Elsevier

International Journal of Forecasting

Volume 24, Issue 4, October–December 2008, Pages 728-743
International Journal of Forecasting

A new approach to characterizing and forecasting electricity price volatility

https://doi.org/10.1016/j.ijforecast.2008.08.002Get rights and content

Abstract

There is a growing need to model the dynamics of electricity spot prices. While many studies have adopted the jump-diffusion model used successfully in traditional financial markets, the distinctive features of energy prices present non-trivial challenges. In particular, electricity price series feature extreme jumps of magnitudes rarely seen in financial markets, and occurring at greater frequency. Standard parametric approaches to estimating jump-diffusion models struggle to disentangle the jump and non-jump variation. This paper explores a recently-developed approach to separating the total variation into jump and non-jump components. Using quadratic variation theory, we non-parametrically estimate jump parameters for five power markets which are known to feature some important physical differences. The unique characteristics of the jump and non-jump components of the total variation are studied for each market. Given the evidence that the two sources of variation in spot prices have distinct dynamics, the paper explores whether volatility forecasts can be improved by explicitly incorporating the jump and non-jump components of the total variation.

Introduction

Modelling electricity spot prices is an emerging, yet increasingly important research area. An understanding of electricity price dynamics is fundamental to speculation, derivative pricing, risk management, and real option valuation. Geman and Roncoroni (2006) note that spot price risk has forced the energy industry to identify, price and hedge the options granted in energy contracts. Hence, accurate modelling of spot prices is the cornerstone of the optimal scheduling of physical assets and valuing of real options (Swinand, Rufin, & Sharma, 2005). Similarly, Byström (2005) and Chan and Gray (2006) emphasize the importance of accurately modelling the stochastic nature of the spot prices for the purpose of calculating Value-at-Risk.

To be useful, a model must accurately capture the distinctive characteristics of the underlying price. The most obvious characteristic of electricity prices is the existence of extreme jumps. Consider, for example, Fig. 1, which plots the time series of spot prices sampled at 30-minute intervals in five regional Australian power markets. Each market exhibits occasional price spikes several orders of magnitude greater than their mean price. These extreme jumps significantly complicate the task of modellers seeking to characterize the stochastic nature of electricity prices.

Building on the seminal work of Johnson and Barz (1999), many studies adopt the jump-diffusion model often used for stock prices and interest rates to model the electricity spot price.3 Andersen, Bollerslev, and Diebold (ABD) (2007) describe the jump-diffusion model as a combination of (i) a smooth continuous sample path process and (ii) a much less persistent discontinuous jump component. While the jump-diffusion framework is intuitive from a theoretical perspective, its econometric implementation has some important deficiencies. In a nutshell, it is difficult to disentangle the jump and non-jump components of the price variation, with the result that jump-diffusion models are very difficult to estimate.4 Given the prevalence of extreme jumps in the electricity price data, accurately characterizing the jumps is crucial to any attempt to build a model of price dynamics. The current paper explores the usefulness of a new approach to estimating jump characteristics in electricity data.

Recent developments in the econometrics literature have shown that it is possible to partition the total variation in returns into jump and non-jump components. First, note that the realized volatility (defined as the sum of squared high-frequency returns) estimates the total variation, including both jump and non-jump components. Second, the realized bipower variation (defined as the sum of the product of adjacent absolute intraday returns) provides a consistent estimate of the continuous non-jump volatility, even in the presence of discontinuous jumps. Finally, the difference between the realized volatility and the bipower variation consistently estimates the discontinuous jump component of the variation.

Based on these ideas, Barndorff-Nielsen and Shephard, 2004, Barndorff-Nielsen and Shephard, 2006 develop a model-free nonparametric test for the existence of jumps in high-frequency dataseries. ABD (2007) illustrate how to use the method to non-parametrically estimate the jump and non-jump components and characterize their respective features. Further, they examine the viability of volatility forecasting models that separately exploit the distinct characteristics of the jump and non-jump components of variation. ABD (2007) also analyze the dynamics of foreign exchange, equity index, and long-term Treasury Bond markets using this approach.

The current paper makes a number of contributions to the electricity-modelling literature. The first is the application of the quadratic-variation approach to the challenging task of disentangling the jump and non-jump components of variation in the electricity-price process. While the method has been applied to a range of financial time series with notable success, power markets represent an ideal environment within which to explore this new approach. Both the prevalence of extreme jumps in energy markets and the noted deficiencies of parametric jump-diffusion approaches motivate the exploration of this non-parametric approach to estimating key jump parameters. Having said that, electricity dynamics differ in several important ways from traditional financial assets. Specifically, the drift in electricity prices exhibits clear intraday, intraweek and seasonal patterns. Unlike traditional financial assets, we cannot assume that price changes have mean zero. The second contribution of the paper is to propose a modification to the established quadratic-variation approach which is designed to accommodate non-zero mean price changes.

