Seasonal Dynamic Factor Analysis and Bootstrap Inference: Application to Electricity Market Forecasting

• Published in: Technometrics Vol. 53; no. 2; pp. 137 - 151
• Main Authors: Alonso, Andrés M., García-Martos, Carolina, Rodríguez, Julio, Jesús Sánchez, María
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.05.2011; The American Society for Quality and The American Statistical Association; American Society for Quality and the American Statistical Association; American Society for Quality
• Subjects: Analytical forecasting; Applied sciences; Bootstrap method; Computer science; control theory; systems; Data processing. List processing. Character string processing; Dimensionality reduction; Discriminant analysis; Economic forecasting models; Electrical engineering. Electrical power engineering; Electrical power engineering; Electricity prices; Energy prices; Exact sciences and technology; Factor analysis; Forecasting; Forecasting models; Inference from stochastic processes; time series analysis; Linear inference, regression; Mathematics; Memory organisation. Data processing; Modeling; Nonstationary; Parameter estimation; Power marketers; Power networks and lines; Probability and statistics; Sciences and techniques of general use; Seasonality; Software; Statistical forecasts; Statistics; Time series; Time series forecasting; Time series models; Uncertainty; Unobserved components; VARIMA models; Parameter estimation; Dynamic analysis; Seasonality; Non stationary process; Unobserved components; Modeling; Autoregressive integrated moving average model; Uncertain system; Seasonal variation; Bootstrap; Reduced order systems; System identification; Dimensionality reduction; Data analysis; Factor analysis; Time series; Non stationary condition; Inference; Coverage; Market survey; Energy prices; Vector method; Statistical forecasting; Long term; Stationary condition; Bootstrapping; Dimension reduction; VARIMA models; Electrical network; Remolded sample; Nonstationary; Factorial design
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/TECH.2011.09050

In this work, we propose the Seasonal Dynamic Factor Analysis (SeaDFA), an extension of Nonstationary Dynamic Factor Analysis, through which one can deal with dimensionality reduction in vectors of time series in such a way that both common and specific components are extracted. Furthermore, common factors are able to capture not only regular dynamics (stationary or not) but also seasonal ones, by means of the common factors following a multiplicative seasonal VARIMA(p, d, q) × (P, D, Q) s model. Additionally, a bootstrap procedure that does not need a backward representation of the model is proposed to be able to make inference for all the parameters in the model. A bootstrap scheme developed for forecasting includes uncertainty due to parameter estimation, allowing enhanced coverage of forecasting intervals. A challenging application is provided. The new proposed model and a bootstrap scheme are applied to an innovative subject in electricity markets: the computation of long-term point forecasts and prediction intervals of electricity prices. Several appendices with technical details, an illustrative example, and an additional table are available online as Supplementary Materials.