Initialization Methods for Multiple Seasonal Holt-Winters Forecasting Models

[EN] 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.Trull, O.; García-Díaz, JC.; Troncoso, A. (2020). Initialization Methods for Multiple Seasonal Holt-Winters Forecasting Models. Mathematics. 8(2):1-17. https://doi.org/10.3390/math8020268S11782Weron, R. (2014). Electricity price forecasting: A review of the state-of-the-art with a look into the future. International Journal of Forecasting, 30(4), 1030-1081. doi:10.1016/j.ijforecast.2014.08.008Taylor, J. W. (2003). Short-term electricity demand forecasting using double seasonal exponential smoothing. Journal of the Operational Research Society, 54(8), 799-805. doi:10.1057/palgrave.jors.2601589Taylor, J. W. (2010). Triple seasonal methods for short-term electricity demand forecasting. European Journal of Operational Research, 204(1), 139-152. doi:10.1016/j.ejor.2009.10.003Holt, C. C. (2004). Forecasting seasonals and trends by exponentially weighted moving averages. International Journal of Forecasting, 20(1), 5-10. doi:10.1016/j.ijforecast.2003.09.015Bowerman, B. L., Koehler, A., & Pack, D. J. (1990). Forecasting time series with increasing seasonal variation. Journal of Forecasting, 9(5), 419-436. doi:10.1002/for.3980090502Initializing the Holt–Winters Methodhttps://robjhyndman.com/hyndsight/hw-initialization/Rasmussen, R. (2004). On time series data and optimal parameters. Omega, 32(2), 111-120. doi:10.1016/j.omega.2003.09.013Trull, Ó., García-Díaz, J., & Troncoso, A. (2019). Application of Discrete-Interval Moving Seasonalities to Spanish Electricity Demand Forecasting during Easter. Energies, 12(6), 1083. doi:10.3390/en12061083Segura, J. V., & Vercher, E. (2001). A spreadsheet modeling approach to the Holt–Winters optimal forecasting. European Journal of Operational Research, 131(2), 375-388. doi:10.1016/s0377-2217(00)00062-xMakridakis, S., & Hibon, M. (1991). Exponential smoothing: The effect of initial values and loss functions on post-sample forecasting accuracy. International Journal of Forecasting, 7(3), 317-330. doi:10.1016/0169-2070(91)90005-gWilliams, D. W., & Miller, D. (1999). Level-adjusted exponential smoothing for modeling planned discontinuities. International Journal of Forecasting, 15(3), 273-289. doi:10.1016/s0169-2070(98)00083-

Forecasting Irregular Seasonal Power Consumption. An Application to a Hot-Dip Galvanizing Process

[EN] The method described in this document makes it possible to use the techniques usually applied to load prediction efficiently in those situations in which the series clearly presents seasonality but does not maintain a regular pattern. Distribution companies use time series to predict electricity consumption. Forecasting techniques based on statistical models or artificial intelligence are used. Reliable forecasts are required for efficient grid management in terms of both supply and capacity. One common underlying feature of most demand-related time series is a strong seasonality component. However, in some cases, the electricity demanded by a process presents an irregular seasonal component, which prevents any type of forecast. In this article, we evaluated forecasting methods based on the use of multiple seasonal models: ARIMA, Holt-Winters models with discrete interval moving seasonality, and neural networks. The models are explained and applied to a real situation, for a node that feeds a galvanizing factory. The zinc hot-dip galvanizing process is widely used in the automotive sector for the protection of steel against corrosion. It requires enormous energy consumption, and this has a direct impact on companies' income statements. In addition, it significantly affects energy distribution companies, as these companies must provide for instant consumption in their supply lines to ensure sufficient energy is distributed both for the process and for all the other consumers. The results show a substantial increase in the accuracy of predictions, which contributes to a better management of the electrical distribution.Trull, O.; García-Díaz, JC.; Peiró Signes, A. (2021). Forecasting Irregular Seasonal Power Consumption. An Application to a Hot-Dip Galvanizing Process. Applied Sciences. 11(1):1-24. https://doi.org/10.3390/app11010075S12411

