Abstract
This study examines two long-term time series of nitrate-nitrogen concentrations from the River Ouse and Stour situated in the Eastern England. The time series of monthly averages were decomposed into trend, seasonal and cyclical components and residuals to create a simple additive model. Residuals were then modelled by linear time series models represented by models of the ARMA (autoregressive moving average) class and nonlinear time series models with multiple regimes represented by SETAR (self-exciting threshold autoregressive) and MSW (Markov switching) models. The analysis showed that, based on the minimal value of residual sum of squares (RSS) of one-step ahead forecast in both datasets, SETAR and MSW models described the time series better than models ARMA. However, the relative improvement of SETAR models against ARMA models was low ranging between 1% and 4% with the exception of the three-regime model for the River Stour where the improvement was 48.9%. In comparison, the relative improvement of MSW models was between 44.6% and 52.5 for two-regime and from 60.4% to 75% for three-regime models. However, the visual assessment of models plotted against original datasets showed that despite a high value of RSS, some ARMA models could describe the analyzed time series better than AR (autoregressive), MA (moving average) and SETAR models with lower values of RSS. In both datasets MSW models provided a very good visual fit describing most of the extreme values. The results of this work could be used as a base for construction of other time series models used to describe or predict nitrate-nitrogen concentrations.