Multivariate Exponential Smoothing and Dynamic Factor Model Applied to Hourly Electricity Price Analysis

Abstract

Thanks to its very simple recursive computing scheme, exponential smoothing has become a popular technique to forecast time series. In this work, we show the advantages of its multivariate version and present some properties of the model, which allows us to perform a dynamic factor analysis. This analysis leads to a simple methodology to reduce the number of parameters (useful when the dimension of observations is large) via a linear transformation that decomposes the multivariate process into independent univariate exponential smoothing processes, characterized by a single smoothing parameter that goes from zero (white-noise process) to one (random walk process). A computer implementation of the expectation-maximization (EM) algorithm has been built for the maximum likelihood estimation of the models. The practicality of the method is demonstrated by its application to hourly electricity price predictions in some day-ahead markets, such as Omel, Powernext, and Nord Pool markets, whose forecasts are given as examples. This article has supplementary material online.

KEY WORDS:

• EWMA
• Forecasting
• Moving average processes
• State space methods
• Time series

ACKNOWLEDGMENTS

This research was supported by Project MTM 2005-08896 from the Spanish Ministry of Science and Innovation. The authors thank Daniele Vallesi, Juan Temboury, and Francisco Pérez-Thoden for their aid in the preliminary stages of this work.