Electricity Forecasting Improvement in a Destination Using Tourism Indicators

[EN] The forecast of electricity consumption plays a fundamental role in the environmental impact of a tourist destination. Poor forecasting, under certain circumstances, can lead to huge economic losses and air pollution, as prediction errors usually have a large impact on the utilisation of fossil fuel-generation plants. Due to the seasonality of tourism, consumption in areas where the industry represents a big part of the economic activity follows a different pattern than in areas with a more regular economic distribution. The high economic impact and seasonality of the tourist activity suggests the use of variables specific to it to improve the electricity demand forecast. This article presents a Holt¿Winters model with a tourism indicator to improve the effectiveness on the electricity demand forecast in the Balearic Islands (Spain). Results indicate that the presented model improves the accuracy of the prediction by 0.3%. We recommend the use of this type of model and indicator in tourist destinations where tourism accounts for a substantial amount of the Gross Domestic Product (GDP), we can control a significant amount of the flow of tourists and the electrical balance is controlled mainly by fossil fuel power plants.Trull Domínguez, O.; Peiró Signes, A.; García-Díaz, JC. (2019). Electricity Forecasting Improvement in a Destination Using Tourism Indicators. Sustainability. 11(13). https://doi.org/10.3390/su1113365636561113Zhang, M., Li, J., Pan, B., & Zhang, G. (2018). Weekly Hotel Occupancy Forecasting of a Tourism Destination. Sustainability, 10(12), 4351. doi:10.3390/su10124351Bakhat, M., & Rosselló, J. (2011). Estimation of tourism-induced electricity consumption: The case study of Balearics Islands, Spain. Energy Economics, 33(3), 437-444. doi:10.1016/j.eneco.2010.12.009Gössling, S. (2000). Sustainable Tourism Development in Developing Countries: Some Aspects of Energy Use. Journal of Sustainable Tourism, 8(5), 410-425. doi:10.1080/09669580008667376Peeters, P., & Schouten, F. (2006). Reducing the Ecological Footprint of Inbound Tourism and Transport to Amsterdam. Journal of Sustainable Tourism, 14(2), 157-171. doi:10.1080/09669580508669050Scott, D., Hall, C. M., & Gössling, S. (2016). A report on the Paris Climate Change Agreement and its implications for tourism: why we will always have Paris. Journal of Sustainable Tourism, 24(7), 933-948. doi:10.1080/09669582.2016.1187623Scott, D., Hall, C. M., & Gössling, S. (2015). A review of the IPCC Fifth Assessment and implications for tourism sector climate resilience and decarbonization. Journal of Sustainable Tourism, 1-23. doi:10.1080/09669582.2015.1062021Scott, D., Gössling, S., Hall, C. M., & Peeters, P. (2015). Can tourism be part of the decarbonized global economy? The costs and risks of alternate carbon reduction policy pathways. Journal of Sustainable Tourism, 1-21. doi:10.1080/09669582.2015.1107080Becken, S., & Simmons, D. G. (2002). Understanding energy consumption patterns of tourist attractions and activities in New Zealand. Tourism Management, 23(4), 343-354. doi:10.1016/s0261-5177(01)00091-7Gössling, S. (2002). Global environmental consequences of tourism. Global Environmental Change, 12(4), 283-302. doi:10.1016/s0959-3780(02)00044-4Gössling, S., Hansson, C. B., Hörstmeier, O., & Saggel, S. (2002). Ecological footprint analysis as a tool to assess tourism sustainability. Ecological Economics, 43(2-3), 199-211. doi:10.1016/s0921-8009(02)00211-2Meng, W., Xu, L., Hu, B., Zhou, J., & Wang, Z. (2016). Quantifying direct and indirect carbon dioxide emissions of the Chinese tourism industry. Journal of Cleaner Production, 126, 586-594. doi:10.1016/j.jclepro.2016.03.067Lee, J. W., & Brahmasrene, T. (2013). Investigating the influence of tourism on economic growth and carbon emissions: Evidence from panel analysis of the European Union. Tourism Management, 38, 69-76. doi:10.1016/j.tourman.2013.02.016Paramati, S. R., Alam, M. S., & Chen, C.