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Forecasting the joint distribution of Australian electricity prices using dynamic vine copulae

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  • Manner, Hans
  • Alavi Fard, Farzad
  • Pourkhanali, Armin
  • Tafakori, Laleh

Abstract

We consider the problem of modelling and forecasting the distribution of a vector of prices from interconnected electricity markets using a flexible class of drawable vine copula models, where we allow the dependence parameters of the constituting bivariate copulae to be time-varying. We undertake in-sample and out-of-sample tests using daily electricity prices, and evidence that our model provides accurate forecasts of the underlying distribution and outperforms a set of competing models in their abilities to forecast one-day-ahead conditional quantiles of a portfolio of electricity prices. Our study is conducted in the Australian National Electricity Market (NEM), which is the most efficient power auction in the world. Electricity prices exhibit highly stylised features such as extreme price spikes, price dependency between regional markets, correlation asymmetry and non-linear dependency. The developed approach can be used as a risk management tool in the electricity retail industry, which plays an integral role in the apparatus of modern energy markets. Electricity retailers are responsible for the efficient distribution of electricity, while being exposed to market risk with extreme magnitudes.

Suggested Citation

  • Manner, Hans & Alavi Fard, Farzad & Pourkhanali, Armin & Tafakori, Laleh, 2019. "Forecasting the joint distribution of Australian electricity prices using dynamic vine copulae," Energy Economics, Elsevier, vol. 78(C), pages 143-164.
  • Handle: RePEc:eee:eneeco:v:78:y:2019:i:c:p:143-164
    DOI: 10.1016/j.eneco.2018.10.034
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    as
    1. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    2. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    3. Dong Hwan Oh & Andrew J. Patton, 2018. "Time-Varying Systemic Risk: Evidence From a Dynamic Copula Model of CDS Spreads," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 181-195, April.
    4. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
    5. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    6. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    7. Chang, Yoosoon & Kim, Chang Sik & Miller, J. Isaac & Park, Joon Y. & Park, Sungkeun, 2016. "A new approach to modeling the effects of temperature fluctuations on monthly electricity demand," Energy Economics, Elsevier, vol. 60(C), pages 206-216.
    8. Pourkhanali, Armin & Kim, Jong-Min & Tafakori, Laleh & Fard, Farzad Alavi, 2016. "Measuring systemic risk using vine-copula," Economic Modelling, Elsevier, vol. 53(C), pages 63-74.
    9. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    10. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    11. Misiorek Adam & Trueck Stefan & Weron Rafal, 2006. "Point and Interval Forecasting of Spot Electricity Prices: Linear vs. Non-Linear Time Series Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-36, September.
    12. Helen Higgs, 2009. "Modelling price and volatility inter-relationships in the Australian wholesale spot electricity markets," Discussion Papers in Economics economics:200904, Griffith University, Department of Accounting, Finance and Economics.
    13. Cartea, Álvaro & Villaplana, Pablo, 2008. "Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2502-2519, December.
    14. Bennedsen, Mikkel, 2017. "A rough multi-factor model of electricity spot prices," Energy Economics, Elsevier, vol. 63(C), pages 301-313.
    15. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    16. Janczura, Joanna & Trück, Stefan & Weron, Rafał & Wolff, Rodney C., 2013. "Identifying spikes and seasonal components in electricity spot price data: A guide to robust modeling," Energy Economics, Elsevier, vol. 38(C), pages 96-110.
    17. Bierbrauer, Michael & Menn, Christian & Rachev, Svetlozar T. & Truck, Stefan, 2007. "Spot and derivative pricing in the EEX power market," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3462-3485, November.
    18. Weron, Rafal & Misiorek, Adam, 2008. "Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models," International Journal of Forecasting, Elsevier, vol. 24(4), pages 744-763.
    19. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    20. De Jong Cyriel, 2006. "The Nature of Power Spikes: A Regime-Switch Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-28, September.
    21. Hans Manner & Olga Reznikova, 2012. "A Survey on Time-Varying Copulas: Specification, Simulations, and Application," Econometric Reviews, Taylor & Francis Journals, vol. 31(6), pages 654-687, November.
