This graduate thesis presents basic terms, properties and results of time series analysis. Models of stationarity and non-stationarity univariate time series are described – moving average processes (MA), autoregressive processes (AR), autoregressive (integrated) moving average processes (ARMA and ARIMA) and seasonal autoregressive (integrated) moving average processes (SARMA and SARIMA). Some examples of these processes are also shown. Out of many multivariate time series models, the vector autoregressive process (VAR) is described. Methods of parameter estimation and order determination are shown and Granger causality is analysed. The diagnostic of models based on the residual analysis and the prediction by the chosen model are also described. Based on the data of pollen concentration in Sombor and the meteorological data from the measuring station Rimski Sanˇcevi, a vector autoregressive model is made with the ˇ aim of predicting the maximum daily pollen concentration. For the needs of the model, the choosen variables are also air humidity and average daily temperature and the order of the model is 16, meaning that for the prediction of the maximum pollen concentration of a single day, we use the values od pollen concentration, air humidity and average temperature od the previous 16 days. The obtained values are divided into the following categories - low, moderate, high and very high concentrations. Since the assumptions on model residuals are not satisfied, the model can not be used for the purpose of interpretation, but for prediction purposes it would be accurate for 92.49 % of observed days. Possible correction of the used model is also mentioned.