This paper discusses a methodology which uses time series cross sectional datafor the estimation of a time dependent regression function depending on explanatory variables and for the prediction of values of the dependent variable. The methodology assumes independent observations and is based on an adaptive semiparametric regression estimate depending on the observations from an adaptive running time window. The adaptation consists in the selection of the length (or horizon) of such a window together with one of numerous alternative parametric, nonparametric, additive and semiparametric estimators by minimization of a cross-validation criterion. In the prediction case the window contains only actual and past observations. It is shown, how to asses the influence of explanatory variables by generalized coefficients of determination which are adapted to the special objective of the statistical analysis. This aspect and our regression methodology is illustrated in the case of an analysis of stock market returns. An extended semiparametric methodology is also presented which allows the estimation of additive individual effects and which may essentially improve a traditional panel data analysis.