Water Consumption Forecasting Using ARIMA and Holt-Winters Methods: A Case Study in Vouzela, Portugal

This study presents an approach to forecasting water consumption using the ARIMA (Autoregressive Integrated Moving Average) method, with an additional comparison to the Holt- Winters method [1], [ 2 ], [ 3], [ 4], [ 5 ]. The work was based on a set of historical data representing the monthly water consumption of a specific area in the parish of Cambra, municipality of Vouzela, Portugal, covering a period of five years (2018-2022). Initially, the natural logarithmic transformation was applied to normalise the data [ 6], followed by the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test to check the stationarity of the time series [ 7]. Differentiation was applied to achieve the necessary stationarity. The Auto-ARIMA method was used to determine the optimal parameters (p,d,q) based on the Akaike Information Criterion (AIC) [ 8], [9]. In addition, the Holt-Winters method was implemented directly, taking advantage of its ability to deal with non-stationary and non-normally distributed series. This method was applied with additive components and Box-Cox transformation [10 ], automatically incorporating the transformation and adjustment processes for seasonality and trend. Both methods were used to forecast water consumption for the 12 months to 2023. After applying Auto-ARIMA, the series was reversed, i.e. differentiated, and exponentially transformed to return to the original values. The performance of both methods was assessed comparatively, using the Mean Absolute Error as a metric [ 11 ], [12]. This study contributes to the efficient management of water resources by providing a robust methodology for forecasting water consumption, with an emphasis on the detailed application of ARIMA and a complementary comparison with Holt-Winters. Throughout this study, both ARIMA and Holt-Winters will be approached as statistical methods that generate models for forecasting data.