Trends and periodic movements in climatic series are treated as non-stationary components. A time series model and Bayesian statistics are combined through a Markov chain Monte Carlo procedure. Gibbs sampling is used in the Monte Carlo application. Monthly series of river flow, rainfall and temperature from northern Italy are used. Some late temperature rises are noted, otherwise there are no systematic increases or decreases in the series. Changes in periodicity are also of a random nature. From the results it is also possible to compare these properties between different locations and climatic indicators.