Time series of daily administrative cardio-respiratory health and environmental information have been extensively used to assess the potential public health impact of ambient air pollution. Both series are subject to strong but unrelated temporal cycles. These cycles must be removed from the time series prior to examining the role air pollution plays in exacerbating cardio-respiratory disease. In this paper, we examine a number of methods of temporal filtering that have been proposed to eliminate such temporal effects. The techniques are illustrated by linking the number of daily admissions to hospital for respiratory diseases in Toronto, Canada for the 11 year period 1981 to 1991 with daily concentrations of ambient ozone. The ozone-hospitalization relationship was found to be highly sensitive to the length of temporal cycle removed from the admission time series, and to day of the week effects, ranging from a relative risk of 0.874 if long wave cycles were not removed at all to 1.020 for models which removed at least cycles greater than or equal to one month based on the interquartile pollutant range. The specific statistical method of adjustment was not a critical factor. The association was not as sensitive to removal of cycles less than one month, except that negative autocorrelation increased for series in which cycles of one week or less were removed. We recommend three criteria in selecting the degree of smoothing in the outcome: removal of temporal cycles, minimizing autocorrelation and optimizing goodness of fit. The association between ambient ozone levels and hospital admissions for respiratory diseases was also sensitive to the season of examination, with weaker associations observed outside the summer months.