School of Mathematics and Statistics Science, Ludong University; School of Information and Electrical Engineering, Ludong University

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
-mixing conditions. Both the real data and simulated examples are provided for
illustration.