A new technique has been developed to study seasonal and diurnal cycles in climatic trends in the mathematical expectation, variance, and other moments of the statistical distribution of climatic variables. The basis of the technique is regression, but with periodical coefficients. The technique is illustrated with applications to trends in satellite observed variations of sea ice extent in the Northern and Southern Hemispheres, and to the seasonal and diurnal variations in observed surface air temperature at a few selected stations. This technique provides users of climatic data with better and more relevant information about climate and its variability, and has many other useful applications.