方式进入单位根模型，证明了自回归参数可以以N速率估计，并基于半参数估计进行了单位根检验。
This paper studies the asymptotic properties of a nonstationary partially linear regression model. In particular, we allow for covariates to enter the unit root (or near unit root) model in a nonparametric fashion, so that our model is an extension of the semiparametric model analyzed in Robinson (1988, Econometrica 56, 931–954). It is proved that the autoregressive parameter can be estimated at rate N even though part of the model is estimated nonparametrically. Unit root tests based on the semiparametric estimate of the autoregressive parameter have a limiting distribution that is a mixture of a standard normal and the Dickey–Fuller distribution. A Monte Carlo experiment is conducted to evaluate the performance of the tests for various linear and nonlinear specifications.We thank Bruce Hansen, Roger Koenker, Helmut Lütkepohl, Peter Phillips, three referees, and participants of the 8th World Congress of the Econometric Society and the 10th Midwest Econometrics Group Meeting for helpful comments on an earlier version of this paper. This investigation was supported by the University of Kansas General Research Fund allocation 2301789-003.