Forecasting of electricity price through a functional prediction of sale and purchase curves

• DOI: http://doi.org/10.1002/for.2624
• Author: Francesco Lisi,Ismail Shah
• Date: 01 March 2020
• Published date: 01 March 2020

Received: 9 January 2018 Revised: 14 December 2018 Accepted: 16 July 2019

DOI: 10.1002/for.2624

RESEARCH ARTICLE

Forecasting of electricity price through a functional

prediction of sale and purchase curves

Ismail Shah1Francesco Lisi2,3

1Department of Statistics, Quaid-i-Azam

University, Islamabad, Pakistan

2Department of Statistical Sciences,

University of Padua, Italy

3Interdepartmental Centre for Energy

Economics and Technology “Giorgio Levi

Cases”,University of Padua, Italy

Correspondence

Francesco Lisi, Department of Statistical

Sciences, University of Padua, Via Battisti

241, 35121 Padua, Italy.

Email: francesco.lisi@unipd.it

Abstract

This work proposes a new approach for the prediction of the electricity price

based on forecasting aggregated purchase and sale curves. The basic idea is to

model the hourly purchase and the sale curves, to predict them and to find the

intersection of the predicted curves in order to obtain the predicted equilibrium

market price and volume. Modeling and forecasting of purchase and sale curves

is performed by means of functional data analysis methods. More specifically,

parametric (FAR) and nonparametric (NPFAR) functional autoregressive mod-

els are considered and compared to some benchmarks. An appealing feature of

the functional approach is that, unlike other methods, it provides insights into

the sale and purchase mechanism connected with the price and demand forma-

tion process and can therefore be used for the optimization of bidding strategies.

An application to the Italian electricity market (IPEX) is also provided, show-

ing that NPFAR models lead to a statistically significant improvement in the

forecasting accuracy.

KEYWORDS

electricity prices, forecasting, functional data, Italian electricity market, sale and purchase curves

1INTRODUCTION

With liberalization, electricity markets underwent major

changes which, in turn, introduced new challenges to their

participants, regarding, among other things, electricity

price forecasting.

In most deregulated electricity markets, prices are deter-

mined the day before the physical delivery of electricity by

means of (semi-)hourly auctions. Thus accurate forecast-

ing is highly important for trading and risk management

purposes. Efficient forecasting helps market participants

to optimize their bidding strategies and to establish a pool

bidding technique in order to maximize their profits.

Modeling and forecasting electricity prices is also a

formidable challenge in the statistical and econometric

literature. High-frequency, multiple periodicities, non-

constant mean and variance, calendar effects, high

volatility—usually much higher compared to other finan-

cial commodity markets—sudden jumps or spikes,etc., are

some features that price series exhibit (Bunn, 2004; Taylor,

De Menezes, & McSharry, 2006; Weron, 2007).

In the literature, several methods have been proposed

and applied to both electricity demand and price time

series prediction, differing in the level of complexity

and degrees of success (Aggarwal, Saini, & Kumar, 2009;

Weron, 2014, and referencestherein). Autoregressive inte-

grated moving average (ARIMA) models, possibly with

exogenous variables (ARIMAX) and sometimes with a

generalized autoregressive conditional heteroskedasticity

(GARCH) component, are widely used in demand and

price forecasting problems (Amjady, 2001; Bosco, Parisio,

& Pelagatti, 2007; Cincotti, Gallo, Ponta, & Raberto, 2014;

Conejo, Contreras, Espínola, & Plazas, 2005; Contreras,

Espinola, Nogales, & Conejo, 2003; Espinoza, Joye,

Belmans, & Moor, 2005; Garcia, Contreras, Van Akkeren,

& Garcia, 2005; Hao, 2007; Knittel & Roberts, 2005;

Journal of Forecasting. 2020;39:242–259.wileyonlinelibrary.com/journal/for© 2019 John Wiley & Sons, Ltd.242

Kristiansen, 2012; Shah & Lisi, 2015; Weron & Misiorek,

2005). To account for possible correlations among differ-

ent load periods, vector autoregressive (VAR) models have

been considered (Fezzi, 2007; Raviv, Bouwman, & Van

Dijk, 2013; Ziel & Weron, 2018). Exponential smoothing

methods, using exponentially weighted averages of past

observations, are often used to model multiple period-

icities in electricity data (Carpio, Juan, & López, 2014;

De Livera, Hyndman, & Snyder, 2011; Taylor, 2010; 2012;

Taylor et al., 2006). Many works are based on multiple

regression models describing the relationships between

the current price/demand levels and other external

factors—for example, temperature, calendar conditions,

fuel prices (Bianco, Manca, & Nardini, 2009; Charlton

& Singleton, 2014; Karakatsani & Bunn, 2008; Nan, Bor-

dignon, Bunn, & Lisi, 2014).

