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In the presented paper, we introduce a partial functional linear model, where a scalar response variable is explained by a multivariate random variable and a functional random variable, and the relationship between the scalar response and both of the predictors is linear. Besides, the model has autoregressive errors. To estimate the model, we first expand the functional predictor and functional regression parametric on the functional principal component basis, and then estimate the coefficients for multivariate and functional regression parametric by a generalized least squares method. Theoretical properties are presented including the asymptotical normality for the multivariate coefficient and the optimal convergence rate for the functional regression parametric. Simulation studies are used to illustrate these characteristics. The proposed method is also applied on the power forecasting of photovoltaic systems data set.

Partial functional linear regression with autoregressive errors