A frequency domain statistical model for the Dobson total column ozone data is introduced. This model extends variance-components analysis to the time series case and incorporates both temporal and spatial association found in the ozone data. A key feature of this model is the inclusion of a common global term representing natural global variations in ozone. The model is used to estimate global trends in ozone possibly related to the release of man-made chlorofluorocarbons and other factors. We assess the ability of models to detect trends, given the current ozone data base.