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Year-ahead forecasting of electricity prices is an important issue in the current context of electricity markets. Nevertheless, only one-day-ahead forecasting is commonly tackled up in previous published works. Moreover, methodology developed for the short-term does not work properly for long-term forecasting.In this paper we provide a seasonal extension of the Non-Stationary Dynamic Factor Analysis, to deal with the interesting problem (both from the economic and engineering point of view) of long term forecasting of electricity prices. Seasonal Dynamic Factor Analysis (SeaDFA) allows to deal with dimensionality reduction in vectors of time series, in such a way that extracts common and specific components. Furthermore, common factors are able to capture not only regular dynamics (stationary or not) but also seasonal one, by means of common factors following a multiplicative seasonal VARIMA(p,d,q)×(P,D,Q) s model. Besides, a bootstrap procedure is proposed to be able to make inference on all the parameters involved in the model. A bootstrap scheme developed for forecasting includes uncertainty due to parameter estimation, allowing to enhance the coverage of forecast confidence intervals. Concerning the innovative and challenging application provided, bootstrap procedure developed allows to calculate not only point forecasts but also forecasting intervals for electricity prices.

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Keywords:Conditional heteroskedasticity Dynamic factor analysis Iberian market Long run Non-stationary Short runThe liberalization of electricity markets more than ten years ago in the vast majority of developed countries has introduced the need of modelling and forecasting electricity prices and volatilities, both in the short and long term. Thus, there is a need of providing methodology that is able to deal with the most important features of electricity price series, which are well known for presenting not only structure in conditional mean but also time-varying conditional variances. In this work we propose a new model, which allows to extract conditionally heteroskedastic common factors from the vector of electricity prices. These common factors are jointly estimated as well as their relationship with the original vector of series, and the dynamics affecting both their conditional mean and variance. The estimation of the model is carried out under the state-space formulation. The new model proposed is applied to extract seasonal common dynamic factors as well as common volatility factors for electricity prices and the estimation results are used to forecast electricity prices and their volatilities in the Spanish zone of the Iberian Market. Several simplified/alternative models are also considered as benchmarks to ¡Ilústrate that the proposed approach is superior to all of them in terms of explanatory and predictive power.

This tutorial paper provides a brief overview of forecasting techniques for hourly electricity price prediction in both the short and the long term, with an emphasis on analytical, nonheuristic procedures. Appropriate background material on time‐series analysis is reviewed first. Short‐term hourly price forecasting (from 12 to 168 hours in advance) is then addressed considering mostly time‐series tools. Illustrative examples based on both European and North American electricity markets are provided to clarify the functioning of the tools described. Unobserved component models are then introduced to address the long‐term forecasting (from 1 week to 1 year in advance) of hourly electricity prices. An illustrative example based on data from a North‐American electricity market is used to clarify the working of an unobserved component model. Appropriate conclusions are finally drawn.

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