    22. Colletaz, Gilbert & Hurlin, Christophe & Pérignon, Christophe, 2013. "The Risk Map: A new tool for validating risk models," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3843-3854.
    23. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    24. Lorán Chollete & Andréas Heinen & Alfonso Valdesogo, 2009. "Modeling International Financial Returns with a Multivariate Regime-switching Copula," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(4), pages 437-480, Fall.
    25. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    26. Michael S. Smith & Quan Gan & Robert J. Kohn, 2012. "Modelling dependence using skew t copulas: Bayesian inference and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 500-522, April.
    27. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    28. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    29. Christian M. Hafner & Hans Manner, 2012. "Dynamic stochastic copula models: estimation, inference and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(2), pages 269-295, March.
    30. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    31. HEINEN, Andréas & VALDESOGO, Alfonso, 2009. "Asymmetric CAPM dependence for large dimensions: the Canonical Vine Autoregressive Model," LIDAM Discussion Papers CORE 2009069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    32. Higgs, Helen & Worthington, Andrew, 2008. "Stochastic price modeling of high volatility, mean-reverting, spike-prone commodities: The Australian wholesale spot electricity market," Energy Economics, Elsevier, vol. 30(6), pages 3172-3185, November.
    33. Silva Filho, Osvaldo Candido da & Ziegelmann, Flavio Augusto & Dueker, Michael J., 2012. "Modeling dependence dynamics through copulas with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 346-356.
    34. Higgs, Helen, 2009. "Modelling price and volatility inter-relationships in the Australian wholesale spot electricity markets," Energy Economics, Elsevier, vol. 31(5), pages 748-756, September.
    35. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 84-108.
    36. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    37. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    38. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large Fixed Costs," Econometrica, Econometric Society, vol. 56(3), pages 549-569, May.
    39. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    40. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    41. Carlos Almeida & Claudia Czado & Hans Manner, 2016. "Modeling high‐dimensional time‐varying dependence using dynamic D‐vine models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(5), pages 621-638, September.
    42. repec:pit:wpaper:321 is not listed on IDEAS
    43. Lindström, Erik & Regland, Fredrik, 2012. "Modeling extreme dependence between European electricity markets," Energy Economics, Elsevier, vol. 34(4), pages 899-904.
    44. Siburg, Karl Friedrich & Stoimenov, Pavel & Weiß, Gregor N.F., 2015. "Forecasting portfolio-Value-at-Risk with nonparametric lower tail dependence estimates," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 129-140.
    45. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    46. Manner, Hans & Türk, Dennis & Eichler, Michael, 2016. "Modeling and forecasting multivariate electricity price spikes," Energy Economics, Elsevier, vol. 60(C), pages 255-265.
    47. Manner, Hans & Segers, Johan, 2011. "Tails of correlation mixtures of elliptical copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 153-160, January.
    48. Low, Rand Kwong Yew & Alcock, Jamie & Faff, Robert & Brailsford, Timothy, 2013. "Canonical vine copulas in the context of modern portfolio management: Are they worth it?," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3085-3099.
    49. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    50. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    51. Moral-Carcedo, Julian & Vicens-Otero, Jose, 2005. "Modelling the non-linear response of Spanish electricity demand to temperature variations," Energy Economics, Elsevier, vol. 27(3), pages 477-494, May.
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    Cited by:

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    2. Macedo, Daniela Pereira & Marques, António Cardoso & Damette, Olivier, 2020. "The impact of the integration of renewable energy sources in the electricity price formation: is the Merit-Order Effect occurring in Portugal?," Utilities Policy, Elsevier, vol. 66(C).
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    4. Nadja Klein & Michael Stanley Smith & David J. Nott, 2020. "Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices," Papers 2010.01844, arXiv.org, revised May 2021.

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    More about this item

    Keywords

    Electricity prices; SCAR model; Dvine copula; Back-testing; Nonlinear dependence;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

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