Stochastic modelling of great letaba river flow process

Abstract

A stochastic approach is presented in view that a time series modelling is achieved through an Autoregressive Moving Average (ARMA) model. The applicability of the ARMA model is then further presented using the Great Letaba River as a case study. River flow discharge for 25 years (1989-2014) for the Great Letaba River was obtained from the Department of Water and Sanitation, South Africa and analysed by Autoregressive (AR), Autoregressive Moving Average (ARMA) and Autoregressive Integrated Moving Average (ARIMA) models. Monte Carlo simulation approach was used to generate forecasts of the ARIMA error model for the next 25 years. Initial model identification was done using the Autocorrelation function (ACF) and Partial Autocorrelation function (PACF). The model analysis and evaluations provided proper predictions of the river system. The models revealed some degree of correlation and seasonality behaviour with decreasing river flow. Hence, in conclusion, the Great Letaba River flow has shown a decreasing trend and therefore, should be effectively used for sustainable future development.