Application of Seasonal Autoregressive Integrated Moving Average (SARIMA) to Model and Forecast Water Demand in Kisumu City, Kenya

Abstract

The study sought to develop a SARIMA(p; d; q)(P;D;Q)12 model for forecasting residential water demand based on the Box-Jenkins methodology. The modelling technique considers the seasonal behaviour present in residential water demand data. Monthly water consumption data obtained from Kisumu Water and Sewerage Company (KIWASCO) for the years 2004 to 2013 was used to estimate the model parameters. The data followed
a 3-parameter log-normal distribution hence logarithm transformed data were used in the modelling process. The KPSS and ADF tests revealed that the data had unit roots at both seasonal and non-seasonal levels which were removed by first difference. The Data were fitted to a Seasonal ARIMA model and the parameters of the model were estimated using Maximum Likelihood Method. SARIMA(1; 1; 1)(0; 1; 1)12 had the least BIC and AIC values of 2205.273 and 2197.282 respectively and was identified as the better fitting model. Compared to the Ordinary Least Square model, the model had the least MAPE and RMSE values of 3.59 and 7476.59 respectively hence a higher forecasting performance. One year forecasts for 2014 showed that the observed values for January and February 2014 were well within the Confidence Limits. The study recommends the integration of the model by water companies in their design of water demand management policies.