Cointegration VAR and VECM and ARIMAX Econometric Approaches for Water Quality Variates

We use vector autoregressive, cointegration, error correction models for water quality to establish relationships between dissolved oxygen (DO), biological oxygen demand (BOD) turbidity and pH, taking into account interdependence between them. Since environmental literature did not use these models, this study fills this gap. Johansen’s method which is based on eigenvalues and eigenvectors because of the matrix representation of the coefficients due to multiple equations is used for estimating functional relationship vectors. Interestingly, it makes no distinction between exogenous and endogenous variables. Johansen’s approach indicates two plausible DO and BOD functions or relationship vectors. These models provide estimates of the errors if the variable deviates from the long run path. In the differenced DO equation, coefficients of differenced DOt-1, temperature, time and error correction are significant, whereas coefficient of differenced BODt-1 is insignificant. However, in differenced BOD and turbidity equations coefficients are insignificant. The error correction model also provides a reasonable explanation of the functional relationship of DO. Alternatively, we also use the ARIMAX model for explaining the dynamic behavior of these variables to contrast with the error correction version of the model. ARIMAX presented functional relationships for BOD and turbidity, although none was found with error correction model.