Transfer Function Models for Forecasting Domestic Water Use

Abstract

The ability of transfer function models to forecast domestic water use is investigated. Five years monthly time series data on domestic water use, total rainfall and average temperature from Muscat was taken for this study. The transfer function models aim to describe the relationship between input and output systems using a ratio of the polynomials representing the Laplace Transforms of the output, input and the noise in the system. Total rainfall and average temperature were considered as the input series and the domestic water use as an out series. The input series were pre-whiten using Seasonal Autoregressive Integrated Moving Average (SARIMA) models which were identified by Sample Autocorrelation (SAC) and Partial Sample Autocorrelation (PSAC). Four preliminary transfer function models were postulated to describe the output series. The graphs of Sample Cross Correlation (SCC) of water use with rainfall and temperature were made. The final transfer function model was identified by investigating the Residual Sample Cross Correlation (RSSC) which had the form SARIMA(1,1,1)x(1,1,1). This model was then used to generate twelve months out of sample forecasts. The accuracy of forecast error was assessed by mean absolute deviation (MAD), mean square error (MSE) and mean absolute percent error (MAPE). All of these measures had reasonably small values which were 0.105, 0.013 and 1.37% respectively.