Application of seasonal Autoregressive integrated moving Average (sarima) to model and Forecast water demand in Kisumu City, Kenya

Abstract

ABSTRACT Increased population of Kisumu City over the past years has resulted into high demand and competition for water and related facilities. This is evident in the persistent water scarcity within the City, use of poor quality water by the residents and inequitable water distribution. The current net water supply capacity of Kisumu City Water Supply System is 5,400m3/day against a demand of 27,000 m3/day. Effective planning and management of the City's water resources is therefore critical in providing reliable forecasts. Models developed for such forecasts ought to take into account the non stationary and seasonality behaviours exhibited by residential water demand data. Research on residential water demand in the Kenyan context have used Ordinary Least Squares, a methodology that does not model the seasonality aspect. In the SARIMA(p,d,q)(P,D,Qh2 which is expressed as ¢p(B)ifJp(Bs)"\ld\ll§xt = eq(B)8Q(BS)et, BS allows for the modelling of the seasonal behaviour in the data. However, the application of SARIMA to model and forecast residential water consumption in the Kenyan Context is scanty. The study therefore sought to propose a SARIMA model for forecasting residential water demand using secondary monthly water consumption data obtained from KIWASCO for the years 2004 to 2013. Preliminary investigation of the data showed that the data followed a 3- parameter log-normal distribution. Therefore, using logarithm values of the data, the study established by both OLS and Kendall's tau test that the residential water demand for Kisumu City had a significant increasing trend. The KPSS and ADF tests revealed that the data had unit roots which were however removed by first difference. The Data was then fitted to a SARIMA model and the parameters of the model were estimated using Maximum Likelihood Method. SARIMA(l, 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 OLS model, SARIMA(l, 1, 1)(0, 1, 1h2 had the least MAPE and RMSE values of 3.59 and 7476.59 respectively implying that it had higher forecasting performance. One year forecasts for 2014 were established together with their CI. The observed values for January and February 2014 were within the Confidence Limits. The study recommends the integration of the model by KIWASCO and other water companies in their design of water demand management policies.