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

Abstract

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.

Electricity Price Forecasting by Averaging Dynamic Factor Models

“…Regarding the length of the historic dataset, the shortest window is preferred for the forecasting horizons of one and seven-days-ahead (forecasts for the short term), while the long window of 1.5 years is preferred for the forecasting horizons of 30-and 60-days-ahead (long-term forecasts); this is consistent with the results in [5]. Furthermore, the MA terms for the factor models are statistically significant for all forecasting horizons, which means that modeling the common factors as ARMA reduces the error in comparison to modeling them as AR.…”

“…To summarize, a key stage when estimating this kind of model is the selection of the number of common factors, r, as well as the model they follow, which implies selecting the orders: p, d, q, P, D, Q. r could be obtained using the test proposed in [11] and could also be selected such that diagnostic checking results (specific factors and errors of the observation equation must be uncorrelated between them, and specific factors without any cross correlation) are reasonable [5]. However, alternative values could satisfy these criteria.…”

“…Working with data for the Iberian market for 2007-2009, they propose extracting common factors from the 24-dimensional price vector and modeling such factors as univariate seasonal AutoRegressive Integrated Moving Average (ARIMA) processes. The work in [5] proposes a technique called Seasonal Dynamic Factor Analysis (SeaDFA), which involves the estimation of a Vector AutoRegressive Integrated Moving Average (VARIMA) model for unobserved common factors having seasonal patterns. The work in [14] also uses a factor model, including not only hours, but also locations.…”

“…. , 24 at day t. Consequently, prices can be presented in a T × 24 dimensional matrix, where T is the number of days in the sample, and modeling should be multivariate (as in [2][3][4][5]). …”

Mexico : Combining monthly inflation predictions from surveys

“…We shall denote this type of fms by L1FM in the forecasting exercise. This model was extended to the non-stationary case by Poncela (2004 y 2006) and Lam, Yao and Bathia (2011), while seasonal dynamic fms were analysed in Alonso and others (2011).…”