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The Stability of Electricity Prices: Estimation and Inference of the Lyapunov Exponent

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Author Info

  • Mikael Bask

    ()
    (Monetary Policy and Research Department, Bank of Finland,)

  • Tung Liu

    ()
    (Department of Economics, Ball State University)

  • Anna Widerberg

    ()
    (Department of Economics,)

Abstract

The aim of this paper is to illustrate how the stability of a stochastic dynamic system is measured using the Lyapunov exponents. Specifically, we use a feedforward neural network to estimate these exponents as well as asymptotic results for this estimator to test for unstable (chaotic) dynamics. The data set used is spot electricity prices from the Nordic power exchange market, Nord Pool, and the dynamic system that generates these prices appears to be chaotic in one case.

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File URL: http://econfac.iweb.bsu.edu/research/workingpapers/bsuecwp200603bask.pdf
File Function: First version, 2006
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Bibliographic Info

Paper provided by Ball State University, Department of Economics in its series Working Papers with number 200603.

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Length: 14 pages
Date of creation: Apr 2006
Date of revision: Apr 2006
Publication status: Published in Physica A, 2007, vol. 376, pp. 565-572
Handle: RePEc:bsu:wpaper:200603

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Keywords: Feedforward Neural Network; Nord Pool; Lyapunov Exponents; Spot Electricity Prices; Stochastic Dynamic System;

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References

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  1. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
  2. Bask, Mikael & de Luna, Xavier, 2001. "EMU and the Stability and Volatility of Foreign Exchange: Some Empirical Evidence," UmeÃ¥ Economic Studies 565, Umeå University, Department of Economics.
  3. Dechert, W D & Gencay, R, 1992. "Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S41-60, Suppl. De.
  4. Oliver Linton & Mototsugu Shintani, 2003. "Nonparametric Neural Network Estimation of Lyapunov Exponents and a Direct Test for Chaos," STICERD - Econometrics Paper Series /2003/455, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  6. Potter, Simon M., 2000. "Nonlinear impulse response functions," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1425-1446, September.
  7. Bask, Mikael & de Luna, Xavier, 2001. "Characterizing the degree of stability of non-linear dynamic models," UmeÃ¥ Economic Studies 564, Umeå University, Department of Economics.
  8. Kuan, Chung-Ming & Liu, Tung, 1995. "Forecasting Exchange Rates Using Feedforward and Recurrent Neural Networks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 347-64, Oct.-Dec..
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Citations

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Cited by:
  1. Bask, Mikael, 2007. "Measuring potential market risk," Research Discussion Papers 20/2007, Bank of Finland.
  2. G. Papaioannou & P. Papaioannou & N. Parliaris, 2014. "Modeling the stylized facts of wholesale system marginal price (SMP) and the impacts of regulatory reforms on the Greek Electricity Market," Papers 1401.5452, arXiv.org.
  3. Bask, Mikael & Widerberg, Anna, 2007. "The Stability and Volatility of Electricity Prices: An Illustration of (lambda, sigma-2) Analysis," Working Papers in Economics 267, University of Gothenburg, Department of Economics.
  4. Giabardo, Paolo & Zugno, Marco & Pinson, Pierre & Madsen, Henrik, 2010. "Feedback, competition and stochasticity in a day ahead electricity market," Energy Economics, Elsevier, vol. 32(2), pages 292-301, March.
  5. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, vol. 31(2), pages 278-288, March.

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