The Holt–Winters models are one of the most popular forecasting algorithms. As well-known, these models are recursive and thus, an initialization value is needed to feed the model, being that a proper initialization of the Holt–Winters models is crucial for obtaining a good accuracy of the predictions. Moreover, the introduction of multiple seasonal Holt–Winters models requires a new development of methods for seed initialization and obtaining initial values. This work proposes new initialization methods based on the adaptation of the traditional methods developed for a single seasonality in order to include multiple seasonalities. Thus, new methods to initialize the level, trend, and seasonality in multiple seasonal Holt–Winters models are presented. These new methods are tested with an application for electricity demand in Spain and analyzed for their impact on the accuracy of forecasts. As a consequence of the analysis carried out, which initialization method to use for the level, trend, and seasonality in multiple seasonal Holt–Winters models with an additive and multiplicative trend is provided.

Electricity management and production depend heavily on demand forecasts made. Any mismatch between the energy demanded with respect to that produced supposes enormous losses for the consumer. Transmission System Operators use time series-based tools to forecast accurately the future demand and set the production program. One of the most effective and highly used methods are Holt-Winters. Recently, the incorporation of the multiple seasonal Holt-Winters methods has improved the accuracy of the predictions. These forecasts, depend greatly on the parameters with which the model is constructed. The forecasters need to deal with these parameters values when operating the model. In this article, the parameters space of the multiple seasonal Holt-Winters models applied to electricity demand in Spain is analysed and discussed. The parameters stability analysis leads to forecasters better understanding the behaviour of the predictions and managing their exploitation efficiently. The analysis addresses different time windows, depending on the period of the year as well as different training set sizes. The results show the influence of the calendar effect on these parameters and if it is necessary or not to update them in order to obtain a good accuracy over time.

Many university students have difficulties when facing statistics related tasks, leading to an increase in their levels of anxiety and poor performance. Researchers have identified negative attitudes towards statistics, which have been shaped through students’ secondary education experience, as a major driver for their failure. In this study we want to uncover the causal recipes of attitudes leading to high and low levels of anxiety in secondary education students, and the role that the learning approach plays in these relationships. We used fuzzy sets comparative qualitative analysis (fsQCA) in a sample of 325 students surveyed on the multifactorial scale of attitudes toward statistics (MSATS) and the revised two factor study process questionnaire (R-SPQ-2F). The results indicate that, respectively, a high or a low level of self-confidence is the most important and a sufficient condition by itself for achieving a low or a high level of anxiety, while the learning approaches and other attitudes are only present in other causal combinations that represent a small number of cases.

Forecasting electricity demand through time series is a tool used by transmission system operators to establish future operating conditions. The accuracy of these forecasts is essential for the precise development of activity. However, the accuracy of the forecasts is enormously subject to the calendar effect. The multiple seasonal Holt–Winters models are widely used due to the great precision and simplicity that they offer. Usually, these models relate this calendar effect to external variables that contribute to modification of their forecasts a posteriori. In this work, a new point of view is presented, where the calendar effect constitutes a built-in part of the Holt–Winters model. In particular, the proposed model incorporates discrete-interval moving seasonalities. Moreover, a clear example of the application of this methodology to situations that are difficult to treat, such as the days of Easter, is presented. The results show that the proposed model performs well, outperforming the regular Holt–Winters model and other methods such as artificial neural networks and Exponential Smoothing State Space Model with Box-Cox Transformation, ARMA Errors, Trend and Seasonal Components (TBATS) methods.