-F. (2016). The Effects of Tourism on Economic Growth and CO2 Emissions: A Comparison between Developed and Developing Economies. Journal of Travel Research, 56(6), 712-724. doi:10.1177/0047287516667848Fortuny, M., Soler, R., Cánovas, C., & Sánchez, A. (2008). Technical approach for a sustainable tourism development. Case study in the Balearic Islands. Journal of Cleaner Production, 16(7), 860-869. doi:10.1016/j.jclepro.2007.05.003Becken, S. (2002). Analysing International Tourist Flows to Estimate Energy Use Associated with Air Travel. Journal of Sustainable Tourism, 10(2), 114-131. doi:10.1080/09669580208667157Becken, S., Simmons, D. G., & Frampton, C. (2003). Energy use associated with different travel choices. Tourism Management, 24(3), 267-277. doi:10.1016/s0261-5177(02)00066-3Tourism and Transport in New Zealand: Implications for Energy Usehttps://core.ac.uk/download/pdf/35459093.pdfTabatchnaia-Tamirisa, N., Loke, M. K., Leung, P., & Tucker, K. A. (1997). Energy and tourism in Hawaii. Annals of Tourism Research, 24(2), 390-401. doi:10.1016/s0160-7383(97)80008-4Becken, S., Frampton, C., & Simmons, D. (2001). Energy consumption patterns in the accommodation sector—the New Zealand case. Ecological Economics, 39(3), 371-386. doi:10.1016/s0921-8009(01)00229-4Katircioglu, S. T. (2014). International tourism, energy consumption, and environmental pollution: The case of Turkey. Renewable and Sustainable Energy Reviews, 36, 180-187. doi:10.1016/j.rser.2014.04.058Katircioglu, S. T., Feridun, M., & Kilinc, C. (2014). Estimating tourism-induced energy consumption and CO2 emissions: The case of Cyprus. Renewable and Sustainable Energy Reviews, 29, 634-640. doi:10.1016/j.rser.2013.09.004Zaman, K., Shahbaz, M., Loganathan, N., & Raza, S. A. (2016). Tourism development, energy consumption and Environmental Kuznets Curve: Trivariate analysis in the panel of developed and developing countries. Tourism Management, 54, 275-283. doi:10.1016/j.tourman.2015.12.001Tsai, K.-T., Lin, T.-P., Hwang, R.-L., & Huang, Y.-J. (2014). Carbon dioxide emissions generated by energy consumption of hotels and homestay facilities in Taiwan. Tourism Management, 42, 13-21. doi:10.1016/j.tourman.2013.08.017,, M. del P. P.-R., Pozo-Barajas, R., & Sánchez-Rivas, J. (2017). Relationships between Tourism and Hospitality Sector Electricity Consumption in Spanish Provinces (1999–2013). Sustainability, 9(4), 480. doi:10.3390/su9040480Pablo-Romero, M., Sánchez-Braza, A., & Sánchez-Rivas, J. (2017). Relationships between Hotel and Restaurant Electricity Consumption and Tourism in 11 European Union Countries. Sustainability, 9(11), 2109. doi:10.3390/su9112109Wang, J. C. (2016). A study on the energy performance of school buildings in Taiwan. Energy and Buildings, 133, 810-822. doi:10.1016/j.enbuild.2016.10.036Warnken, J., Bradley, M., & Guilding, C. (2005). Eco-resorts vs. mainstream accommodation providers: an investigation of the viability of benchmarking environmental performance. Tourism Management, 26(3), 367-379. doi:10.1016/j.tourman.2003.11.017Financing Europe’s Low Carbon, Climate Resilient Futurehttps://www.eea.europa.eu/themes/climate/financing-europe2019s-low-carbon-climatePace, L. A. (2016). How do tourism firms innovate for sustainable energy consumption? A capabilities perspective on the adoption of energy efficiency in tourism accommodation establishments. Journal of Cleaner Production, 111, 409-420. doi:10.1016/j.jclepro.2015.01.095Sozer, H. (2010). Improving energy efficiency through the design of the building envelope. Building and Environment, 45(12), 2581-2593. doi:10.1016/j.buildenv.2010.05.004Hobbs, B. F., Jitprapaikulsarn, S., Konda, S., Chankong, V., Loparo, K. A., & Maratukulam, D. J. (1999). Analysis