This study is to develop a method of time series analysis that could determine whether the recent occurrences of extreme rainfalls in Taiwan are part of a long-term shift in precipitation patterns due to climate change, or random events without long-term implications. In this study, Fuzzy C-Means (FCM) method is applied to the analysis of climatic time series data. The concept of fuzzy membership allowed one to break up the time series into distinguishable data clusters. The degree of data clustering was quantified using three clustering indices, which were obtained through regression equations from the number of time series data and the coefficient of variation. High degree of data clustering would signify a temporal shift in time series induced by climate change. A null hypothesis framework for validating a temporal shift in time series was constructed, and a threshold value for the clustering indices were determined for the hypothesis validation. Comparing three clustering indices used, the FCM method perform best in identifying temporal shifts when the validity partition entropy (VPE) index was used. Also, when time series data was divided into two parts, a greater accuracy in identifying the years of climate change was achieved if the two parts were of more or less equal time spans. The accuracy of the identification could increase with the time span of the data series, yet a large difference between the time spans of the two component data series could lead to greater errors in the identification. In conclusion, based on the results of applicability testing against simulation and real precipitation data, the method proposed in this study can provide a basis for the identification of climate change in time series data. Hopefully, future research and application could be built on the results of this study.