Modeling of water usage by means of ARFIMA-GARCH processes

This paper addresses an important problem of modeling and prediction of phenomena with antipersistent behavior and variance changing in time. As a proper stochastic model we propose an autoregressive fractionally integrated moving average (ARFIMA) process with generalized autoregressive conditional heteroskedasticity (GARCH) noise. First, we introduce a simple identification and validation algorithm for such model. Second, we apply the algorithm to weekday data of hot water usage at urban residential blocks. We extract the deterministic sinusoidal component from the data and fit successfully the ARFIMA-GARCH model to the stochastic part. The goodness of fit is checked by examining model errors and prediction performance. All analyses are performed by the rigorous statistical procedure. The proposed model allows for real-time accurate predictions and when implemented at a hot water supply level will lead to a better optimization of the control system and energy efficiency use.