Estimating and forecasting partially linear models with non stationary   exogeneous variables
  This paper presents a backfitting-type method for estimating and forecasting a periodically correlated partially linear model with exogeneous variables and heteroskedastic input noise. A rate of convergence of the estimator is given. The results are valid even if the period is unknown. 
Xavier Brossat and Georges Oppenheim and Marie-Claude Viano
math.ST stat.TH