Neural network (ANN), fuzzy systems and support vec-

tor machine (SVM) are examples of the so-called artificial

intelligence methods, mapping the input/output relation-

ship without any specification of the underlying process.

They have been extensively used in forecasting both price

and loads (Amjady, 2006; Chen, Chang, & Lin, 2004;

Hayati & Shirvany, 2007; Niu, Li, & Li, 2007; Pai &

Hong, 2005; Panapakidis & Dagoumas, 2016; Pao, 2007;

Ranaweera, Hubele, & Karady, 1996; Singhal & Swarup,

2011). Hybrid models have been also suggested for predic-

tion purposes. These models combine linear and nonlinear

modeling capabilities of different models in order to cap-

ture different patterns in the data that often improve the

forecast (Bordignon, Bunn, Lisi, & Nan, 2013; Nowotarski

& Weron, 2016; Raviv, Bouwman, & van Dijk, 2015;

Shafie-Khah, Moghaddam, & Sheikh-El-Eslami, 2011;

Zhang, Tan, & Yang, 2012).

In the literature on electricity markets, there are few

works based on functional data analysis (FDA). This is

a relatively recent methodology in which data are repre-

sented by curves in a functional space where each func-

tion (curve) is seen as a single structured object, rather

than a collection of data points (Aneiros-Pérez, Cao, &

Vilar-Fernández, 2011; Ramsay & Silverman, 1997; 2002).

Ferraty and Vieu (2006) consider the FDA for predic-

tion of the US monthly electricity consumption for resi-

dential and commercial purposes from 1973 to 2001. In

their work, the functional object is the annual profile

and its discretization is represented by the 12 month val-

ues. Antoch, Prchal, Rosa, and Sarda (2010) use a func-

tional linear regression model linking observations of a

functional response variable with measurements of an

explanatory functional variable to analyze electricity con-

sumption in Sardinia. Vilar,Cao, and Aneiros-Pérez (2012)

refer to a nonparametric approach to functional analysis.

They forecast the daily profile of the hourly electricity

demand and price on the Spanish market. They also

compare the results with those obtained by a naive method

and ARIMA models. Liebl (2013) considers spot prices of

the German power market, traded at the European Energy

Exchange (EEX). He suggests to interpret hourly electricity

spot prices as noisy discretized points of smooth aggre-

gate price–demand functions. Through the estimation of

such functions he provides h-day-ahead (h=1,…,20)

price forecasts. Shah and Lisi (2015) use nonparametric

autoregressive functional models to forecast the next-day

demand on the Italian and British electricity markets. The

curve of interest is the daily profile, which is estimated

using hourly and semi-hourly data. Aneiros-Pérez, Vilar,

and Raña (2016) predict next-day electricity demand and

price daily curves given the information contained in past

curves for the Spanish market. They base their analyses on

functional principal components and nonparametric mod-

els with functional response and covariates. Chen and Li

(2017) consider hourly log-prices of the Californian elec-

tricity market. Each day, they obtain the daily price curve

by smoothing the discrete 24 hourly observations over a

continuous time interval. Finally, theymodel these curves

by means of an adaptive functional autoregressive model.

A direct comparison of all these methods, starting from

the literature, is almost impossible due to the heterogene-

ity of the data sets, the different markets, the frequency of

data, and the time periods. However,all the previous works

share an important drawback:They do not provide insights

into the sale and purchase mechanism connected to the

price/demand formation process, which, in fact, is essen-

tial for the study of price dynamics. Indeed, in the current

deregulated scenario, the price formation process follows

the basic law of sale and purchase, frequently found in

finance and macroeconomics.

Most wholesale electricity markets are organized in auc-

tions where buyers and producers submit their bids and

offers. According to that, in a competitive market the price

of a commodity should reflect the relative paucity of the

sale for a given purchase level. Offers from suppliers are

rejected with higher incremental costs if the demand level

is low, and hence those with the lowest incremental costs

remain in the competition, resulting in relatively low equi-

librium prices (Figure 1). With the increase in demand,

the suppliers with lower incremental cost use up their pro-

duction capacity first, followed by increasingly expensive

suppliers that eventually raise the equilibrium price.

The information provided by participants in these auc-

tions is not public and, in particular, it is not known by the

other participants. It is clear that, if this information were

available, it certainly would help the agents to improve

their bidding strategies and end up with significant prof-

its. As this is not the case, market players have to handle

incomplete information about their competitors. As a

SHAH AND LISI 243