This paper presents statistical methods for the evaluation and future prediction of the filtration stability of the Liptovska Mara dam in Slovakia. Three statistical methods are tested: a linear regression model, the linear stochastic model ARMA_22, and the non-linear stochastic STAR model. The aim is to assess the level of agreement between predicted and measured levels of water seepage. According to the results there was excellent agreement between the predicted and measured values at the Liptovska Mara dam using the ARMA_22 model. The linear model had the lowest ability to predict the water level in the observation well of the water reservoir when compared to the STAR and ARMA_22 models. The significance of this paper is the ability to predict the water level in observation wells at dam sites and total filtration stability of the dams by using real measures in time series. This is a desirable step to ensure adequate safety with the possibility to solve potential defects earlier.