We present a new technique to study the seasonal cycle of climatic trends in the expected value, variance, and other moments of the statistical distribution. The basis of the technique is multiple linear regression, but with periodic basis functions. The technique allows us to provide comprehensive information on statistical parameters of climate for every day of an observational period. Using daily data, the technique has no problems caused by different lengths of months or the leap-year cycle. Without needing to assume the stationarity of contemporary climate, the technique allows the study of statistical parameters of climatic records of arbitrary length. We illustrate the technique with applications to trends in the satellite observed variations of sea ice extent in the Northern and Southern Hemispheres. We show that a significant part of the variability in hemispheric sea ice extents for the period 1978--1999 is related to linear trends.