Functional time series forecasting in electricity marketsa novel parametric approach

Abstract

This thesis addresses the problem of forecasting functional time series by proposing a model that extends the classical ARIMA methodology to the functional framework. Functional Time Series (FTS) are time sequences of observations in which each observation is a continuous function defined on a closed interval. These processes of functional observations appear frequently in nature, social sciences or industrial systems. In particular, there exists numerous applications in the electricity market sector where FTS are found. As some examples, the electricity demand which is usually considered as a discrete process is in fact a continuous process as the power consumption is a continuous function of time. Electricity prices can also be analyzed as a FTS considering daily and weekly price profiles as functional data. Moreover, FTS can also be obtained from the bidding information of market auctions. Aggregated offer curves and Residual Demand Curves can be calculated as functions that model the competitive behavior of agents in the market. Hence, time sequences of hourly curves are observed. Being able to forecast these FTS is of utmost importance for market agents, which aim at optimizing their business, market operation and bidding strategy in the market. These FTS that appear in electricity markets share some common features. They are sensitive to weather conditions and to the effects of business and everyday activities that lead to weekly and daily seasonalities. Therefore, an appropriate forecasting model for these series should account for all of these effects. This thesis develops a functional parametric forecasting model that makes use of integral operators in the Hilbert space for operating with the functional observations. In a functional regression problem, the kernel of the integral operator models the relation between the input curve and the output curve. Inspired on neural networks, this thesis models the operator's kernel as a sum of sigmoid functions. In order to estimate the kernel that best fits the output, the sigmoids' parameters are optimized by minimizing the prediction error. This flexible estimation method allows us to develop the SARIMAHX model, which is an Autoregressive Moving Average Hilbertian model that accounts for seasonality and dependencies on functional and scalar explanatory variables. The proposed SARIMAHX model is successfully applied to forecast different FTS in electricity markets, including the application to the Ancillary Services market, the forecasting of electricity prices, the forecasting of Offer Curves and Residual Demand Curves.