Climatic variability can be characterized by invariant quantities arising from the analysis of scaling properties of paleoclimatic records. In this paper we discuss a stochastic model that reproduces the variability and the long-range correlation observed in dendrochronological time series. We have found that non-Gaussian distributions are better suited to describe the climatic variability embedded in these data. Our results indicate that Gaussian distribution fails to capture the large fluctuation -extreme events- that characterized climatic variability in these time series. This might have applications on the study of extreme weather events on future climate scenarios.