LIKELIHOOD-BASED INFERENCE IN TRENDING TIME SERIES WITH A ROOT NEAR UNITY
研究了带确定性趋势的自回归时间序列模型中，基于似然的联合估计和检验方法，给出了M估计量的渐近分布，并通过蒙特卡洛实验考察了有限样本表现。
This paper studies likelihood-based estimation and tests for autoregressive time series models with deterministic trends and general disturbance distributions. In particular, a joint estimation of the trend coefficients and the autoregressive parameter is considered. Asymptotic analysis on the M -estimators is provided. It is shown that the limiting distributions of these estimators involve nonlinear equation systems of Brownian motions even for the simple case of least squares regression. Unit root tests based on M -estimation are also considered, and extensions of the Neyman–Pearson test are studied. The finite sample performance of these estimators and testing procedures is examined by Monte Carlo experiments.