Abstract
Statistical analysis of relationships between time series of data exhibiting seasonal variation is often of great interest in environmental monitoring and assessment. The present study focused on regression models with time‐varying intercept and slope parameters. In particular, we derived and tested semiparametric models in which rapid interannual and interseasonal variation in the intercept were penalized in the search for a model that combined a good fit to data with smoothly varying parameters. Furthermore, we developed a software package for efficient estimation of the parameters of such models. Test runs on time series of runoff data and riverine loads of nutrients and chloride in the Rhine River showed that the proposed smoothing methods were particularly useful for analysis of time‐varying linear relationships between time series of data with both seasonal variation and temporal trends. The predictivity of the semiparametric models was superior to that of conventional parametric models. In addition, normalization of observed annual loads to mean or minimum runoff produced smooth curves that provided convincing evidence of human impact on water quality. Copyright © 2001 John Wiley & Sons, Ltd.