Partial Linear MIDAS Model

Consider the Linear Regression Model y=X?+?,where dependent variable and independent variable occur in the same frequency.But we often encounter the dependent variable as a low-frequency variable and the independent variable as a high-frequency variable in economics.In this case,an Mixed Data Sampling(MIDAS)model was proposed that allows the dependent variable and independent variable to be variables of different frequencies.Based on the actual high frequency data,MIDAS model takes into account the order of the variable and the weight function to obtain the parameter estimation of the model.In this paper,the MIDAS model was further extended,and a partial linear MIDAS model where independent variable X and dependent variable Y are related to covariate variable was proposed as follows y=X?+f(T)+?.First,the kernel estimators (?)_Y(T) of dependent variable's conditional expecation (?)_Y(T) and (?)_X(T) of independent variable's conditional expecation (?)_X(T) were obtained by using Nadaraya-Watson estimation method.The smoothing spline and Kalman filter method were used to punish the objective function to obtain the estimation of .Then the consistency and asymptotic normality of estimation were proved.Finally,the numerical simulation for different weight function was carried out.