A time-series autoregressive-moving average model is fit to Umkehr data from Arosa for the time period March 1961 through December 1977. The ozone data in Umkehr levels 7, 8, and 9 and examined for trend commencing in January 1970. The summed data in levels 7, 8, and 9 are also examined. No significant trend is found at the 5% significance level. Models are then refit for the entire sample period, and detection thresholds are estimated for time periods after December 1977. The change in O3 due to trend over the next 10 years would need to be as large as 3.5, 10.4, and 23.3% in levels 7, 8, and 9, respectively, for tests based on these models to conclude there was a significant nonzero trend in the future. The trend in the summed data would need to be 5.3%. Thus we find that the data in Umkehr level 7 provide the smallest detection threshold for future detection of trend in upper level O3. The detection thresholds found here are compared to detectability limits from total O3 data.