Functional Instrumental Regression for Energy Price Forecasting

• Activity Number: 109
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Sebastien Van Bellegem*+
• Companies: Universite Catholique de Louvain
• Keywords: Functional regression ; Inverse problem ; Endogeneity ; Energy price ; Forecasting

Abstract

A modern research question in energy forecasting is to relate spot prices and future market prices. Spot prices are available almost continuously over time, and a natural statistical challenge is to forecast the market of future contracts from spot prices. An appropriate setting for this task is the functional linear model, in which the regressors are spot prices. We show that estimating the forecasting function is a linear ill-posed inverse problem, with a known but data-dependent operator. We also consider the case where covariates are endogenous and assume the existence of instrumental variables to identify the model. We provide the rate of convergence of the Tikhonov regularized estimator, when we premultiply the problem by an instrument dependent operator. This extends the technology of Generalized Method of Moments to functional (GMM) to functional data. We then discuss the optimal choice of the premultiplication operator and propose an extension of the notion of ``weak instrument' to this nonparametric framework. The performance of the resulting nonparametric estimator is studied through simulations and real data from energy markets.