Yong ZHANG;Xiaoyun YANG;Zhishan DONG;Dehui WANG
This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let $\{X_t\}$ be a linear process defined by $X_t=\sum_{k=0}^{\infty}\psi_k\varepsilon_{t-k}$, where
$\{\psi_k,k\geq 0\}$ is a sequence of real numbers and $\{\varepsilon_k,~ k=0,\pm1,\pm2,\cdots\}$ is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that $\{\varepsilon_k, k\geq 1\}$ is a sequence of asymptotically linear negative quadrant dependent (ALNQD) random variables, the authors find the limiting distributions of the least
squares estimator and the associated regression $t$ statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d. innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive
parameter $\alpha$ when $\{\varepsilon_k, k\geq 1\}$ is a sequence of negatively associated (NA) random variables, and $\psi_0=1, \psi_k=0,$~$k\geq 1$.
