Varying coefficient model has been popular in the literature. In this paper, we propose a profile least squares estimation procedure to its regression coefficients when its random error is an auto-regressive (AR) process. We further study the asymptotic properties of the proposed procedure, and establish the asymptotic normality for the resulting estimate. We show that the resulting estimate for the regression coefficients has the same asymptotic bias and variance as the local linear estimate for varying coefficient models with independent and identically distributed observations. We apply the SCAD variable selection procedure (Fan and Li, 2001) to reduce model complexity of the AR error process. Numerical comparison and finite sample performance of the resulting estimate are examined by Monte Carlo studies. Our simulation results demonstrate the proposed procedure is much more efficient than the one ignoring the error correlation. The proposed methodology is illustrated by a real data example.

中文翻译：

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具有自相关误差过程的数据的变系数模型

变系数模型在文献中很流行。在本文中，当其随机误差是自回归 (AR) 过程时，我们对其回归系数提出了轮廓最小二乘估计程序。我们进一步研究了所提出程序的渐近特性，并为结果估计建立渐近正态性。我们表明，回归系数的结果估计与具有独立和同分布观测值的变系数模型的局部线性估计具有相同的渐近偏差和方差。我们应用 SCAD 变量选择程序（Fan 和 Li，2001）来降低 AR 错误过程的模型复杂性。蒙特卡罗研究检查了所得估计值的数值比较和有限样本性能。我们的模拟结果表明，所提出的程序比忽略错误相关性的程序更有效。所提出的方法由一个真实的数据示例说明。