中文摘要：

在某些场合，回归模型中的预测变量与响应变量不能被直接观测，而是受到某个可观测变量的影响，在这种情况下人们提出了协变量调整模型．本文在时间序列场合下讨论协变量调整非参数回归模型（CANR），提出了回归函数的两步估计法，在α-混合条件下讨论了估计的大样本性质，最后研究了模型在模拟和实际金融数据中的应用．

英文摘要：

The covariate-adjusted regression model was initially proposed for the situations where both the predictors and the response variables are not directly observed, but are distorted by some common observable covariates. In this paper, we investigate a covariate-adjusted nonparametric regression （CANR） model and consider the proposed model on time series setting. We develop a two-step estimation procedure to estimate the regression function. The asymptotic property of the proposed estimation is investigated under the α-mixing conditions. Both the real data and simulated examples are provided for illustration.