Statistical time series modeling was applied to the monthly average total ozone data taken at Arosa, Switzerland over the period 1932--74. The analysis led to a model that provided a significantly good representation of the Arosa data, and indicated that a much discussed decline in ozone for the first half of the 1970's is a predictable phenomenon from historical patterns in the Arosa data prior to 1970. If historical patterns persist, such as a clearly identified 133 month cycle, a return or upward trend could be expected in the late 1970's. No significant phase lag relationship could be detected between solar sunspot data and the Arosa data, nor did the sunspot periodicity seem to explain the 133 month cycle. The modeling approach is proposed as a tool for atmospheric scientists when evaluating the significance of future trends in ozone from one or a multiple of ozone recording centers around the world.