# Stability of Multiple Seasonal Holt-Winters Models Applied to Hourly Electricity Demand in Spain
Moreover, the same parameter can highly vary from one method to another using the same dataset. Thus, it is a big deal for forecasters to understand the behaviour of the model considering the locally optimised parameters. The future predictions accuracy will be closely related to the smoothing parameters. The optimisation procedure is using an optimisation algorithm, that do not take care concerning the reality of the series. The forecaster needs to make use of the own experience to validate and approve the obtained parameters. These actions are crucial for the entire process. Some factors have an influence on the parameter values. The method to obtain initial values for seeding the model impact on the forecasting accuracy [14] although after an optimisation of the parameters, accuracy differences are also minimised [15]. Climate conditions are not a big deal in terms of short-term forecasting accuracy [12]. However, it seems reasonable the parameters ought to be influenced. If only two seasonal patterns are considered, seasons modify the trend, whereas if three seasonalities are considered, the intra-year seasonal parameter should be influenced. The calendar also has a huge influence on the predictions and parameters, that must deal with some irregularities of the series [16; 17; 18]. Therefore, forecasters should always pay close attention to the parameters values. The forecasting procedure performed by TSOs must ensure continuously accurate forecasts for the electricity system. These predictions are used by the TSO for the operational planning and unit assignment, while they are also used by the market for the spot price settlement [19; 20]. The Spanish electricity market (OMIE) operates similarly [21; 22], where the unique Spanish TSO, Red Electrica de Espana (REE), supplies forecasts of demand for the next week every Wednesday, for the next 24 h every day, and a revision of the daily demand every six hour [23]. The market uses this information for the bidding process, as well as REE itself to carry out operational planning. Thus, there is an enormous responsibility in such eagerly awaited forecasts. In fact, REE uses a complex algorithm [24] to provide forecasts. With such high frequency forecasting, there is a need for the model to be updated continuously. The forecaster must deal with the varying smoothing parameters and take decisions on the engaged forecasts. In the Holt-Winters literature there is a strong discussion about whether the parameters should be continuously readjusted as the series progresses, or on the contrary, they must be immobile and try to exploit them for as long as possible. The values of the parameters are also discussed, since high values of the parameters indicate a great damping to adapt to the new observed values, compared to low values, where the initial values are given greater weight. Before this doubt, the following question is added: how do the parameters respond to a specific time series, such as the hourly electricity demand in Spain? Make it sense the obtained values? What is their stability? All these questions have not been answered in the previous literature. This article describes how we have performed a stability analysis on the parameters of the nHWT models applied to the electricity demand series in Spain. The main objective was to understand the behaviour of smoothing parameters against several different datasets with changes in climate conditions, time series components such as trend or seasonal, calendar effects among others. This analysis will help the forecasters to face the optimised model before making forecasts, considering the values of the parameters. It is also important to check whether it is necessary or not to update the smoothing parameters of the Holt-Winters models in order to obtain a good accuracy over time. On the other hand, the results of this study will show the influence of the calendar effect on these parameters, and therefore the need to develop new Holt-Winters models that take it into account [16].