In the present explorative study, different time-series analysis methods, such as moving average, deterministic methods (linear trend with seasonality), and non-parametric Mann–Kendall trend test, were applied to monthly precipitation data from January 1871 to December 2014, with the aim of comparing the results of these methods and detecting the signs of climate change. The data set was provided by the University of Pannonia, and it contains monthly precipitation data of 144 years of measurements (1,728 data points) from the Keszthely Meteorological Station. This data set is special because few stations in Hungary can provide such long and continuous measurements with detailed historical background. The results of the research can provide insight into the signs of climate change in the past for the region of West Balaton. Parametric methods (linear trend and t-test for slope) for analyzing time series are the simplest ones to obtain insight into the changes in a variable over time. These methods have a requirement for normal distribution of the residuals that can be a limitation for their application. Non-parametric methods are distribution-free and investigators can get a more sophisticated view of the variable tendencies in time series.