of the value for unit commitment of improved load forecasts. IEEE Transactions on Power Systems, 14(4), 1342-1348. doi:10.1109/59.801894Bilan, Y., Streimikiene, D., Vasylieva, T., Lyulyov, O., Pimonenko, T., & Pavlyk, A. (2019). Linking between Renewable Energy, CO2 Emissions, and Economic Growth: Challenges for Candidates and Potential Candidates for the EU Membership. Sustainability, 11(6), 1528. doi:10.3390/su11061528Pfenninger, S., & Keirstead, J. (2015). Renewables, nuclear, or fossil fuels? Scenarios for Great Britain’s power system considering costs, emissions and energy security. Applied Energy, 152, 83-93. doi:10.1016/j.apenergy.2015.04.102Aguiló, E., Alegre, J., & Sard, M. (2005). The persistence of the sun and sand tourism model. Tourism Management, 26(2), 219-231. doi:10.1016/j.tourman.2003.11.004Weron, R. (2014). Electricity price forecasting: A review of the state-of-the-art with a look into the future. International Journal of Forecasting, 30(4), 1030-1081. doi:10.1016/j.ijforecast.2014.08.008Cancelo, J. R., Espasa, A., & Grafe, R. (2008). Forecasting the electricity load from one day to one week ahead for the Spanish system operator. International Journal of Forecasting, 24(4), 588-602. doi:10.1016/j.ijforecast.2008.07.005Suganthi, L., & Samuel, A. A. (2012). Energy models for demand forecasting—A review. Renewable and Sustainable Energy Reviews, 16(2), 1223-1240. doi:10.1016/j.rser.2011.08.014Bianco, V., Manca, O., & Nardini, S. (2009). Electricity consumption forecasting in Italy using linear regression models. Energy, 34(9), 1413-1421. doi:10.1016/j.energy.2009.06.034De Felice, M., Alessandri, A., & Ruti, P. M. (2013). Electricity demand forecasting over Italy: Potential benefits using numerical weather prediction models. Electric Power Systems Research, 104, 71-79. doi:10.1016/j.epsr.2013.06.004Taylor, J. W. (2008). An evaluation of methods for very short-term load forecasting using minute-by-minute British data. International Journal of Forecasting, 24(4), 645-658. doi:10.1016/j.ijforecast.2008.07.007Gardner, E. S., & Mckenzie, E. (1985). Forecasting Trends in Time Series. Management Science, 31(10), 1237-1246. doi:10.1287/mnsc.31.10.1237Taylor, J. W. (2003). Exponential smoothing with a damped multiplicative trend. International Journal of Forecasting, 19(4), 715-725. doi:10.1016/s0169-2070(03)00003-7Williams, D. W., & Miller, D. (1999). Level-adjusted exponential smoothing for modeling planned discontinuities. International Journal of Forecasting, 15(3), 273-289. doi:10.1016/s0169-2070(98)00083-1Taylor, J. W. (2003). Short-term electricity demand forecasting using double seasonal exponential smoothing. Journal of the Operational Research Society, 54(8), 799-805. doi:10.1057/palgrave.jors.2601589Taylor, J. W. (2010). Triple seasonal methods for short-term electricity demand forecasting. European Journal of Operational Research, 204(1), 139-152. doi:10.1016/j.ejor.2009.10.003Gardner, E. S. (2006). Exponential smoothing: The state of the art—Part II. International Journal of Forecasting, 22(4), 637-666. doi:10.1016/j.ijforecast.2006.03.005Trull, Ó., García-Díaz, J., & Troncoso, A. (2019). Application of Discrete-Interval Moving Seasonalities to Spanish Electricity Demand Forecasting during Easter. Energies, 12(6), 1083. doi:10.3390/en12061083Pardo, A., Meneu, V., & Valor, E. (2002). Temperature and seasonality influences on Spanish electricity load. Energy Economics, 24(1), 55-70. doi:10.1016/s0140-9883(01)00082-2Taylor, J. W., & McSharry, P. E. (2007). Short-Term Load Forecasting Methods: An Evaluation Based on European Data. IEEE Transactions on Power Systems, 22(4), 2213-2219. doi:10.1109/tpwrs.2007.907583Almeida García, F., Balbuena Vázquez, A., & Cortés Macías, R. (2015). Resident’s attitudes towards the impacts of tourism. Tourism Management Perspectives, 13, 33-40. doi:10.1016/j.tmp.2014.11.00