Third, the availability of ultra high-frequency electricity spot data over an extended time period is opportune.5 Barndorff-Nielsen and Shephard, 2004, Barndorff-Nielsen and Shephard, 2006 asymptotic theory for bipower variation relies on high-frequency intraday sampling over lengthy periods (i.e., long-span asymptotics). The current study utilizes electricity spot price data sampled at 30-minute intervals over a period of nearly 3,000 days, giving a sample of over 140,000 prices in each market. Fourth, the paper follows ABD (2007) in exploring whether separately identifying the jump and non-jump components results in an improved forecast accuracy for the total variation. Naturally, power-market participants stand to benefit greatly from any improvement that can be achieved in volatility forecast accuracy.

The remainder of the paper is organized as follows. Section 2 provides a brief overview of quadratic-variation theory, introducing relevant terminology and concepts. Section 3 describes the data used in the empirical study and presents some preliminary plots of the various power markets. From the graphical analysis, it is apparent that the quadratic variation approach used in prior literature requires modification to accommodate the unique features of electricity time series. Section 4 develops a model of the drift of the price process designed to capture the stylized features of electricity data. Appropriate modifications to the quadratic variation approach are outlined.

The empirical analysis is presented in Section 5. For a number of power markets, the quadratic variation approach is employed to identify significant electricity price jumps, and to partition the total realized variation into jump and non-jump components. The distinct characteristics of each component are studied, and non-parametric estimates of key jump parameters (e.g., jump intensity and magnitude) are reported. Section 6 explores the abilities of two models to forecast future volatility. In particular, we examine whether volatility forecasts can be improved by separating the total variation into jump and non-jump components, since these components are shown to have unique characteristics. Finally, Section 7 concludes the paper.

Section snippets

An overview of quadratic variation theory

This section provides a brief overview of quadratic variation theory (QVT). Detailed theoretical expositions can be found in Barndorff-Nielsen and Shephard, 2004, Barndorff-Nielsen and Shephard, 2006 and ABD (2007). Let p(t) denote the spot price of an asset, and assume that the price process is governed by a continuous-time stochastic-volatility model with an additive jump component:dp(t)=μ(t)dt+σ(t)dW(t)+κ(t)dq(t),where μ(t) and σ(t) are the drift and instantaneous volatility, W(t) is a

Sample data

In Australia, the National Electricity Market Management Company (NEMMCO) serves as the market operator of the National Electricity Market (NEM) and the operator of the power system that underpins the NEM operation. Electricity spot prices are publicly available on the NEMMCO website (www.nemmco.com.au). The empirical analysis utilizes electricity spot prices from five power markets operating in different regions in Australia, namely, Victoria (VIC), New South Wales (NSW), Queensland (QLD), the

A modification to QVT for electricity Prices

In light of the evidence that half-hourly electricity price changes are not mean-zero, we propose the following modification to the quadratic-variation approach. First, the drift of the price process is modelled parametrically to estimate conditional mean prices. Second, by subtracting the estimated drift from the observed price changes, common patterns in price changes are removed. Third, the general QVT described in Section 2 is then applied to the ‘de-meaned’ price changes.

We follow the

Characteristics of the total variation components

On each sample day t, the total realized volatility (RV) is calculated and partitioned into its continuous variation (CV) and jump variation (JV) components. Further, the signed jumps (Jt) are calculated on days where a significant jump is identified. Table 3 reports summary statistics for each volatility estimator, presented in their standard deviation form.14

Table 3 panel A

Predictive power of volatility components

The analysis in Section 5 identifies two clear components of the total realized variation, namely, the continuous sample path variation and discontinuous jumps. In attempting to forecast volatility, it is plausible that the components of the total variation may impact on the future volatility in different ways. This section explores whether electricity volatility forecasts can be improved by explicitly recognizing the jump and non-jump components of total variation.17

Conclusions

The deregulation of electricity markets in many countries has spawned a heightened interest in modelling and forecasting electricity prices. Electricity dynamics present a number of challenges to the modeller, especially in relation to occasional extreme jumps. The modelling approaches that are successful for traditional financial series have proven problematic when applied to electricity data. In particular, maximum-likelihood estimation of the jump-diffusion model struggles to disentangle the

Acknowledgements

We are grateful to James Taylor (the Editor of this special issue) and two anonymous referees for their helpful comments and suggestions, which have led to substantial improvements to this paper.

References (35)

  • WeronR. et al.

    Modelling electricity prices: Jump diffusion and regime switching

    Physica A

    (2004)
  • WeronR. et al.

    Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models

    International Journal of Forecasting

    (2008)
  • AndersenT. et al.

    An empirical investigation of continuous-time models for equity returns

    Journal of Finance

    (2002)
  • AndersenT.G. et al.

    Roughing it up: Including jump components in the measurement, modelling and forecasting of return volatility

    Review of Economics and Statistics

    (2007)
  • AndersenT.G. et al.

    Modelling and forecasting realized volatility

    Econometrica

    (2003)
  • AndersenT.G. et al.

    Continuous-time models, realized volatilities and testable distributional implications for daily stock returns. Working paper

    (2006)
  • Barndorff-NielsenO. et al.

    Power and bipower variation with stochastic volatility and jumps

    Journal of Financial Econometrics

    (2004)
  • Cited by (63)

    View all citing articles on Scopus
    1

    Tel.: +617 3365 6988.

    2

    Tel.: +649 373 7599x89557.

    View full text