Anxiety towards Statistics and Its Relationship with Students' Attitudes and Learning Approach

[EN] 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.Peiró Signes, A.; Trull, O.; Segarra-Oña, M.; García-Díaz, JC. (2021). Anxiety towards Statistics and Its Relationship with Students' Attitudes and Learning Approach. Behavioral Sciences. 11(3):1-13. https://doi.org/10.3390/bs11030032S11311

Initialization Methods for Multiple Seasonal Holt–Winters Forecasting Models

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

One-day-ahead electricity demand forecasting in holidays using discrete-interval moving seasonalities

[EN] Transmission System Operators provide forecasts of electricity demand to the electricity system. The producers and sellers use this information to establish the next day production units planning and prices. The results obtained are very accurate. However, they have a great deal with special events forecasting. Special events produce anomalous load conditions, and the models used to provide predictions must react properly against these situations. In this article, a new forecasting method based on multiple seasonal Holt-Winters modelling including discrete-interval moving seasonalities is applied to the Spanish hourly electricity demand to predict holidays with a 24-h prediction horizon. It allows the model to integrate the anomalous load within the model. The main results show how the new proposal outperforms regular methods and reduces the forecasting error from 9.5% to under 5% during holidays.The authors would like to thank the Spanish Ministry of Science, Innovation and Universities for the support under the project TIN201788209C2; and Red Electrica de Espana S.A. for providing the data used in this article.Trull, O.; García-Díaz, JC.; Troncoso, A. (2021). One-day-ahead electricity demand forecasting in holidays using discrete-interval moving seasonalities. Energy. 231:1-12. https://doi.org/10.1016/j.energy.2021.120966S11223

Multiple seasonal STL decomposition with discrete-interval moving seasonalities

[EN] The decomposition of a time series into components is an exceptionally useful tool for understanding the behaviour of the series. The decomposition makes it possible to dis-tinguish the long-term and the short-term behaviour through the trend component and the seasonality component. Among the decomposition methods, the STL (Seasonal Trend decomposition based on Loess) method stands out for its versatility and robustness. This method, however, has one main drawback: it works with a single seasonality, and does not deal with the calendar effect. In this article we present a new decomposition method, based on the STL, which allows the use of different seasonalities while allowing the cal-endar effect and special events to be introduced into the model using discrete-interval moving seasonalities (MSTL-DIMS). To show the improvements obtained, the MSTL-DIMS technique is applied to short-term load forecasting in some electricity systems, and the results are discussed.Trull, O.; García-Díaz, JC.; Peiró Signes, A. (2022). Multiple seasonal STL decomposition with discrete-interval moving seasonalities. Applied Mathematics and Computation. 433:1-9. https://doi.org/10.1016/j.amc.2022.1273981943

Monitorización del proceso de galvanizado por inmersión en baño caliente de zinc

[ES] La industria del automóvil requiere de la utilización en grandes cantidades de acero galvanizado. El proceso de obtención industrial más utilizado en España es el de galvanizado continuo por inmersión en baño caliente de zinc. El proceso del baño es altamente dependiente de las cantidades de aluminio presentes en el baño, lo cual requiere un control exhaustivo de calidad. En este artículo proponemos un método efectivo de control de calidad basado en gráficos de control basado en residuos que ha sido aplicado en la industria. Se muestra el método empleado y los resultados obtenidos.García-Díaz, JC.; Trull, O.; Peiró Signes, A. (2021). Monitorización del proceso de galvanizado por inmersión en baño caliente de zinc. Compobell. 167-170. http://hdl.handle.net/10251/19132216717

Previsión de demanda eléctrica en días festivos. Utilización de DIMS para la mejora de la previsión.

[ES] El correcto funcionamiento del sistema eléctrico español se basa en la posibilidad de realizar previsiones acertadas de la demanda eléctrica futura. los operadores del sistema de transmisión como Red Eléctrica de España utilizan una gran cantidad de recursos para realizar dichas previsiones.Trull, O.; García-Díaz, JC.; Peiró Signes, A. (2021). Previsión de demanda eléctrica en días festivos. Utilización de DIMS para la mejora de la previsión. Compobell. 45-48. http://hdl.handle.net/10251/191344454

Anxiety towards Statistics and Its Relationship with Students’ Attitudes and Learning Approach

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